ACCURACY ASSESSMENT OF THE DEM AND ORTHOIMAGE GENERATED FROM ASTER


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1 ACCURACY ASSESSMENT OF THE DEM AND ORTHOIMAGE GENERATED FROM ASTER A THESIS SUBMITTED TO THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES OF MIDDLE EAST TECHNICAL UNIVERSITY BY ALİ ÖZGÜN OK IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN GEODETIC AND GEOGRAPHIC INFORMATION TECHNOLOGIES SEPTEMBER 005
2 Approval of the Graduate School of Natural and Appled Scences Prof. Dr. Canan ÖZGEN Drector I certfy that ths thess satsfes all the requrements as a thess for the degree of Master of Scence. Assst. Prof. Dr. Zuhal AKYÜREK Head of Department Ths s to certfy that we have read ths thess and that n our opnon t s fully adequate, n scope and qualty, as a thess for the degree of Master of Scence. Examnng Commttee Members Assoc. Prof. Dr. Mustafa TÜRKER Supervsor Prof. Dr. Vedat TOPRAK (METU, GEOE) Assoc. Prof. Dr. Mustafa TÜRKER (HU, JDZ) Prof. Dr. Volkan ATALAY (METU, CENG) Assst Prof. Dr. M. Onur KARSLIOĞLU (METU, GGIT) Dr. Uğur Murat LELOĞLU (TUBITAK)
3 I hereby declare that all nformaton n ths document has been obtaned and presented n accordance wth academc rules and ethcal conduct. I also declare that, as requred by these rules and conduct, I have fully cted and referenced all materal and results that are not orgnal to ths work. Name, Last name: Al Özgün OK Sgnature :
4 ABSTRACT ACCURACY ASSESSMENT OF THE DEM AND ORTHOIMAGE GENERATED FROM ASTER OK, Al Özgün M.Sc., Department of Geodetc and Geographc Informaton Technologes Supervsor: Assoc. Prof. Dr. Mustafa TÜRKER September 005, 36 pages In ths study, DEMs and orthomages were generated from ASTER magery and ther accuraces were assessed. The study ste covers an area of approxmately 60 x 60 km and encloses the cty of Ankara. Frst, DEMs were generated from stereo ASTER mages. In order to fnd the best GCP combnaton, dfferent number of GCPs (8, 16, 4, and 3) was used. The accuraces of the generated DEMs were then assessed based on the check ponts (CP), slopes and land cover types. It was found that 16 GCPs were good compromse to produce the most accurate DEM. The post processng and blunder removal ncreased the overall accuracy up to 38%. It was also found that there s a strong lnear relatonshp between the accuraces of DEMs and the slopes of the terran. The accuraces computed for water, urban, forest, mountanous, and other areas were found to be 5.01 m, 8.03 m, 1.69 m, m, and 10.1 m, respectvely. The overall accuracy was computed as 10.9 m. v
5 The orthorectfcaton of the ASTER mage was carred out usng 1 dfferent mathematcal models. Based on the results, the models Frst Order D Polynomal, Drect Lnear Transformaton and Frst Order Polynomal wth Relef have produced the worst results. On the other hand, the model Second Order Ratonal Functon appears to be the best model to orthorectfy the ASTER mages. However, the developed model Second Order Polynomal wth Relef provdes smplcty, consstency and requres less number of GCPs when compared to the model Second Order Ratonal Functon. Keywords: ASTER, Dgtal Elevaton Model (DEM), Orthorectfcaton, Accuracy, Mathematcal Models. v
6 ÖZ ASTER DEN ÜRETİLEN SYM VE ORTOGÖRÜNTÜLERİN DOĞRULUK ANALİZLERİ OK, Al Özgün Yüksek Lsans, Jeodez ve Cograf Blg Teknolojler E.A.B.D. Tez Yönetcs: Doç. Dr. Mustafa TÜRKER Eylül 005, 36 sayfa Bu çalışmada, ASTER görüntüsünden SYM ler ve ortogörüntüler üretlmş ve doğrulukları test edlmştr. Çalışma alanı, Ankara yı da çne alan 60 x 60 km lk br alanı kapsamaktadır. İlk olarak, bndrmel ASTER görüntülernden SYM ler üretlmştr. En y YKN dağılımını bulablmek çn farklı sayıda YKN ler (8, 16, 4, and 3) kullanılmıştır. Daha sonra, doğruluklar bağımsız denetm noktalarında (BDN), belrl eğm aralıklarına ve araz örtüsü türlerne göre değerlendrlmştr. Doğruluğu en yüksek SYM nn 16 YKN kullanılarak oluşturulduğu bulunmuştur. Hataları düzeltme ve kaba hataları temzleme şlemler genel doğruluğu %38 lere varan düzeylerde artırdığı hesaplanmıştır. Ayrıca, SYM doğrulukları ve araz eğm arasında kesn doğrusal br lşk olduğu da bulunmuştur. Su yüzeyler, şehrsel, ormanlık, dağlık, ve dğer alanlar çn doğruluklar sırasıyla 5.01 m, 8.03 m, 1.69 m, m ve 10.1 m olarak hesaplanmıştır. Genel doğruluk se 10.9 m olarak bulunmuştur. v
7 ASTER görüntüsünün ortorektfkasyonu 1 farklı matematksel model kullanılarak yapılmıştır. Elde edlen sonuçlara göre, en kötü ortorektfkasyon doğrulukları Brnc Dereceden Boyutlu Polnom, Drekt Lneer Dönüşüm ve Rölyef Düzeltmel Brnc Dereceden Polnom Modellernde hesaplanmıştır. Dğer taraftan, ASTER görüntülernn ortorektfkasyonunda en y sonuç İknc Dereceden Rasyonel Fonksyon da elde edlmştr. Ancak, gelştrlen Rölyef Düzeltmel İknc Dereceden Polnom Model, İknc Dereceden Rasyonel Fonksyona göre bastlk ve tutarlılık sağlamakta ve daha az YKN gerektrmektedr. Anahtar Kelmeler: ASTER, Sayısal Yükseklk Model (SYM), Ortorektfkasyon, Doğruluk, Matematksel Modeller. v
8 To My Parents v
9 ACKNOWLEDGMENTS I would lke to gratefully thank to my supervsor Assoc. Prof. Dr. Mustafa TÜRKER for hs great gudance, contnuous support and motvaton durng both the development of ths thess and my master program. Ths research would have been mpossble wthout hs valuable techncal assstance. I would also lke to thank Assst. Prof. Dr. Mahmut Onur KARSLIOĞLU for sharng hs valuable knowledge throughout the preparaton of ths thess. I would lke to thank Prof. Dr. Vedat TOPRAK, Prof. Dr. Volkan ATALAY and Dr. Uğur Murat LELOĞLU for readng and revewng my thess. Ther evaluaton and comments mproved ths thess consderably. I wsh to express my deepest grattude to Prof. Dr. Ülkü YETİŞ, Prof. Dr. Ayhan İNAL and Prof. Dr. Flz B. AKIN for ther endless support and motvaton. I wll never forget your assstance and postve approach. I would lke to thank Hacettepe Unversty, Faculty of Engneerng, Department of Geodesy and Photogrammetry for supplyng the precous reference data. I also thank Brol GÜÇLÜER who suppled the dfferental GPS recevers wthout any cost for a long perod of tme. I would lke to thank my dear frends Evren AKYÜZ, Oya DİNLER, Murat ATALAY, Mert AYDIN, Eren ÖZMEN, Murat KUŞ and Metn KUŞ for ther nvaluable frendshp durng ths thess. Extraordnary drvng and helps of Evren AKYÜZ, Murat ATALAY and Mert AYDIN durng the feldworks wll always be remembered. x
10 I would lke to express thanks to Özgün BALKANAY and Nlhan ÇİFTÇİ for ther endless support and thoughtful frendshp durng my study n METU. It was my chance to get a vew of such love and relatonshp between you two. Once more, t wll be my honor to be at your weddng. I am thankful to my dear frends Dlek KOÇ and Aslı ÖZDARICI for ther supportve approach and knd frendshp all the way to conclude my master program. I want you to know that wthout your postve approach, ths thess would not have been concluded. I would lke to express thanks to Lord Kıvanç ERTUĞAY and Pasha Serkan KEMEÇ for ther tolerance and understandng durng the preparaton of ths thess. The games played wth two of you have always been a relaxve effect and reduced the stress on me. Thank you for everythng. I would lke to thank Gülcan SARP, Reşat GEÇEN, Arzu ERENER, Pınar ASLANTAŞ and Ayten KOÇ for ther supportve atttude towards me. Specal thanks go to Gülcan SARP for helpng my wrtng process whch was reduced my task sgnfcantly. I wsh to thank my colleagues M. Alper TEMEL, Sema Nur GÜLAL TEMEL, Brol YILMAZ, Bumn Kağan ÖZTÜRK, Özkan ÖZER and Al Vehb BUTUK for ther understandng durng the development of ths thess. Specal thanks go to M. Alper TEMEL for tryng to fnd a vtal data whch s essental n ths thess. I would lke to thank Emre SÜMER and Emre ERDOĞAN for ther motvaton and knd frendshp durng ths study. Ther suggestons and supportve approach was crucal to recover my morale n my desperate tmes. x
11 I would lke to express my deepest grattude to Sad YETİŞ and İhsan YETİŞ, my maternal uncles, for purposely loosng the backgammon games whch we played durng ths thess. Ther support and postve atttude forms one of the key ponts of my success n my educaton. Specal thanks go to Tuğçe, Serra, Begüm and Medha YETİŞ for supportng me all the tme even when I lost the backgammon games. They do really mean a lot to me and thanks for everythng. I cordally would lke to dedcate ths thess to my dear parents Nur OK and Semra OK. Ther contnuous affecton, encouragement, patence and belef made me who I am. I am really glad to have a father and mother lke you. Thank you for everythng. x
12 TABLE OF CONTENTS PLAGIARISM... ABSTRACT...v ÖZ...v DEDICATION... v ACKNOWLEDGEMENTS...x TABLE OF CONTENTS... x LIST OF TABLES... xv LIST OF FIGURES... xv CHAPTER 1. INTRODUCTION Scope and Purpose The Software Used Organzaton of the Thess PAST STUDIES RELATED TO ASTER AND SPOT DEM GENERATION DEM GENERATION AND ORTHORECTIFICATION FROM SATELLITE IMAGERY DEM Generaton Stereoscopy Stereoscopc Acquston Geometry Adjacenttrack Stereoscopy Acrosstrack Stereoscopy Alongtrack Stereoscopy Stereoscopc Processng x
13 Stereo Image Data Acquston System and the Stereo Model Rgorous Geometrc Models Smple Geometrc Models D Polynomal Functons D Polynomal Functons Ratonal Functons (RFs) Projectve Transformaton Drect Lnear Transformaton (DLT) GCP collecton and Refnement Elevaton Parallax Extracton Areabased Methods Featurebased Methods Hybrd Methods D stereo Intersecton PostProcessng and Projectng the Generated DEM Nose Identfcaton Nose Removal Orthorectfcaton STUDY AREA AND DATA SETS The Study Area Data Sets ASTER Image Data Vector Data Dgtal Orthophotos Preperaton of the Reference DEM Data from exstng 1:1000 Scale Vector Data The Collecton of the GCPs GCP Collecton from 1:5000 Scale Dgtal Orthophotos x
14 4.3. GCP Collecton through Dfferental GPS Measurements DEM GENERATION FROM STEREO ASTER IMAGERY Earth Observaton Satellte Terra Advaced Spaceborne Thermal Emsson and Reflecton Radometer (ASTER) The VNIR Instrument The SWIR Instrument The TIR Instrument Clouds and Earth s Radant Energy System (CERES) Multangle Imagng SpectroRadometer (MISR) Moderateresoluton Imagng Spectroradometer (MODIS) Measurements of Polluton n Troposphere (MOPITT) Dgtal Elevaton Model Generaton from ASTER data Radometrc Correcton Collecton of the Stereo GCPs DEM Generaton Postprocessng and Geocodng the Generated DEM Evaluaton of the DEMs The Assessment of the ASTER DEMs The Results of Least Squares Bundle Adjustment The Assessment of the DEMs ORTHORECTIFICATION OF ASTER IMAGERY The Orthorectfcaton of ASTER Data The Assessment of the Orthorectfed ASTER Imagery The Results of the Toutn s Model The Results of the Orun and Natarajan Model The Results of the D Polynomal Functons The Results of the Ratonal Functons The Results of the 3D Polynomal Functons xv
15 6..6 The Results of the Drect Lnear Transformaton The Results of the Projectve Transformaton The Comparatve Evaluaton of the Results of the Orthorectfcaton Process CONCLUSIONS AND RECOMMENDATIONS Conclusons Recommendatons REFERENCES APPENDICES A. THE DERIVATION OF THE COLLINEARITY EQUATIONS B. THE DEFINITIONS AND DERIVATION OF THE LEAST SQUARES SOLUTION C. THE GENERATED AND CORRECTED VECTOR DATA SEGMENTS DURING THE MERGING PROCESS D. THE COORDINATES OF THE GCPS DETERMINED FROM ORTHOPHOTOS AND DIFFERENTIAL GPS E. THE RMSE VALUES OF THE GCPS AND THE CPS FOR FOUR SETS OF GCPS F. THE INFORMATION REPORTS FOR THE DEMS GENERATED AND THE ELEVATION RMS ERRORS RELATED TO THE GCPS AND THE CPS FOR ALL GCP SETS G. THE RESULTS OF THE ELEVATION DIFFERENCES FOR THE NONEDITED AND THE EDITED DEMS FOR ALL GCP SETS... 0 H. THE RESIDUALS FOR THE NADIR AND BACKWARD IMAGES FOR ALL GCP SETS... 1 I. THE DEFINITIONS OF THE COORDINATE SYSTEMS... 0 J. THE ERROR VECTOR DIAGRAMS... 5 xv
16 LIST OF TABLES TABLES Table 3.1 Descrpton of error sources Table 3. The propertes of smple geometrc functons... 3 Table 3.3 The comparson between smple and rgorous geometrc models Table 4.1 The geographc coordnates of the ASTER mages Table 4. The techncal characterstcs of the ASTER mages... 5 Table 4.3 Transverse Mercator projecton system detals... 5 Table 5.1 The orbt characterstcs of the Terra satellte Table 5. ASTER nstrument characterstcs Table 5.3 Sgnfcant ASTER functons and components Table 5.4 VNIR band (1,, 3N) Table 5.5 VNIR band (3B) Table 5.6 The Results of the least squares adjustment for the four sets of GCPs Table 5.7 The maxmum errors computed for all sets Table 5.8 The results of the DEMs generated wthout postprocessng 90 Table 5.9 The total number of the blunders detected n the generated DEMs Table 5.10 The results of the DEMs generated after postprocessng... 9 Table 5.11 The results of the DEMs generated usng four GCP sets Table 5.1 The dfferences between the reference DEM and the DEM generated usng GCP set Table 5.13 The accuraces of the DEM based on the selected terran slope ntervals Table 6.1 The result of the least square adjustment of the GCPs for the Toutn s model xv
17 Table 6. The results of the least squares adjustment of the CPs for the Toutn s model Table 6.3 The results of the least squares adjustment of the GCPs for the Orun and Natarajan model Table 6.4 The Results of the least squares adjustment of the CPs for the Orun and Natarajan model Table 6.5 The Varance  Covarance matrx of the unknowns for the second order polynomal model Table 6.6 The accuraces of the GCPs for the frst, second, and thrd order D polynomal functons Table 6.7 The accuraces of the CPs for the frst, second and thrd order D polynomal functons Table 6.8 The overall accuraces of the GCPs for the frst, second and thrd order ratonal functons Table 6.9 The overall accuraces of the CPs for the frst, second, and thrd order ratonal functons Table 6.10 The overall results of the GCPs for the frst and second order polynomal functons wth relef... 1 Table 6.11 The Results of the least squares adjustment of the GCPs for the DLT functon Table 6.1 The results of the least squares adjustment of the CPs for the DLT model Table 6.13 The assessment results of the least squares adjustment of the GCPs for the Projectve Transformaton model Table 6.14 The results of the least squares adjustment of the CPs for the DLT model Table 6.15 The summary of the RMSE of the Orthorectfcaton of ASTER Imagery usng twelve models xv
18 LIST OF FIGURES FIGURES Fgure 3.1 Acrosstrack stereo mage acquston Fgure 3. Alongtrack stereo mage acquston Fgure 3.3 The collnearty condton (Wolf, 000) Fgure 3.4 The comparson of the effect of small changes n parameters for frame and pushbroom sensors (Orun and Natarajan, 1994)... 1 Fgure 3.5 Areabased matchng usng reference and search arrays (Wolf, 000) Fgure 3.6 Eppolar geometry (Wolf, 000) Fgure 3.7 3D stereo ntersecton (Wolf, 000)... 4 Fgure 3.8 Relef dsplacement (Mkhal et. al., 001) Fgure 3.9 Forward and backward projecton (Mkhal et. al., 001) Fgure 4.1 ASTER Nadr mage of the study area. (A) represents the cty center of Ankara, (B) represents Lake Mogan, (C) represents the mountanous stes, (D) represents the forestry areas, and (E) represents the agrcultural and open lands Fgure 4. The whte colored vector polygon shows the coverage of the exstng vector data and orthophotos Fgure 4.3 An error caused by the mssng elevaton values Fgure 4.4 An error caused by the mssng ndvdual pont measurements Fgure 4.5 Three GCPs on the mage and ther correspondng locatons on the orthophotos Fgure 5.1 ASTER stereo geometry Fgure 5. Before and after preprocessng operaton... 7 xv
19 Fgure 5.3 Four sets of GCPs and CPs. The red ponts ndcate the locaton of the GCPs, whereas the yellow ponts ndcate the locaton of the CPs. The dstrbuton of (A) 8 GCPs, (B) 16 GCPs, (C) 4 GCPs, and (D) 3 GCPs Fgure 5.4 The eppolar mages that are generated from the (a) nadr and (b) backward mages Fgure 5.5 The llustraton of the pxel samplng ntervals Fgure 5.6 (A) The eppolar mage of the nadr mage of ASTER, (B) the stereo extracted eppolar DEM usng GCP set, (C) mage matchng falure over Lake Mogan, and (D) multple blunders occurred durng mage matchng Fgure 5.7 The planmetrc total RMS error values for the GCPs and CPs for all sets Fgure 5.8 The elevaton RMS error values for the GCPs and check ponts for all sets Fgure 5.9 The blunders occurred after generatng the DEM Fgure 5.10 The resultng scenes after applyng postprocessng... 9 Fgure 5.11 The (a) horzontal, (b) vertcal and (c) dagonal transects that were taken for the profle comparson between the generated DEM and the reference DEM Fgure 5.1 The comparsons of the profles of the generated ASTER DEM and the reference DEM. The frst fgure represents the horzontal profle, the mddle fgure represents the vertcal profle, and the thrd fgure represents the dagonal profle. 95 Fgure 5.13 The vsually classfed ASTER magery Fgure 5.14 The relatonshp between the accuraces and fve classes 99 Fgure 6.1 The general archtecture of a macro wrtten n Matlab Fgure 6. The accuraces of the GCPs and CPs for the Toutn s model Fgure 6.3 The accuraces of the GCPs and CPs accuraces for the Orun and Natarajan model xx
20 Fgure 6.4 The accuraces of the GCPs for the D polynomal functons Fgure 6.5 The accuraces of the CPs for the D polynomal functons Fgure 6.6 Error versus h at CPs for the second order ratonal functons Fgure 6.7 Error versus h at CPs for the thrd order ratonal functons Fgure 6.8 The accuraces of the GCPs for the ratonal functons Fgure 6.9 The CP accuraces for the ratonal functons Fgure 6.10 The GCP accuraces for the frst and second order 3D polynomals wth relef Fgure 6.11 The CP accuraces for the frst and second order polynomals wth relef Fgure 6.1 The overall accuraces of the GCPs and CPs for the DLT model Fgure 6.13 The overall accuraces of the GCPs and CPs for the Projectve Transformaton model Fgure 6.14 The comparsons of the models n terms of the accuraces of GCPs Fgure 6.15 The comparsons of the models n terms of the accuraces of CPs xx
21 CHAPTER 1 INTRODUCTION 1.1 Scope and Purpose Dgtal elevaton models (DEM) are mportant resource used for geospatal analyss. When the frst commercal satellte was launched, the mportance and the applcaton areas of the satellte mages were apparent. Untl that tme, the mprovements n remote sensng and computng technologes have evolved many research areas ncludng the photogrammetry and mappng and gave new opportuntes to researchers. One mportant nnovaton n these areas s the modelng and vsualzaton of the Earth s surface n dgtal representaton. Nowadays, the demand for DEMs s gettng ncreased wth ther utlzaton n GIS for many leadng applcatons. The ncorporaton of DEM n a GIS has a broad range of applcatons lnked to land management and terran modelng, ral and road nfrastructure studes, telecommuncaton plannng, ol and gas exploraton, mltary mappng, flght and arport landng smulatons, 3D cty modelng and the lke. Elevaton data, ntegrated wth satellte magery s also used for many purposes such as generatng orthomages and perspectve vews, route plannng for transportaton and toursm. The orthorectfcaton of the satellte mages enables users to utlze mages n conjuncton wth a DEM and other spatal nformaton n a GIS. For ths reason, the generaton of DEMs and orthomages s qute mportant for many applcatons n the feld of remote sensng. Despte a 1
22 broad range of applcatons, DEMs and orthomages are stll not avalable for many areas of the Earth surface. The SPOT satellte seres are the frst satelltes whch enable contguous stereoscopc coverage. Therefore, stereo SPOT mages have been extensvely used for DEM generaton. Today, a seres of Earth observaton satelltes are montorng our planet and acqurng a large number of stereo mages. SPOT 4 and 5, TERRA (ASTER), IRS 1 C/D, IKONOS, EROS A1, QUICKBIRD, and ORBVIEW3 are the most popular satelltes that acqure stereo mages. Of these satelltes, the TERRA (ASTER) s consdered to be an mportant satellte because t provdes the largest coverage wth mnmum cost. It s therefore beleved that, TERRA (ASTER) can provde DEMs and orthomages that can be used for many applcatons. However, suffcent accuracy of DEMs and orthomages are requred for such studes. The objectve of ths study s to assess the accuraces of DEMs and orthomages generated from ASTER magery. To do that, DEMs were generated usng four dfferent sets of GCPs to assess the accuraces based on the number of GCPs. In addton, the accuraces of the DEMs were assessed based on the slopes and land cover types. The orthorectfcaton of the ASTER magery was performed usng twelve dfferent mathematcal models. Wth the mplementaton of the twelve models not only the accuraces of the orthomages generated were assessed but also the best mathematcal model for orthorectfyng the ASTER magery was determned. 1. The Software Used Durng ths study, the PCI Geomatca mage analyss software was used to generate the DEMs from ASTER mages. The mathematcal model
23 provded by the software s one of the models used for the orthorectfcaton process. Ths software was also used for generatng the reference DEM and slope map, data transferrng etc. Mcrostaton SE dgtal photogrammetrc workstaton software was used to merge and transfer the vector data to the PCI Geomatca software. The SPSS statstcal analyss software was used for the mplementaton of Pearson s correlaton test and several graphcal presentatons. The Mcrosoft Excel was used for preparng the tables and most of the fgures n the thess. Fnally, the mplementaton and processng of the eleven mathematcal models for performng the orthorectfcaton were carred out usng MATLAB 6.5, whch s a hghperformance language for techncal computng. Usng MATLAB, the orthorectfed mages were obtaned for each of the eleven mathematcal models both textual and graphcal presentatons. 1.3 Organzaton of the Thess Ths thess s composed of seven chapters. The next chapter (chapter ) provdes the lterature revew about DEM generaton and orthorectfcaton from ASTER magery. In chapter 3, the theoretcal bases of DEM generaton from satellte stereo mages are descrbed. Ths chapter starts wth the explanatons of stereoscopy and stereoscopc acquston technques. Then, the stereoscopc processng stages are explaned. Fnally, the orthorectfcaton of the satellte magery usng the forward and backward algorthm are provded. The study area and data sets used n the study are provded n chapter 4. After descrbng the study area, the mage data, reference vector and orthophoto data are explaned. Next, the method for generatng the 3
24 reference DEMs from vector data s explaned. Fnally, the GCPs and ther collecton methods are descrbed. The followng chapter (chapter 5) presents the DEM generaton steps from ASTER stereo magery. Frst, the Terra satellte, whch carres the ASTER sensor, s explaned. Second, the DEM generaton process from stereo ASTER mages s descrbed. Fnally, the results of the assessment of the generated DEMs are provded. The results comprse of two sectons, () the results of the least squares bundle adjustment and () the results of DEM accuracy evaluaton. Chapter 6 nvolves the orthorectfcaton of ASTER magery. Frst, the processng steps of the orthorectfcaton procedure performed durng ths study wth the use of MATLAB software are provded. Then, the results of orthorectfcaton of the nadr ASTER mage usng dfferent twelve models are gven. In the fnal chapter, the conclusons derved from ths study and the recommendatons that can be useful for further studes are provded. 4
25 CHAPTER PAST STUDIES RELATED TO ASTER DEM GENERATION The DEM accuracy analyss for ASTER mages has started before the launch of the Terra satellte. One of the frst studes on ASTER DEM accuracy was performed by Welch et. al. (1998) wth a smulated data. The 10 m SPOT stereo panchromatc mages were resampled to 15 m to obtan the ASTER mage resoluton. The stereo mages were taken for two dfferent ASTER valdaton stes. The stereo model was regstered to the UTM coordnate system wth a RMSE of ±14.5 m usng sx GCPs. DEMs were then generated by RWEL DMS software wth a 30 m grd spacng usng 13 x 13 correlaton wndow sze. The vertcal accuracy was assessed usng 16 ponts and a comparson between the computed elevaton coordnates aganst the known elevaton coordnates produced an accuracy of ±17.4 m. In ths respect, t was stated that the ASTER stereo mages would provde accuraces between ±15 and ±5 m. Toutn (001) evaluated the automated DEM accuracy usng a stereo par of ASTER data. The selected study area was semard wth few cultural features and vegetaton. Sxty percent of the area was relatvely flat and the rest was steep and rugged. The elevaton range was between 1300 and 600 m above sea level. For the entre DEM generaton process and the accuracy assessment the Orthoengne module of PCI Geomatca mage analyss software was used. Eght GCPs and sx check ponts were collected durng the study. The GCPs were collected usng DGPS wth an accuracy of ±1 m and located from wthn the borders of the mages and at the hgh and low elevaton ponts. The generated DEM was compared wth 5
26 a USGS 7.5mnute DEM. The accuracy of the reference DEM was around 7.5 meters. To compute the statstcs of the dfference between the ASTER DEM and the USGS DEM, 150,000 elevaton ponts were used. The accuracy was found to be 11.8 m wth a level of confdence of 85 percent. It was stated that 30meter contour lnes can be derved from the generated ASTER DEMs. Toutn (00) nvestgated the accuracy of DEMs generated from ASTER stereo data. The study area was characterzed by rugged topography where the elevaton ranged from 34 m to 137 m wth a mean slope of 10º and slopes approachng 87º. The land cover composed of conferous and decduous trees wth patches of agrcultural land and clearcut areas. Topographc data havng the planmetrc accuracy of 530 m and the vertcal accuracy of 10 m was used for GCP collecton and the assessment. The man processng stages for DEM generaton ncluded () mage preprocessng, () stereomodel setup, () data extracton or capture by mage matchng, (v) 3D stereo ntersecton and (v) DEM edtng. Dfferent GCP/ICP confguratons were evaluated to fnd the optmum number of GCPs. After seven combnatons of GCP/ICP confguratons, ffteen GCPs and twenty ICPs were selected n order to keep redundancy n the least square adjustment and to nsure the pxel accuracy. DEM accuracy was evaluated as a functon of dfferent parameters lke preprocessng, postprocessng and slope analyses. Frst, the analyss was carred out based on the radometrc preprocessng of the ASTER mages. It was stated that ths preprocessng ncreased the overall accuracy a lttle less than 10%. Smlarly, the postprocessng of the lakes mproved the accuracy of the fnal DEM by 10%. The fnal results of 8 m and 51 m were obtaned for the 68% and 90% confdence levels wth the correcton of lake elevatons, but wthout takng nto account the msmatched areas. It was also found that the generated DEM was almost 6
27 nversely correlated wth the terran slopes, and 0 m accuracy could be obtaned on a medum topography usng ASTER stereo mages. An accuracy comparson between DEMs generated from ASTER and SPOT 4 stereo mages was conducted by Toutn and Cheng (00). The DEMs were generated over an area of hlly mountans whch was manly semard and conssted of few cultural features and lttle vegetaton. In the area, the dfference between the lowest and hghest pont was around 1300 m. The ASTER level 1A data (61.5 by 63 km) were chosen due to ther better reflectance of the magng geometry. The SPOT 4 stereo par (60 by 60 km) was acqured wth 30 days apart wth the angles of +1.4 and Eght stereo GCPs and sx ndependent check ponts were used n ths study. The GCPs used n the study were obtaned by Dfferental GPS (DGPS) wth an accuracy of submeter. For generatng the DEMs for both ASTER and SPOT 4 stereo mages Toutn s satellte geometrc model whch was mplemented n PCI Geomatcs Orthoengne software was used. The resultng DEMs for ASTER and SPOT 4 were compared wth a USGS DEM whch had an accuracy of 7.5 m. A total of elevaton ponts were used for the comparson. The resultng DEM accuracy acheved for ASTER and SPOT 4 mages were 11.6 and 4.6 m, respectvely. It was stated that the SPOT 4 extracted DEM results were closer to the USGS DEM than the ASTER DEM results. A detaled study for generatng DEMs from ASTER stereo mage data was performed by Hrano et. al. (003). The study examned ASTER stereo DEM results usng four dfferent test stes. The study stes were selected n dfferent parts of the world, whch contans varous terran and land use types such as rce felds, lava flow areas, densely populated regons, forest and agrcultural lands. The hghest and the lowest total releves n the test stes were 00 m and 300 m, respectvely. DEMs were generated by usng the RWEL DMS software. The GCPs were collected from 7
28 topographc maps and/or from DGPS surveys wth varyng numbers for each test ste. Stereo correlaton was undertaken usng 13 x 13 and 19 x 19 correlaton wndows. It was ndcated that the success of the correlaton was ranged from 97% to 99%. For each test ste, the generated DEMs were compared wth dfferent reference data. The evaluatons of the vertcal accuracy resultng from stereo correlaton ndcated that ±7 to ±15 m accuracy could be expected from ASTER stereo mages. In a smlar study, Cuartero et. al. (004) nvestgated the accuracy of ASTER stereoscopc mages by automated stereomatchng technques usng two dfferent commercal softwares, OrthoBase PRO and Orthoengne. The maged topography ncluded steep slopes and flat surfaces and the elevaton ranged between m wth an average heght of 1060 m. They have generated 55 DEMs n order to analyze the nfluence of some aspects, such as number and spatal dstrbuton of GCPs, the data structure and the sample nterval. A set of 315 randomly dstrbuted check ponts whose coordnates were determned by DGPS technques were used. Accordng to the results, the Orthoengne obtaned the best ASTER DEM wth 30 m cell sze, usng 15 GCPs. On the other hand, the Orthobase PRO generated the most accurate DEM usng 1 GCPs, 13 x 13 correlaton wndow and an acceptance threshold value of 0.6. Another recent study on the accuracy analyss of ASTER mages was performed by Goncalves and Olvera (004). The regon (160 km ) for the comparson they used had heghts rangng from 30 to 600 meters. 11 GCPs were collected from 1:5000 scaled topographc maps. A DEM produced by the army mappng servce, whch had an accuracy of m, was used to assess the ASTER stereo DEM. The evaluatons showed that the accuracy of the ASTER stereo DEM was around 8.7 meters. One nterestng part of ths study was the radometrc correcton of the ASTER 8
29 mages. The authors performed 7 unts of grayscale value shftng to the even lnes n the ASTER mages rather than usng the coeffcents provded n the HDF format. On the contrary to the Toutn (00), they also stated that ths radometrc mprovement dd not effect the matchng process and the overall DEM accuracy. Fnally, Eckert et. al. (005) nvestgated the ASTER stereo DEM accuracy n three dfferent mountan stes. The accuracy was tested usng three dfferent reference DEMs whch have dfferent resolutons. They found that wth the accurate and well dstrbuted GCPs, the accuraces between 15 m and 0 m n hlly terran and about 30 m n mountanous terran can be acheved. They also stated that flat regons and smooth slopes produce accuraces around ±10 m. It s also affrmed that the generated DEMs contan extreme errors of a few hundred meters. 9
30 CHAPTER 3 DEM GENERATION AND ORTHORECTIFICATION FROM SATELLITE IMAGERY Remotely sensed data provdes crucal nformaton for many researches n varous felds. Two mportant parts n these felds are the dgtal elevaton model generaton and the orthorectfcaton of satellte magery. In ths chapter, frst the theoretcal bases of the DEM generaton from satellte stereo mages are descrbed. Then, the orthorectfcaton of the satellte magery usng the forward and backward algorthm are provded. 3.1 DEM Generaton A DEM s defned as a fle or a database contanng elevaton ponts over a contguous area (Manual of Photogrammetry, 004). In ths part, the theoretcal bases and the processng steps of the DEM generaton from satellte stereo mages are descrbed Stereoscopy Stereoscopy s the scence and art that deals wth the use of mages to produce a three dmensonal vsual model wth characterstcs analogous to those of actual features vewed usng true bnocular vson (Manual of Photogrammetry, 1980). There are two man factors that nfluence the percepton of the space n bnocular vson: () Bnocular dsparty (also called bnocular parallax) and () Convergence angle. The bnocular dsparty s the dfference between the mages of an object projected onto 10
31 each retna (Toutn, 001). Besdes, convergence angle determnes the degree of dsparty between two projected mages. In order to produce DEMs, the prncples of bnocular vson are mplemented usng the stereo mages. The success of the stereoscopc processng s closely related to the parallax nhert n the stereo mages. In ths respect, stereoscopc acquston geometry s of great mportance because t drectly determnes the degree of parallax Stereoscopc Acquston Geometry In order to obtan stereoscopy wth mages, three solutons are possble (Toutn, 1999): The adjacenttrack stereoscopy usng two dfferent orbts The acrosstrack stereoscopy usng two dfferent orbts The alongtrack stereoscopy usng the same orbt usng fore and aft mages Adjacenttrack Stereoscopy The frst attempts of the elevaton nformaton extracton from satelltes started wth only nadr vew capable sensors. Due to the lack of a steerng mechansm, these sensors could be able to acqure stereo mages only n successve orbts. Ths successve orbt stereo acquston technque s called adjacenttrack stereo and used frequently for LANDSAT (MSS or TM). Because the stereo mages are acqured from two adjacent quaspolar orbts the overlappng area coverage grows from around 10% at the Equator to about 85% at 80 lattude. From 50 north and south the coverage overlap (45%) enables quasoperatonal experments for 11
32 elevaton extracton (Toutn, 001). The nature of the acquston geometry of adjacenttrack stereoscopy only allows poor B/H ratos that are between 0.1 and 0.. The stereoscopc capabltes and applcabltes of adjacenttrack stereoscopc satellte data stll reman lmted because (Toutn, 001): t can be used for large area only n lattude hgher than 45 to 50 north and south, t generates a small B/H rato leadng to elevaton errors of more than 50 m, and only medum to hgh relef areas are sutable for generatng enough vertcal parallaxes Acrosstrack Stereoscopy In order to acheve large ntersecton angles to generate better stereo geometry, acrosstrack stereoscopy can be used. Lke the prevous method, dfferent orbts are used but ths tme rather than usng the consecutve orbts nonsuccessve orbts are used. Ths s acheved by usng the advantage of not only the steerable sensors but also the rollable satelltes and gves perfect B/H ratos that are sutable for terran elevaton determnaton. B/H ratos of 0.6 to 1. are the typcal values to meet the requrements of topographc mappng (Lght, 1980). The SPOT and IKONOS systems can generate such B/H ratos by usng acrosstrack steerng capabltes and IRS system can generate such B/H ratos by rollng the satellte (Fgure 3.1). 1
33 By usng the acrosstrack stereo data more symmetrcally vewed mages can be obtaned. On the other hand, the man drawback of usng an acrosstrack stereopar data s the use of multdate stereo data wth radometrc varatons due to the dfferent dates and seasons or envronmental condtons (Toutn, 00). The tme dfference between the two stereo mages can produce dffcultes for automated matchng process whch can be hghly affected from the clouds, sun llumnaton condtons, vegetaton growth, cultvated areas, water bodes etc. Fgure 3.1 Acrosstrack stereo mage acquston Alongtrack Stereoscopy On the contrary to prevous two methods, stereo mage acquston can also be taken on the same orbt by steerng the sensor or by changng the ptch of the platform to the forward and backward drectons. Ths technque s called alongtrack stereoscopy and used n several satelltes such as ASTER and IKONOS (Fgure 3.). Agan B/H ratos that are convenent for topographc mappng can be easly obtaned from alongtrack stereoscopy. 13
34 The smultaneous alongtrack stereo data acquston gves a strong advantage n terms of radometrc varatons versus the multdate stereo data acquston wth acrosstrack stereo (Toutn, 001). Because the stereo mages are acqured n terms of seconds or mnutes the consstency and qualty of the stereo mages are much better than those that are acqured by other methods. Therefore, the resultng stereo pars are well prepared for the automated matchng process. Besdes, ths type of acquston technque compensates for the weaker geometry compared to the acrosstrack technque resultng one mage s taken from the nadr or forward and the other s taken from backward vewng drecton. Fgure 3. Alongtrack stereo mage acquston. 14
35 3.1.3 Stereoscopc Processng The dfferent processng steps to produce DEMs usng stereo mages can be descrbed n broad terms as follows (Toutn, 001): To acqure the stereo mage data wth supplementary nformaton such as ephemers and atttude data f avalable To collect GCPs to compute or refne the stereo model geometry To extract elevaton parallax To compute the 3D cartographc coordnates usng 3D stereontersecton To create and postprocess the DEM (flterng, 3D edtng and smoothng) Convertng the DEM to a desred Map Projecton Stereo Image Data Acquston System and the Stereo Model Raw mages that are taken from dfferent acquston systems generally contan several dstortons. These geometrc dstortons vary consderably wth dfferent factors. However, t s possble to group them nto two man categores (Toutn, 004): 15
36 The observer or the acquston system dstortons The observed system dstortons The observer system dstortons may nclude dstortons due to platform varatons, sensor, nstrument and vewng angle errors. Atmospherc effects, Earth based dstortons and map projecton errors are grouped nto the observed system dstortons. Table 3.1 summarzes these errors (Toutn, 004): Category The Observer system The Observed system Table 3.1 Descrpton of error sources. Descrpton of error Subcategory sources Varaton of the movement Platform Varaton n platform atttude Varaton n sensor mechancs Sensor Vewng/look angles Panoramc effect Tme varatons or drft Measurng Instruments Clock synchroncty Atmosphere Refracton and turbulence Curvature, rotaton, Earth topographc effect Geod to ellpsod Map Ellpsod to map 16
37 All these dstortons must be modeled and corrected by usng a specfc mathematcal model. Several mathematcal models can be used for ths purpose but the avalablty of the ephemers and atttude data drectly nfluences the model type. If the poston and the atttude data of the sensor are known durng the mage acquston, then a rgorous (physcal) model can be used. Otherwse, a smple geometrc model must be used n order to cope wth the dstortons Rgorous Geometrc Models A rgorous model s a complex model whch uses the physcal realty of the sensor by ntegratng the knowledge of the ephemers and atttude data. Several models and consderable research have been carred out but the mlestone of all the models to derve a rgorous model s the very well known photogrammetrc collnearty equatons (Fgure 3.3): x a = x 0 m11( X f m31( X A A X X L L ) + m ) + m 1 3 ( Y ( Y A A Y Y L L ) + m ) + m ( Z ( Z A A Z Z L L ) ) y a = y 0 m f m 1 31 ( X ( X A A X X L L ) + m ) + m 3 ( Y ( Y A A Y Y L L ) + m ) + m 3 33 ( Z ( Z A A Z Z L L ) ) where (x a, y a ) are the mage coordnates of the pont a, (X A, Y A, Z A ) are the object space coordnates of the pont A, (X L, Y L, Z L ) are the object space coordnates of the exposure staton, f s the focal length of the sensor, x 0 and y 0 are the coordnates of the prncpal pont usually known from camera calbraton and m j are the elements of the rotaton matrx (Wolf, 000). The dervaton of the collnearty equatons can be found n Appendx A. 17
38 Fgure 3.3 The collnearty condton (Wolf, 000). The three dmensonal character of the photogrammetrc formulaton allows to consder all physcal aspects of satellte orbtng and of the Earth magng, together wth geometrc condtons of the tmedependent ntersecton of correspondng magng rays n the model space (Kratky, 1989). As a result, hgh modelng accuracy can be obtaned whch s usually less than one pxel n many condtons. The types of the optcal sensors are based on dfferent technques such as frame, whskbroom and pushbroom. Realzng the magng geometry of all these dfferent sensors requre dfferent sensor models. In addton, the platforms (arborne or spaceborne) where the mages acqured are also an mportant factor n the sensor modelng. A frame camera uses the collnearty equatons to relate the mage space and the object space. However, because the pushbroom mage acquston technque use lne perspectve geometry when acqurng the mages, the collnearty condtons cannot be mplemented n the same way. The 18
39 mathematcal model of the collnearty equatons must be modfed to lne perspectve (Novak, 199): x a = x m11( X f m31( X X X ) + m1( Y ) + m ( Y Y Y ) + m13( Z ) + m ( Z Z Z A L A L A L 0 A L 3 A L 33 A L ) ) 0 = y m1( X f m31( X X X ) + m ) + m ( Y ( Y Y Y ) + m ) + m ( Z ( Z Z Z A L A L 3 A L 0 A L 3 A L 33 A L ) ) where x a s the coordnate n scan lne, orthogonal to the drecton of travel. Because the mages are acqured n lnes, y dmenson can be neglected and defned as zero. Another dfference between the frame and pushbroom sensors s the exteror orentaton parameters of the acqured mages. Because a frame sensor acqures the whole mage n an nstantaneous of tme the exteror orentaton parameters of a frame camera mages are fxed. On the other hand, because the pushbroom sensors acqure the mages n a perod of tme they have dfferent exteror orentaton parameters for each scan lne whch makes the computatons much more complcated than the frame sensor. Untl now, the change of the exteror orentaton parameters has been approxmated by dfferent polynomal orders of tme. The frst order polynomal approach was used n Salamonowcz (1986), Gugan (1987), Gugan and Dowman 1 (1988), Westn (1990), and Novak (199) who assumed the change based on a lnear varaton n exteror orentaton parameters. The lnear polynomal formulaton of the change n exteror orentaton was expressed as follows: X L = X L + a1 t ω = ωl + a 4 t L = YL + a t ϕ = ϕl + a 5 t Y L = Z L + a3 t κ = κ L + a 6 t Z 19
40 where are the exteror orentaton parameters of lne, are the postonal exteror orentaton parameters of the centerlne of the scene, L L L Z Y X,, L L L Z Y X,, L L L κ ϕ ω,, are the rotatonal exteror orentaton parameters of the centerlne of the scene, a 1, a, a 3, a 4, a 5 and a 6 are the lnear coeffcents of the exteror orentaton parameters and t s the tme of lne. In ths case, there are addtonal 6 unknown parameters (a 1, a, a 3, a 4, a 5 and a 6 ) to the regular 6 unknown parameters ( L L L L L L Z Y X κ ϕ ω,,,,, ) when compared to the frame sensors. Gugan and Dowman (1988), Kratky (1989), Chen and Lee (1993), Zoej and Petre (1998), Frtsch and Stallmann (000) used the second order polynomal to model the change for the exteror orentaton parameters. In ths case, the unknowns of the parameters ncreased to a total of 18. The quadratc polynomal formulaton of the change n exteror orentaton was defned as: 1 1 L L t b t a X X + + = 4 4 L t b t a + + = ω ω L L t b t a Y Y + + = 5 5 L t b t a + + = ϕ ϕ 3 3 L L t b t a Z Z + + = 6 6 L t b t a + + = κ κ Later, Radhadev et al. (1998), L et. al. (00), used the thrd order polynomal approxmatons to the exteror orentatons parameters. The cubc form of the estmaton brngs much more computaton burden relatve to the frst and second order estmatons and formed as: L L t c t b t a X X = L t c t b t a = ω ω 3 L L t c t b t a Y Y = L t c t b t a = ϕ ϕ L L t c t b t a Z Z = L t c t b t a = κ κ 0
41 The mathematcal formulatons to the exteror orentaton parameters look so nonproblematc. However, there s a problem whch causes from the nature of the pushbroom sensor. For nstance, n the case of a second order polynomal approxmaton to the exteror orentaton parameters, 18 unknowns cannot be solved n a sngle estmaton procedure due to the correlatons between the parameters. Unlke the frame sensor, the results of the least squares estmaton are unstable due to the one dmensonal nature of the sensor. Ths problem was explaned and solved by Orun and Natarajan (1994). Fgure 3.4 shows the dfferences between the frame sensor and pushbroom sensor after performng small changes n the exteror orentaton parameters. Fgure 3.4 The comparson of the effect of small changes n parameters for frame and pusbroom sensors (Orun and Natarajan,1994). 1
42 It s shown that for pushbroom sensors a small change (dω) n ω s ndstngushable from a small change (dy) n Y. Smlarly, a small change (dφ) n φ cannot be dfferentated from a small change (dx) n X. Therefore, t s necessary to elmnate ether ω or Y and ether φ and X from the set of parameters to remove the nstablty (Orun and Natarajan, 1994). The proposed resultng model for the exteror orentaton was: X = X + a t + b t L L 1 1 ω = ω + a t + b t L 4 4 L = YL + a t + b t L Y ϕ = ϕ L = Z L + a3 t + b3 t L Z κ = κ The resultng model changes the ptch and roll orentatons to tme ndependent values, whle other parameters reman unchanged. As a result, 16 unknowns n the general model reduce to 1 unknown parameters n the Orun and Natarajan model. The dfferent forms of the extensons of the general exteror orentaton model were also performed. Rodrguez et al. (1988) assume the whole orentaton parameters as constants whle Prebbenow and Clerc (1988) assume a lnear varaton for yaw and roll orentatons and a quadratc varaton for ptch orentaton. All these models try to estmate the exteror orentaton parameters more accurately by tryng to model the movement of the sensor Smple Geometrc Models A smple geometrc model usually nvolves mathematcal functons, whch are easer to understand and do not requre the knowledge of mage sensor physcs (Toutn, 00). These systems nether use nor requre nformaton related to the sensor, platform and Earth and do not reflect the
43 geometry of descrbed dstortons. In ths respect, smple geometrc models requre mathematcal functons to relate the mage space and object space. The general form of the D and 3D functons can be wrtten as: = f ( X Y ) y = f ( X, Y ) x, 1 = f ( X, Y Z ) y = f ( X, Y, Z ) x, 3 4 where x and y are the mage coordnates, X, Y and Z are the object coordnates and f 1, f, f 3 and f 4 are the mathematcal functons whch perform the relaton between the mage and object space. It s also possble to wrte the nverse form as: = f ( x y) Y = f ( x, y) X, 5 = f ( x, y Z ) Y = f ( x, y, Z ) X, The mathematcal functon parameters are solved wth the help of the GCPs collected throughout the mage by usng the least squares adjustment process. Once the mathematcal functon parameters are determned, the correct postons of each pxel n the mage can be estmated by these functons. These functons are based on dfferent mathematcal models: D Polynomal Functons 3D Polynomal Functons 3D Ratonal Functons Projectve Transformaton Drect Lnear Transformaton 3
44 D Polynomal Functons In ths method, the relaton between the mage space and the object space s performed by usng the planmetrc coordnates of the GCPs only. The general mathematcal formulaton of a D polynomal functon can be expressed as (Toutn, 004): P D ( x, y) = m n = 0 j= 0 a X Y j j where X and Y are the planmetrc coordnates of the GCPs, and j are the ncreament values, m and n determnes the order of the polynomal model, generally between one and fve, and a j are the polynomal coeffcents to be determned by the least squares adjustment. The order of the model manly depends on the number of avalable GCPs, and n general, the more the number of GCPs, the more the accuracy acheved (Novak, 199). Because D polynomal functons do not take nto account the elevatons of the GCPs these models can be effcently used when the maged area s relatvely flat, namely where the mage s not nfluenced by the topographc effects. Ther usage s generally lmted to mages whch have few or small dstortons, such as nadrvewng mages (Bannar et. al., 1995). In order to acheve a good accuracy, GCPs have to be accurate, numerous and evenly dstrbuted. The elementary transformatons such as the rotaton, shft and scale are accomplshed by the frst order polynomal model whch s also called the D affne model. Ths polynomal has the form: x = a0 + a1 X + ay y = b0 + b1 X + by 4
45 When the second order polynomal functons are used, n addton to the prevous transformatons, torson and convexty are taken nto account (Toutn, 004). The second order polynomal functons have the form: x = a0 + a1 X + ay + a3x + a4y + a5xy y = b0 + b1 X + by + b3 X + b4y + b5 XY The hgher order polynomal functons do not correspond to any physcal realty of the mage acquston system and t should be remembered that, n general, a hgher degree D polynomal wll ft the GCPs better but t wll produce undesred dstortons far away from them (Pala and Pons, 1995) D Polynomal Functons 3D polynomal functons are generated by addng the elevaton coordnates of the GCPs to the D polynomal functons usng new parameters. However, because they are smlar to the D order polynomal functons, the problems of the D order polynomal functons are also vald for these functons except for the topography. They stll requre accurate, numerous and evenly dstrbuted GCPs. The general form of the 3D polynomal functons can be expressed as (Toutn, 004): P 3 D( x, y) = m n p = 0 j= 0 k= 0 a jk X Y j Z k where X,Y and Z are the coordnates of the GCPs,, j and k are the ncreament values, m, n and p determnes the order of the polynomal model, generally between one and three (Tao and Hu, 001), and a j are the polynomal coeffcents to be determned by the least square 5
46 adjustment. Smlar to the D polynomals, frst order of the 3D polynomal functon s called 3D affne model and can be wrtten as: x = a0 + a1 X + ay + a3z y = b0 + b1 X + by + b3z Specal forms of the 3D polynomal functons are also avalable. Pala and Pons (1995) have modfed the frst order 3D polynomal model by takng nto account the relef dsplacement effect. They derved the 3D polynomal model for the mages that are acqured from hgh alttude and they assumed a flat Earth model. The generated model has 4 addtonal unknowns for x, y when compared to the frst order polynomal model and comprses a total of 1 unknown parameters: x = a1 + ax + a3y + a4z + a5xz + a6yz y = b1 + b X + b3y + b4z + b5 XZ + b6yz They tested the model usng Landsat, SPOT Pan and XS data wth around 30 GCPs and found very good results approachng to the results of the rgorous model. The author extended ths model for the second order polynomal functons. Instead of usng the frst order polynomal model, the second order polynomal functons were used as the startng pont. The resultng specal form of the polynomal functons double the unknowns wth respect to the frst order specal functon and can be expressed as: x = a1 + ax + a3y + a4x + a5y + a6 XY + a7z + a8 XZ + a9yz + a10x Z + a11y Z + a1xyz y = b1 + b X + b3y + b4 X + b5y + b6 XY + b7z + b8 XZ + b9yz + b10x Z + b11y Z + b1xyz 6
47 Ratonal Functons (RFs) Ratonal Functons perform transformatons between the mage and the object spaces through a rato of 3D polynomals. Ratonal Functons can be expressed as (OGC, 1999; Tao and Hu, 001; Tao and Hu, 00; D et. al., 003; Fraser and Hanley, 003): x = n P1 ( X P ( X n n, Yn, Z, Y, Z n n n ) ) y = n P3 ( X P ( X 4 n n, Yn, Z, Y, Z n n n ) ) where, polynomals P (=1,,3 and 4) have the general form of the 3D Polynomal Functons. One mportant dfference s that both the mage coordnates (x, y) and the object coordnates (X, Y, Z) are normalzed to ft the range from 1 to +1 to mnmze the errors durng the computatons and mprove the numercal stablty of the equatons. The dfferences between the normalzed and unnormalzed computaton results and the stablty were demonstrated n Tao and Hu (00). The normalzaton of the coordnates can be done usng the followng equatons (Url 8): x x = 0 xn xs y y = 0 yn ys X X = 0 X n X s Y Y = 0 Yn Ys X X = 0 X n X s where, x n and y n are the normalzed mage space coordnates, X n, Y n and Z n are the normalzed object space coordnates, x 0 and y 0 are the offset values for the mage coordnates, X 0, Y 0 and Z 0 are the offset values for the object coordnates, x s and y s are the scale values for the mage coordnates and X s, Y s and Z s are the scale values for the object 7
48 coordnates. The general form of the ratonal functons can be wrtten as (Toutn, 004): R x y 3 D(, ) = m n p = 0 j= 0 k= 0 m n p = 0 j= 0 k= 0 a b jk jk X Y X Y j j Z Z k k m n p = 0 j= 0 k= 0 a jk X Y j Z k = a + a X + a Y + a Z + a X + a 10 X + a Y + a + a Z Y + a XYZ Z a Y + a Z + a XY + a XZ + a YZ+ + a X Y + a X Z + a Y X + a Y Z + a Z X where, a jk are the polynomal coeffcents that are called Ratonal Functon Coeffcents (RFCs). The frst order terms represent the dstortons caused by the optcal projecton, the second order terms are for the Earth curvature, atmospherc refracton, lens dstorton and the thrd order terms handle the unknown and accdental dstortons (Tao and Hu, 001). Two general estmatons of the RFCs are possble, that are: Terran Independent Method, and Terran Dependent Method The popularty of the ratonal functons has ncreased when some of the mage vendors and the government agences dd not want to delver satellte nformaton to the end users. Thus, these vendors looked for an alternatve way to correct the mage. As a result, they tred to approxmate the 3D physcal model results usng the ratonal functons. They frst corrected the mage by usng a 3D physcal model of ther own and then solved the RFCs by usng the result of the exstng 3D physcal model. 8
49 Later, they appended the RFCs wth the mage for the end users to correct ther mage wthout usng any of the satellte nformaton. Ths method s commonly known as the terran ndependent method and the methodologcal steps are explaned n Tao and Hu (001). On the other hand, ths method ncludes some errors and bases whch have to be removed wth the help of the GCPs (Hu and Tao, 00; Fraser and Hanley, 003). Therefore, the usage of at least one GCP to remove these errors or bases occurred usng ths method turns the method terran dependent (Toutn, 004). The second method totally uses the GCPs for the estmaton of the RFCs. However, because they are the general form of the polynomal functons the general problems for the D and 3D polynomals are also vald for the ratonal functon polynomals. For the thrd order ratonal functons, f the denomnator constants of the functons are set to 1, a total of 78 parameters need to be solved usng at least 39 GCPs. One mportant dsadvantage s that the ncrease of the unknown RFCs also ncreases the possblty of the correlaton between the RFCs and can make the least squares estmaton nstable Projectve Transformaton The projectve transformaton descrbes the relatonshp between the two planes (Novak, 00). It s the basc fractonal model whch can relate the mage space and the object space. It ntegrates only the planmetrc coordnates as the D polynomal model. The projectve transformaton s also called eght parameter transformaton because the total of unknowns of the model are eght: a1 X + ay + a x = c X + c Y b1 X + by + b3 y = c X + c Y
50 where, a 1, a, a 3, b 1, b, b 3, c 1, c and c 3 are the eght unknown parameters of the functons. Of course, projectve transformaton s wrtten for the frame sensors. Based on the assumpton that each scanlne has a dfferent perspectve and all are ted to a straght lne approxmatng the orbt, the functon has modfed to the form (Novak, 199): a1 X + ay + a = c X + c Y x y = b1 X + by + b3 1 where, y s the flyng drecton whereas x represents the pxel n a scan lne. Because the functon performs the relaton n two planes ths method has lttle practcal sgnfcance for satelltes (Novak, 199). On the other hand, Sh and Shaker (003) mplemented the projectve transformaton on IKONOS magery and found that the accuracy acheved usng the projectve transformaton s not sgnfcantly dfferent from the accuraces acheved usng the D polynomal models Drect Lnear Transformaton (DLT) The DLT models the transformaton between the mage pxel coordnate system and the object space coordnate system as a lnear functon (Mkhal et. al., 001). It has been wdely used n closerange photogrammetry and can also be used for the satellte mage geometrc correcton. Actually, the DLT model s often used to derve the approxmate ntal values of unknown parameters for the collnearty equatons (Tao and Hu, 001). The general collnearty equatons are modfed nto the DLT functons so the collnearty equaton unknowns are hdden n the 11 DLT unknown parameters. The collnearty equatons are also modfed for pushbroom sensors and the dervaton steps are explaned n ElManadl and Novak (1996). The model can be expressed as: 30
51 x = L1 X + LY + L3Z + L4 L X + L Y + L Z y = L5 X + L6Y + L7Z + L8 L X + L Y + L Z where, L 1, L,..., L 10, L 11 are the lnear orentaton parameters between two dmensonal mage space and the three dmensonal object space. Later, Okamoto et. al. (1999) extended the DLT model by addng two more parameters: L1 X + LY + L3Z + L4 a L X + L Y + L Z x = xy L X + L Y + L Z + L = L X + L Y + L Z y a 13 y It was stated that ths mprovement to the model ncreases the performance when compared to the other rectfcaton methods for the SPOT magery. In addton to the type of the functon, the orders of the functons must also be consdered. The order of the functons determnes the number of the coeffcents. The mnmum number of GCPs vares wth the order of the polynomals, namely the number of the unknown coeffcents n the polynomal terms. Because each GCP yelds two equatons, the mnmum number of GCPs s equal to the half of the number of unknowns. The model unknowns and the mnmum number of GCPs requred to solve the models are summarzed n Table 3.. Snce the smple geometrc models are completely ndependent of the geometry of the sensor they are less accurate when compared to the rgorous models. On the other hand, they are easer to understand and have an advantage of smplcty. A smple geometrc model s not recommended unless the mage sensor nformaton s not avalable at all (Toutn, 00). 31
52 Table 3.. The propertes of smple geometrc functons. Functon Type Mnmum Model Model Model GCP Order Coeffcents Unknowns number D polynomal Functon D polynomal Functon Polynomal Functon wth Relef D RFs Projectve Transformaton DLT A comparson between the two methods s summarzed by Toutn (1999) n Table 3.3: 3
53 Table 3.3 The comparson between smple and rgorous geometrc models. Smple Geometrc Model Does not respect the vewng geometry Not related to dstortons Does not ntroduce atttude data Corrects mage locally at the GCPs Does not flter blunders Indvdual adjustments of one mage Needs many (>0) GCPs Senstve to GCP dstrbuton Rgorous Model Respects the vewng geometry Reflects the dstortons Uses ephemers and atttude data Corrects the mage globally Flters blunders wth the knowledge of the geometry Smultaneous adjustment of more than one mage Need few (38) GCPs Not senstve to GCP dstrbuton GCP collecton and Refnement Ground control ponts (GCP) refer to ponts whose ground postons are known wth respect to a reference coordnate system and/or a reference datum. Whatever the geometrc model used for the stereo model, a number of GCPs have to be acqured to refne the stereo model n order to obtan cartographc standard accuracy (Toutn, 001). The requred number of GCPs s manly dependent on the geometrc model types; whether rgorous or smple. Snce the smple model does not reflect the real acquston geometry, t requres many more GCPs than the mnmum requrement. Any number of redundances above the mnmum requrement s taken care by the teratve least squares adjustment soluton. The defntons and the dervaton of the least squares adjustment process can be found n Appendx B. Other factors that affect the number and the accuracy of the GCPs nclude the method of collecton, sensor 33
54 type and resoluton, mage spacng, study ste, physcal envronment, GCP defnton and accuracy and the fnal expected accuracy (Toutn, 004). When the type of the GCPs s to be consdered, three dfferent types of GCPs can be defned (Toutn, 001): Full control ponts wth known XYZ coordnates Altmetrc ponts wth known Z coordnate Te ponts wth unknown cartographc coordnates. The last two are used to renforce the stereo model geometry and fll areas on the mages where the full control ponts are mssng. When the method of collecton property s to be consdered, the GCP coordnates can be collected through usng dfferent methods and sources such as GPS surveys, paper or dgtal maps, orthorectfed mages or photos etc. All these sources have varyng accuracy outcomes, for example dfferental GPS survey accuraces can go up to centmeter accuracy, whereas paper or dgtal map accuraces can deterorate down to 50 meters. Thus, the collecton method of the GCPs s a defntely crucal factor that affects the GCP accuracy and the fnal expected accuracy of a project. One other mportant matter s the resoluton of the mage to be processed. For nstance, f the GCPs are to be collected for Landsat magery, there s no need to collect the GCPs usng DGPS method wth centmeter accuracy. Smlarly, f the nput mage s IKONOS wth 1 m resoluton, 1:5000 or 1:50000 map GCPs would be ncapable to be used for any knd of IKONOS processng. 34
55 The number of GCPs s also dependent to the study ste to be nvestgated. If the terran observed n the ste s very steep and rugged and addtonally f the mage resoluton s relatvely coarse, the GCP collecton wll be challengng. For ths knd of stuaton, t s not easy to fnd GCPs to cover all planmetrc and elevaton ranges n the study ste. Thus, the resultng accuracy of any knd of output wll be far away to accomplsh the desred accuracy for both the rgorous and smple geometrc models. The last mportant factor s that the requred fnal accuracy of an output. In terms of the smple models, when the accuracy of the GCPs s n the same magntude as the resoluton of the magery, t s safer to collect more than twce the mnmum requred number of GCPs (Toutn, 004). Snce the rgorous models correct the mage globally, the desred output accuracy can be easly reached by spreadng the GCPs at the border of the mages and by coverng the full elevaton range of the study ste Elevaton Parallax Extracton Parallax s defned as the apparent dsplacement of the poston of a body caused by a shft n the pont of observaton wth respect to a reference pont or a system. Smlarly, stereoscopc parallax (also called mage parallax) can be defned as the apparent dsplacement of the locaton of a partcular object caused by the satellte moton and/or vewng angle dfferences wth respect to the prncple pont of each stereo mage. There are two types of possble stereoscopc parallaxes; () x parallax whch occurs along the flght axs and () y parallax whch s perpendcular to the flght axs. The x parallax s a natural result of the movement of the spacecraft and forms the key pont of the elevaton generaton from the observed objects. On the other hand, the y parallax generally occurs from mproper orentaton of the stereo mages and can be removed wth the knowledge of the mage acquston parameters. 35
56 Image matchng forms the key part to retan the elevaton parallaxes between the stereo mages. Two methods prncpally can be used to extract the elevaton parallax usng mage matchng (Toutn, 001): The computerasssted (vsual) methods Automatc methods. These methods can also be combned to extract the elevaton parallaxes more rgd and proper. The computer asssted method works on a stereoplotter and uses the tradtonal photogrammetrc method to extract the elevaton parallaxes. It then requres full stereoscopc capabltes to generate the onlne 3D reconstructon of the stereo model and the capture n real tme of 3D planmetrc and elevaton features (Toutn, 001). However, ths technque requres a long and expensve process and commonly used wth paperformat mages. The recent research studes are drectly affected from not only the tedous process of the computer asssted method but also the rapd ncrease of the producton of the dgtal stereo mages. In the last two decades most of these studes are changed ther vews towards on the second method whch s the automatc methods. Obvously, the automatc methods use the advantage of the computer technology and ts speed. The automatc methods developed to extract the elevaton parallaxes from dgtal stereo mages nclude (Wolf, 000): Area based methods, Feature based methods, and Hybrd methods. 36
57 Area Based Methods Area based methods perform the mage matchng based on the ntensty values of the stereo mages. Matchng ponts between the left and the rght mages are determned by userdefned reference and search wndows. The process s llustrated n Fgure 3.5. Frst a small wndow array (reference array) s selected from the frst mage. In order to fnd the correspondng poston of the reference array n the second mage, a search area s defned n the second mage. Then, small subarrays whch are the same sze of the reference array are selected nsde the search area and each of them s statstcally compared wth the reference wndow. The degree of relatonshp can be determned by usng several statstcal technques such as normalzed crosscorrelaton coeffcent, the sum of mean normalzed absolute dfference, the stochastc sgn change or the outer mnmal number estmator (Toutn, 00). The maxmum of the computed relatonshp values above the threshold n the search area s assumed to be the matchng pont for the reference wndow. Fgure 3.5 Areabased matchng usng reference and search arrays (Wolf, 000). 37
58 Among the statstcal technques, the normalzed crosscorrelaton coeffcent s consdered to be the most accurate one (Leberl et al. 1994). The correlaton coeffcent s computed by the followng equaton (Wolf, 000): c = m n = 1 j= 1 m = 1 j= 1 [( A A)( B B) ] m n ( A A) ( B B) j n j j = 1 j= 1 j where, c s the correlaton coeffcent, m and n are the numbers of rows and columns, respectvely, n the subarrays; A j s the dgtal number from subarray A at row, column j; A s the average of all dgtal numbers n subarray A; BBj s the dgtal number from subarray B at row, column j; B s the average of all dgtal numbers n subarray B. The correlaton coeffcent can range from 1 to ndcates a perfect negatve correlaton, 0 ndcates no correlaton and +1 ndcates a perfect postve correlaton. Due to some reasons such as nose, the tme nterval between the two mages and the acquston geometry, a perfect postve correlaton s extremely hard to obtan. A threshold value of 0.7 s selected n many cases and f the correlaton coeffcent exceeds ths value, the subarrays, namely the center pxel of the subarrays are assumed to be matched (Wolf, 000). A second areabased matchng method s the least squares matchng technque whch s able to obtan the correspondng locaton of the matchng pxels n terms of a fracton of a pxel. The most common formulaton of ths method s: 38
59 A( x, y) = h0 + h1 B( x, y ) x = a + a x + a y 0 y = b + b x + b y where, A( x, y) s the dgtal number from the canddate subarray of the left mage at locaton x, y; B ( x, y ) s the dgtal number from a subarray n the search area of the rght mage at locaton x, y ; h 0 s the radometrc shft; and h 1 s the radometrc scale. Equatons relate the left and the rght mages wth the affne transformaton (frst order polynomal). Due to the nature of the least squares approach, ths technque requres ntal approxmaton values to the unknowns (h 0, h 1, a 0, a 1, a, b 0, b 1 and b ). Each soluton requres formng the lnearzed equatons, obtanng the correctons and addng to the correctons to the ntal approxmatons. The process contnues untl the results for the unknowns are satsfactory and the correctons are neglgble. One mportant factor that affects the accuracy of the area based methods s the subarray sze. Generally, a subarray sze of 0 x 0 to 30 x 30 gves satsfactory results (Wolf, 000). If the subarray sze s smaller, possble matchng ponts may not be found. On the contrary, f the subarray sze s larger, multple matchng ponts can be found. Both condtons would produce problematc condtons. One soluton to the problems s producng the eppolar mages from the raw stereo mages pror to matchng. The left and rght stereo mages are resampled n a way that the y parallaxes n the mages are removed (Fgure 3.6). Therefore, the search area s reduced from dmensons to 1 dmenson. Ths resamplng preprocessng prevents the matchng of false pxels and brngs a substantal search tme decrease when compared to the D searchng. 39
60 Fgure 3.6 Eppolar geometry (Wolf, 000) Feature Based Methods Feature based methods seek to extract and match the common features from the two mages (Fonseca, 1996). In ths respect, two sequental processes are requred n order to fnd the matchng locatons; () feature extracton and () feature matchng. An mage can be represented n two dfferent domans when performng the feature extracton part. In the spatal doman, common features are edges, lnes, ntersectons, regons etc. In general, regon boundares and edges are extracted durng ths procedure by usng dfferent feature extracton technques such as Canny, Roberts, Prewtt, Sobel, FreChen, regon growng algorthms etc. On the other hand, n the transform doman where mages are represented as a set of transform coeffcents, the mage s decomposed. The edge nformaton n the mage can be extracted by usng classcal transform doman functons such as Fourer, Wavelet etc. The matchng accuracy of the feature based methods s extremely dependent to the feature extracton method whch s hghly affected from 40
61 the sensor geometry, the wavelength and nose. Because they do not drectly use the pxel values whch compose the mages they often requre sophstcated mage processng algorthms. Despte ther complex nature, they do not guarantee better results when compared to the area based methods Hybrd Methods Aforementoned methods have ther own partcular advantages and dsadvantages. For example, area based methods are straghtforward and commonly used n many systems. However, feature based methods are more complcated and can manage better n certan crcumstances. The combnaton of the two approaches s called hybrd method and t frstly nvolves extracton of edges by usng the second method. Then, these ponts are used as seed ponts for the frst method. Consequently, the ntegraton of the two approaches gves users to combne the advantages of both. In addton, there are also other hybrd methods that can be used to fnd the matchng pxels n both mages D Stereo Intersecton 3D stereo ntersecton method s a geometrcal ssue that s used to convert the extracted parallax values to absolute elevaton values. The method uses the dea that the correspondng rays to the same object pont n the overlap area of the two mages must ntersect at that pont (Fgure 3.7). 41
62 Fgure 3.7 3D stereo ntersecton (Wolf, 000). In order to calculate the coordnates of a pont, the collnearty equatons must be wrtten. Afterwards, these equatons must be solved by usng the least squares parameter estmaton technque. However, to solve the lnearzed equatons of the least squares for the unknown coordnates of the pont (X p, Y p and Z p ), 6 exteror orentaton parameters must be known ntally ether from mage meta data or from space resecton algorthm performed pror to the space ntersecton. As a result, two equatons can be wrtten for the pont on the left mage and two more for the pont on the rght mage. Hence four equatons are enough to solve three unknowns wth a least squares estmaton. Iteratons to fnd the coordnates of the pont are carred out up untl the results for the unknowns are satsfactory and the correctons are neglgble. Agan, for these calculatons the ntal approxmatons for the unknowns must be determned PostProcessng and Projectng the Generated DEM All matchng ponts that are found from the parallax extracton step are converted to absolute elevaton values by usng the prevous stage. The resultng DEM s nether n a common coordnate system (f t s not 4
63 mmedately geocoded after the DEM generaton) nor free from errors. The errors may occur durng the processngs ncludng the blunders, msmatched areas, falure of specfc areas etc. Therefore, whatever the matchng method s used, there s always a need for postprocessng the extracted elevaton data (Toutn, 00). Dfferent methods can be used to correct these errors: () manual, () automatc, or () nteractve (Toutn, 00). Obvously, manual methods completely dependent to the human vson and percepton durng the edtng process. The automatc methods use the advantage of the computer technology and ts effcency. Some algorthms to correct the blunders or nose nherent n the DEM are successfully adapted to be performed automatcally. To correct the large msmatched areas (for example more than 00 pxels), an operator should seed stereo extracted ponts nteractvely. To reduce the largest errors, an operator can also extract some specfc features pror to the correcton. In the followng secton, several automatc methods that are used for the nose dentfcaton and the nose removal are descrbed Nose Identfcaton Nose refers to pxels that contan falure values. The algorthms used to detect the nose are based on the assumpton that pxels that are adjacent to the faled pxels tend to contan ncorrect values. Namely, the surroundng pxels of a pxel determne that the pxel s faled or not. Three methods can be used to defne whether a pxel s faled or not (Orthoengne user gude, 003): The frst method calculates the average and varance of the eght elevaton values mmedately surroundng each pxel, 43
64 excludng faled and background pxels. If the center pxel s more than two standard devatons away from the average, t s replaced wth the faled value. The second method counts the number of faled values mmedately surroundng each pxel. If fve or more faled pxels border the center pxel, then the center pxel s also set to a faled value. Snce pxels adjacent to faled pxels tend to contan ncorrect values as well, the thrd method replaces the eght pxels around each faled pxel wth the faled value Nose Removal Nose removal functons use exstng flters whch are based on statstcal computatons (mean, standard devaton). In general, three flters are used for ths process (Orthoengne user gude, 003): The Medan flter ranks the pxel values wthn a pxel frame accordng to brghtness. The medan s the mddle value of those mage pxel values, whch s then assgned to the pxel n the center of the frame. The Smoothng flter s a flter that calculates the weghted sum of all the pxels n a threebythree pxel frame and assgns the value to the center pxel n the frame. Faled and background pxel values are not replaced by the flter and are not used n the calculaton. 44
65 The Interpolate flter replaces faled values wth an estmate weghted by dstance calculated from the vald pxels surroundng the faled pxel(s). After elmnatng the blunders occurred n a DEM, the last stage s projectng the eppolar DEM nto the desred map projecton system. Ths s agan performed usng the collected GCPs and the computed stereo model. The map projecton of the generated eppolar DEM pror to the postprocessng step s not recommended because the falure areas can be examned by swtchng back and forth between the eppolar mage channel and the eppolar DEM. Thus, the falure areas can be observed and dentfed straghtforwardly. 3. Orthorectfcaton Unrectfed satellte mages contan varous dstortons whch are explaned n secton These dstortons make the raw mages mpossble to be nput to a Geographc Informaton System (GIS), or overlayng and edtng wth any knd of data already ncorporated n a GIS (Lllesand et. al., 004). In ths respect, all these dstortons have to be removed pror to the usage of the mages. Therefore, the rectfcaton of the remotely sensed mages to a standard map projecton enables users to utlze mages n conjuncton wth the other spatal nformaton n a GIS. In general, two common processes are used for correctng such raw mages; () rectfcaton, and () orthorectfcaton. The accuracy of the resultng fnal product s the man dfference between the two methods. The rectfed mages are typcally generated usng smple mathematcal models. Consequently, the resultng magery s free from any knd of dstorton except for the relef dstorton. On the other hand, for an orthorectfed mage an elevaton source that fully models the terran 45
66 surface s used so relef dsplacement errors are removed or mnmzed (Manual of Photogrammetry, 004). In a frame mage, the perspectve center s the sngle pont where the rays of lght pass before ntersectng the mage plane. Ths occurs because the perspectve projecton and ponts at the same horzontal locaton but at dfferent elevatons wll therefore be maged at dfferent locatons n the mage (Fgure 3.8). On the contrary, an orthomage can be descrbed as a dgtal mage n whch the pxels are corrected to an orthographc projecton rather than the perspectve projecton (Manual of Photogrammetry, 004). Because n an orthographc projecton the projecton of the rays s perpendcular to the horzontal plane the change n the elevaton of a pont does not dffer from ts poston. Fgure 3.8 Relef dsplacement (Mkhal et. al., 001). 46
67 The basc prncpals and methods of orthomage generaton were descrbed by Konecny (1979), Novak (199), Krupnk (003), and Toutn (004). There are two basc approaches to generate an orthomage, () the forward projecton and () backward projecton (Novak, 199). In the former one, the object space coordnates are frst determned by projectng the raw mage onto DEM. Then, the object space coordnates are projected nto the orthomage. Snce the spaces between the ponts projected nto the orthomage vary due to terran varaton and perspectve effects, the fnal orthomage pxels must be determned by nterpolatng between the projected ponts. Fgure 3.9.a llustrates the forward projecton. In backward projecton, the object space X, Y coordnates correspondng to each pxel of the fnal orthomage are calculated. The elevaton values for each pxel s determned from the DEM and the object space coordnates are projected nto the raw mage to obtan a gray level or a color value for the orthomage pxel. Snce the projected object space coordnates wll not fall exactly at pxel centers n the raw mage, resamplng must be done n the raw mage (Mkhal et. al., 001). Fgure 3.9.b llustrates the backward projecton. If the orthomages are generated, they can be easly ntegrated for any knd of applcaton such as map revson, forestry, geology, envronmental studes etc. and offer users to use mages lke maps. However, a dsadvantage of the rectfed or orthorectfed mage product s that t has been resampled from the raw mage and may have been prepared from a DEM whch does not accurately model the surface. Thus, the product may loose some of ts orgnal resoluton and the accuracy may be degraded because of the errors n the DEM (Manual of Photogrammetry, 004). It s crucal to be aware of the nput DEM characterstcs such as elevaton accuracy, postonng accuracy and grd spacng for the level of detals. The last property gets more mportance when the mages get hgher resoluton because poor grd spacng when compared to the mage 47
68 spacng could generate problematc areas for lnear features (roads, edges etc.) n the output orthomage (Toutn, 004). (a) (b) Fgure 3.9 Forward and backward projecton. (Mkhal et. al., 001) 48
69 CHAPTER 4 STUDY AREA AND DATA SETS In ths chapter, the study area and the data sets used n the study are provded. After descrbng the study area, the mage data of ASTER are explaned. Later, the generaton method of the reference DEMs from 1:1000 scale vector data s explaned. Fnally, the GCPs and ther collecton methods are gven. 4.1 The Study Area The study area (Fgure 4.1) s located n central Anatola. It covers an area of approxmately 60 x 60 km and encloses the cty of Ankara. There are also several scattered small towns and the lakes Mogan and Eymr are stuated n the central part of the study area. The area also contans randomly dstrbuted several small water bodes. The eastern and a part of the northern area are rather mountanous. The forest areas are mostly located n the southern part of the cty of Ankara and n the south western part of the mountanous areas. The rest of the study area s characterzed by the agrcultural felds and open lands. The elevatons range from approxmately 700 m for the flat areas to 1900 m for the mountanous areas yeldng a total relef around 100 m. The slopes change sharply n mountanous regons approachng up to 70 degrees. Ths area was selected due to contanng varous landuse and landcover types such as urban, forest, water, mountanous, agrculture and open lands. The other reason s that both n the cty of Ankara and n rural 49
70 Fgure 4.1 ASTER Nadr mage of the study area. (A) represents the cty center of Ankara, (B) represents Lake Mogan, (C) represents the mountanous stes, (D) represents the forestry areas, and (E) represents the agrcultural and open lands. 50
71 areas, many roads and paths exst that can be very sutable for the selecton and collecton of GCPs and check ponts (CP). 4. Data Sets Three data sets were used n the study: () stereo ASTER mage data, () vector data, and () orthophotos ASTER Image Data Stereo ASTER mages were acqured on July 6, 00 wth a dfference of 55 seconds. The mages that were taken from the nadr and backward drectons compose the stereo nature wth an overlappng area of approxmately 57.5 x 6 km. Both scenes were completely free from clouds, snow and other effects such as haze and dust. The geographc coordnates of the four corners and the center of the mages are gven n Table 4.1. Some techncal characterstcs of the mage data are provded n Table 4.. Table 4.1 The geographc coordnates of the ASTER mages. Poston Nadr Image Backward Image Longtude Lattude Longtude Lattude Upper Left Upper Rght Lower Left Lower Rght Center
72 Table 4. The techncal characterstcs of the ASTER mages. Property Nadr Image Backward Image Acquston Date Acquston Tme 08:5:33 08:53:8 Sensor Near Infrared Near Infrared Instrument VNIR 3N VNIR 3B Bts per pxel Number of lnes Number of pxels Processng Level 1A 1A 4.. Vector Data In ths study, 576 peces of 1:1000scale vector data wth approxmately 0 cm accuracy both n planmetry and heght were avalable to be utlzed as reference DEMs. In turn, the reference DEMs wll be used to evaluate the generated DEMs. The vector dataset were compled n 1999 and referred to the European ED 50 datum and Transverse Mercator (Gauss  Krueger) projecton. The necessary nformaton regardng the projecton system s gven n Table 4.3. Table 4.3 Transverse Mercator projecton system detals. True Orgn Longtude 33º 00' " E Lattude 0º 00' " N False Eastng Northng Scale
73 The vector dataset were bult usng the Mcrostaton SE dgtal photogrammetrc workstaton software and composed of more than one hundred layers. Of these layers, those correspondng to contour lnes, ndvdual heght ponts, road network, valley creeks and the attrbutes were utlzed for the study. The contour lnes were drawn wth 50 cm nterval. The area covered by the vector data was around 1963 km Dgtal Orthophotos In ths study, the 1:5000scale dgtal orthophotos were avalable. The date and the projecton system of the orthophotos were same as the vector data. The area covered by the orthophotos was llustrated n Fgure 4.. Fgure 4. The whte colored vector polygon shows the coverage of the exstng vector data and orthophotos. 53
74 4..4 The Preparaton of the Reference DEM Data from exstng 1:1000 Scale Vector Data Intally, the attrbute layer, whch caused several techncal problems when transferrng the vector data to the PCI Geomatca software, was removed automatcally from all vector data usng Mcrostaton SE software. Next, 576 separate 1:1000 scale vector fles were attempted to be merged to make a sngle fle usng Mcrostaton SE. Because of the fle sze lmtaton of ths software, unfortunately ths process was not able to be mplemented. Later, 576 peces of 1:1000 scale vector data were merged frst nto smaller subsets. After ths frst mergng process, a total of 114 new vector data segments were generated. The complete names of the fles can be found n the Appendx F. Then, all the merged vector data were mported to PCI Geomatca software usng the Focus module and a reprojecton procedure was performed to them. The output projecton used was WGS 84 ellpsod and UTM zone36 rows. After the reprojecton procedure, 114 DEMs wth 1 m resoluton were created usng the Import & Buld DEM menu of the Orthoengne module. Ths module uses the Fnte Dfference nterpolaton method to generate the DEMs. Ths method performs the nterpolaton n three steps. In the frst step, the vector elevaton values are assgned nto the correspondng pxels n raster DEM. Next, the elevatons for the remanng pxels are nterpolated usng the Dstance Transform algorthm, whch estmates the values from those pxels equdstant from the pxels assgned n the frst step. In the last step, the Fnte Dfference algorthm teratvely smooths the raster DEM. Durng the teratons, the pxels that were assgned n the frst step are not changed, whle the nterpolated pxel values are updated based on the neghbourhood values (Orthoengne user gude, 003). Two parameters determne the completon of the process, the () Number of Iteratons and the () Tolerance. The Number of Iteratons specfes the maxmum number of tmes the smoothng s appled on raster DEM. The 54
75 Tolerance restrcts the number of tmes the smoothng s appled accordng to how t changes the elevaton values of the pxels. For the Fnte Dfference nterpolaton method, the default values for the Number of Iteratons and the Tolerance s 10 and 1, respectvely. If the tolerance value of a generated DEM s lower than 1 at the end of 10 teratons, the DEM s accepted. Otherwse, the DEM s consdered to contan errors. In ths case, the DEM s rejected and the vector data s scrutnzed. In the present case, the number of corrected DEMs was 68 and the vector IDs can be found n the Appendx C. The errors generally caused by the mssng elevaton or wrongly entered elevaton values ether n lnes, ndvdual ponts or roads. An example for the mssng elevaton values s llustrated n Fgure 4.3. In ths example, the resultng tolerance value for the generated DEM was hgher than the acceptable tolerance value. When the generated DEM s vsually analyzed, the error can be easly detected even on the overvew secton (Fgure 4.3b). If the vector data s supermposed on the generated DEM (Fgure 4.3c), the erroneous contour lne s apparent. The wrong elevaton values that le along that lne were then corrected wth the help of the elevaton values of the adjacent lnes. After the edtngs, the DEM was generated usng the same method and the resultng DEM tolerance value was found to be better than the acceptable tolerance value (Fgure 4.3d). Fgure 4.4 llustrates an error of mssng ndvdual pont measurements. Smlarly, the resultng tolerance value for the generated DEM was hgher than the acceptable value. Because the ndvdual ponts were errant, the true elevatons of these ponts could not be precsely known. Therefore, these ponts were removed from the data segment. After removng the ponts, the DEM was regenerated and the resultng tolerance value was found to be better than the acceptable tolerance value. 55
76 (b) (a) (c) (e) (d) (f) Fgure 4.3 An error caused by the mssng elevaton values. 56
77 (b) (a) (c) (e) (d) (f) Fgure 4.4 An error caused by the mssng ndvdual pont measurements. 57
78 The total number of the corrected vector data parts were 68. Then, two reference DEMs one havng 1 m resoluton and the other havng 30 m resoluton were generated usng the whole vector dataset. The former was used to obtan the elevatons of the GCPs collected wth the help of the orthophotos. On the other hand, the latter was used as the reference DEM. 4.3 The Collecton of the GCPs Majorty of the study area was covered by 1:5000 scale dgtal orthophotos, whch were used as the man source to collect the GCPs. For the areas that were not covered by the orthophotos, the GCPs were collected through dfferental GPS measurements GCP Collecton from 1:5000 Scale Dgtal Orthophotos On orthophotos, the ground features presented are n ther correct orthographc postons. Therefore, the orthophotos are geometrcally equvalent to conventonal planmetrc maps whch compose of lne and symbols. Because they are planmetrcally correct, the dgtal orthophotos can be effcently used as dgtal maps to select and dentfy GCPs. Frst, the Nadr mage wth false color composte was dsplayed usng the Orthoengne module and the canddate GCP locatons were selected from the mage. The canddate GCP locatons are the possble GCP locatons that can be found on the Nadr mage. A total of 158 canddate GCPs were selected throughout the mage. Then, the areas covered by the dgtal orthophotos were vsually analyzed and 108 GCPs were found to be fallng wthn the area covered by the orthophotos. Durng the collecton of the GCPs, the dgtal orthophotos and the ASTER nadr mage were also dsplayed smultaneously on the screen and fnally a total of 101 GCPs 58
79 wth the Eastngs and the Northngs were successfully collected. Seven of the canddate GCPs were not able to be collected because t appears that the ponts were formed after producton of the orthophotos n Of the collected 101 GCPs, 4 ponts were elmnated because ther locatons were outsde the border of the prevously generated 1 m resoluton DEM. Hence, the elevaton values of these ponts could not be determned. Because the GCPs had to be collected both on the nadr and backward mages, 7 GCPs were also removed as ther locatons were not able to be found on the backward mage. Furthermore, 5 ponts very close to other GCPs and 4 erroneous ponts were also removed. As a result, a total of 40 GCPs were elmnated and 61 GCPs were kept to be used for the subsequent processes. The coordnates of the 61 GCPs are provded n Appendx D. For three GCPs, the locatons on the mage and ther correspondng locatons on the orthophoto are llustrated n Fgure GCP Collecton through Dfferental GPS Measurements The coordnates of the Dfferental GCPs (DGCPs) were measured n the feld usng ASHTECH ZSurveyor recevers. These recevers are double frequency sensor type recevers. After completng the feld work, the row dfferental GPS postonng data were evaluated usng ASHTECH Offce sute verson.0. Fnally, the DGCPs were obtaned based on European ED 50 datum and the Transverse Mercator (Gauss  Krueger) projecton. The output coordnate system of the GCPs was reprojected to WGS 84 ellpsod and UTM zone36 rows projecton. The dfferental GPS observatons were made between 18 October 004 and 05 November 004. Of the two GPS recevers, one was placed at a base staton whose coordnates are precsely known and the other was moved to each pont whose coordnates are to be measured. At each GCP 59
80 Fgure 4.5 Three GCPs on the mage and ther correspondng locatons on the orthophotos. 60
81 to be measured, the rover recever receved satellte sgnals for approxmately 10 mnutes. Ten mnute recevng tme was suffcent for determnng the coordnates of a pont wth at least 1 meter accuracy. Of the collected 158 canddate GCP ponts, 108 ponts were wthn the regon covered by the exstng reference dgtal orthophotos. For the remanng 50 ponts, t was necessary to make measurements on the ground. Due to the medum resoluton of the ASTER stereo mages, the locatons of the canddate GCPs were not qute dstnct to be dentfed. Therefore, for preventng possble confusons about the locatons of the ponts, for each pont, the ste on the mage was prnted on A3 sze paper and also dsplayed on the screen of a notebook computer. Of the 50 canddate ponts, 36 GCPs were dentfed on the ground and ther coordnates were measured usng the DGPS method n three dmensonal mode. Unfortunately, the locatons of the 14 ponts were not able to be found on the ground and they were dscarded. Of the collected 36 GCPs, 11 out of 0 ponts were elmnated due to ther hgh resdual errors. The remanng 9 ponts were removed because ther correspondng pont locatons were not able to be found on the backward mage. Consequently, 16 GCPs were successfully collected both on the nadr and backward mage for the subsequent processes. The coordnates of the 16 GCPs determned through DGPS are provded n Appendx D. 61
82 CHAPTER 5 DEM GENERATION FROM STEREO ASTER IMAGERY In ths chapter, the Terra satellte whch carres the ASTER sensor s explaned. Later, the DEM generaton process from stereo ASTER mages s gven. Fnally, the results of the assessment of the generated DEMs are gven. The results of DEM accuracy analyss comprse two sectons, () the results of the least squares bundle adjustment and () the results of DEM accuracy evaluaton. 5.1 Earth Observaton Satellte Terra The advanced methods n computng and mage processng technologes let the users to use space magery n a useful manner more than ever. Today, a seres of Earth observaton satelltes montor our planet and collect huge number of mages that could be utlzed for many studes. Landsat and Spot seres are probably the most consdered and famous satelltes. On the other hand, the Terra satellte, a part of Earth Observng System (EOS) of NASA, s one of the flagshps to take on the role of observng the Earth. The mages taken by the Terra satellte gve opportunty to researchers to montor the Earth s contnents, atmosphere and oceans only from a sngle platform. The Terra satellte was launched n December 1999 and began operatons n February 000. It carres fve ndependent sensors () ASTER, () CERES, () MISR, (v) MODIS and (v) MOPITT. The satellte s orbt s roughly perpendcular to the Earth s spn and operates sunsynchronous 6
83 Table 5.1 The orbt characterstcs of the Terra satellte. Parameter Specfcaton Orbts / cycle 33 Cycle duraton 16 days Number of orbts per day 14 Alttude 705 km Inclnaton 98.3 deg Orbtal Perod mn Equatoral crossng at local tme 10:30 am orbt wth an nclnaton of 98.3 deg, at an alttude of 705 km. The satellte takes mnutes to complete one revoluton around the Earth and completes about 14 orbts per day. Terra s pattern of orbts repeats tself every 16 days or 33 orbts. The orbt characterstcs of the Terra satellte are gven n Table Advanced Spaceborne Thermal Emsson and Reflecton Radometer (ASTER) ASTER s a cooperatve effort between NASA and Japan s Mnstry of Economy Trade (METI), wth the collaboraton of scentfc and ndustral organzatons n both countres (Abrams et. al., 003). ASTER s advanced multspectral mager that covers a wde spectral regon wth 14 bands from the vsble to thermal nfrared wth varyng spatal, spectral and radometrc resolutons. The stereo coverage s provded by an addtonal backward lookng nearnfrared band. ASTER s composed of three dfferent subsystems: () the Vsble and NearInfrared (VNIR), () the Shortwave Infrared (SWIR) and () the Thermal Infrared (TIR) (Yamaguch et. al., 1998). The VNIR has three 63
84 bands wth a spatal resoluton of 15 m, and an addtonal backward telescope for stereo coverage. The SWIR has 6 bands wth a spatal resoluton of 30 m. The TIR has fve bands wth a spatal resoluton of 90 m. Each subsystem operates n a dfferent spectral regon wth ts own telescope(s) The VNIR Instrument The VNIR subsystem conssts of two ndependent telescope assembles to mnmze mage dstorton n the backward and nadr lookng telescopes. The detectors for each of the bands consst of 5000 element slcon chargecoupled detectors (CCD s). Only 4000 of the detectors are used at a tme. A tme lag occurs between the acquston of the backward mage and the nadr mage. Durng ths tme Earth rotaton dsplaces the mage center. The VNIR subsystem automatcally extracts the correct 4000 pxels based on orbt poston nformaton suppled by the EOS platform (Abrams et. al, 003). Despte the focal plane of the nadr telescope contans three lne arrays, the backward lookng telescope focal plane contans a sngle detector array. Onboard calbraton of the two VNIR telescopes s accomplshed wth ether of two ndependent calbraton devces for each telescope. The stereo mage acquston of ASTER s accomplshed by the VNIR subsystem. Two ndependent nadr and backward lookng telescopes work together to obtan alongtrack stereoscopc mages. The mages taken from the nadr and backward lookng telescopes compose the stereo nature wth a B/H rato of about 0.6 and an ntersecton angle of 7.6. Fgure 5.1 llustrates the alongtrack stereo mage acquston system of the ASTER sensors. (Hrano et. al., 003). Snce the two telescopes can be rotated up to 4 to provde extensve acrosstrack pontng capablty 64
85 and fve day revst capablty, acrosstrack stereo magng wth a B/H rato (close to 1) s also possble (Toutn, 00) The SWIR Instrument The SWIR subsystem uses a sngle aspherc refractng telescope. The detector n each of the sx bands s a Platnum SlcdeSlcon (PtSS) Schottky barrer lnear array cooled to 80 K. The onorbt desgn lfe of the cooler s hours. Sx optcal bandpass flters are used to provde spectral separaton. A calbraton devce smlar to that used for the VNIR subsystem s used for nflght calbraton (Abrams et. al, 003). Fgure 5.1 ASTER stereo geometry. 65
86 The TIR Instrument Unlke the VNIR and SWIR telescopes, the telescope of the TIR subsystem s fxed wth pontng and scannng done by a mrror. Each band uses 10 MercuryCadmumTellurde (HgCdTe) detectors n a staggered array wth optcal band pass flters over each detector element. The ASTER Instrument characterstcs and sgnfcant ASTER functons and components are summarzed n Table 5. and Table 5.3, respectvely (Abrams et. al, 003). Subsystem VNIR SWIR TIR Table 5. ASTER nstrument characterstcs. Spectral Spatal Quantzaton Band No. Range(μm) Resoluton(m) Level(bts) N B
87 Table 5.3 Sgnfcant ASTER functons and components. Parameter VNIR SWIR TIR Telescope Pushbroom Pushbroom Whskbroom Optcs Focal D=8.5 mm Plane(Detector) (Nadr) D=94.8 mm D=190 mm D=40 mm (Back.) Cross Track Pontng Telescope rotaton ±4 Pontng mrror rotaton ±8.55 Scan mrror rotaton ± Clouds and the Earth s Radant Energy System (CERES) There are two dentcal CERES nstruments aboard Terra that measures the Earth s total radaton budget and provde cloud property estmates that enable scentsts to assess the clouds roles n radatve fluxes from the surface to the top of the atmosphere. Ceres has a coarse spatal resoluton whch s 1 km. One CERES nstrument wll operate n a crosstrack scan mode and the other s a baxal scan mode. The crosstrack mode wll essentally contnue the measurements of the Earth Radaton Budget Experment (ERBE) msson as well as the Tropcal Ranfall Measurng Msson (TRMM), whle the baxal scan mode wll provde new angular flux nformaton that wll mprove the dervaton of the Earth s radaton balance (Web 1) Multangle Imagng SpectroRadometer (MISR) To fully understand the Earth s clmate, and to determne how t may be changng, we need to know the amount of sunlght that s scattered n 67
88 dfferent drectons under natural condtons. MISR s desgned to address ths need by usng cameras ponted at nne dfferent angles. One camera ponts at nadr the others provde forward and backward vewng angles. As the nstrument fles, each regon of the Earth s surface s successvely maged by all nne cameras n each of four wavelengths (blue, green, red and nearnfrared). MISR has a spatal resoluton of 75 m (Web ) Moderateresoluton Imagng Spectroradometer (MODIS) MODIS s vewng the entre Earth s surface every 1 to days and acqurng data n 36 spectral bands. These data wll mprove our understandng global dynamcs and processes occurrng on the land, n the oceans and n the lower atmosphere. MODIS s playng a vtal role n the development of valdated, global and nteractve Earth system models to predct global change accurately (Web 3). The nstrument provdes hgh radometrc senstvty (1 bts) rangng n wavelength from 0.4 μm to 1.4 μm. Two bands are maged at a resoluton of 50 m at nadr, wth fve bands at 500 m and the remanng 9 bands at 1km. A ±55 degree scannng pattern acheves a 330 km swath wdth (Web 4) Measurements of Polluton n Troposphere (MOPITT) MOPITT s an nstrument desgned to enhance our knowledge of the lower atmosphere and to partcularly observe how t nteracts wth the land and ocean bospheres. MOPITT s spatal resoluton km at nadr and t sees the Earth n swaths that are 640 km wde. MOPITT has 8 channels and scans across the satellte flght track ±6.1 deg n 13 seconds (Web 5). 68
89 5. Dgtal Elevaton Model Generaton from ASTER Data The dgtal elevaton models (DEM) were generated usng the Orthoengne module of the PCI Geomatca software. Ths module uses a rgorous mathematcal model (Toutn s model) developed n Canada Centre for Remote Sensng (CCRS) and reflects the physcal realty of the complete vewng geometry and ntegrates all the dstortons generated durng mage acquston (Toutn and Cheng, 00). The module has also specfc mathematcal model for aeral mages and capabltes to rectfy satellte or aeral mages by usng polynomal and ratonal functon based models. The dstortons handled by the Toutn s model are as follows: Dstortons due to platform Dstortons due to the sensor Dstortons due to the Earth Deformatons due to the cartographc projecton. Integratng all these dstortons n a mathematcal model produces a set of correlated unknown parameters whch later reduced to a set of ndependent uncorrelated set (Toutn and Cheng, 00). Toutn s model s sad to be the only satellte mathematcal model that can be appled to varous VIR and SAR sensors (ASAR, ASTER, EOC, EROS, ERS, IRS, IKONOS, JERS, LANDSAT, MERIS, QUICKBIRD, RADARSAT and SPOT). Based on the qualty of the GCPs, the accuracy of the Toutn s model was proven to be wthn onethrd of a pxel for medum resoluton VIR mages, one to two pxels for hghresoluton VIR mages, and wthn one resoluton cell for SAR mages (Toutn and Cheng, 00). 69
90 5..1 Radometrc Correcton The ASTER data was purchased n level 1A data format. The level 1A data format conssts of mage data, the radometrc coeffcents, the geometrc coeffcents and other auxlary data wthout applyng the coeffcents to the mage data to mantan the orgnal data values (ASTER Users gude part II, 003). Because the orgnal data values are preserved n Level 1A format, PCI Geomatca recommends t to obtan the hghest DEM accuracy (Orthoengne user gude, 003). Frst, the projecton of the output DEMs was determned as Unversal Transverse Mercator (UTM) zone 36 and row S on WGS 84 ellpsod. Then, the projecton nformaton of the GCPs was determned same as the output projecton of the DEMs and the output pxel spacng of the DEMs to be generated was determned as 15 m. The output pxel spacng s trval at ths stage because the output pxel spacng nformaton can also be determned at the fnal stage of the DEM generaton. Next, because the radometrc coeffcents were not appled on Level 1A data, the radometrc preprocessng was carred out. The algorthm used to preprocess the data was descrbed as (ASTER Users gude part II, 003): L = A V / G + D L = A V + C V + D (for VNIR and SWIR bands) (for TIR bands) where, L s the radometrcally corrected value, A s the lnear coeffcent value, V s the raw Dgtal Number (DN) value, G s the gan value, D s the offset value and C s the nonlnear coeffcent value. The frst formula was used to correct the nadr and backward VNIR ASTER mages. Tables 5.4 and 5.5 show the structure of the radometrc coeffcents avalable for nadr and backward mages. 70
91 Table 5.4 VNIR band (1,, 3N). Table 5.5 VNIR band (3B). Detector Lnear Offset Number coeffcent Gan 1 D[1] A[1] G[1] D[] A[] G[] 3 D[3] A[3] G[3] 4 D[4] A[4] G[4] 4098 D[4098] A[4098] G[4098] 4099 D[4099] A[4099] G[4099] 4100 D[4100] A[4100] G[4100] Detector Lnear Offset Number coeffcent Gan 1 D[1] A[1] G[1] D[] A[] G[] 3 D[3] A[3] G[3] 4 D[4] A[4] G[4] 4998 D[4998] A[4998] G[4998] 4999 D[4999 A[4999] G[4999] 5000 D[5000] A[5000] G[5000] The radometrc correcton formula was also ntegrated nto the Orthoengne module by PCI Geomatca tself. When the raw mages are loaded nto the module, the software automatcally reads the radometrc coeffcents avalable n the header fle and performs the radometrc preprocessng operaton automatcally. In order to be sure of the correctness of the preprocessng operaton, several parts of the mage were randomly selected and the manually calculated values were checked wth the output values of the software. It was found that the manually collected values were dentcal to the output values of the software. Fgure 5. shows for two selected areas of the nadr mage before and after the preprocessng operatons. The mportance of the preprocessng step was demonstrated n a prevous study conducted by Toutn (00) who states that the preprocessng operaton mproves the overall DEM accuracy by a factor of 10% (Toutn, 00). 71
92 Fgure 5. Before and after preprocessng operaton. 5.. Collecton of the Stereo GCPs After the radometrc correcton of the nadr and backward mages, both mages were dsplayed on the screen to collect the stereo GCPs by usng the GCP collecton menu of the Orthoengne module. In ths module, varous nput sources are avalable for the GCPs. The GCPs can be collected ether manually from the mages, from another geocoded mage, from vectors, from chp databases or from tablets. The menu also allows 7
93 users to mport GCPs that are avalable n a text fle composed n a specfc format. In the present case, the GCPs were collected manually. To collect the GCPs from a stereo mage, frst, both mages were dsplayed smultaneously on the screen. When two mages were dsplayed, the one n a vewer was labeled workng and the other was labeled reference. The GCP collecton wndow collects and dsplays the GCPs from the mage from the workng vewer only. Intally, the nadr mage was labeled workng and the backward mage was labeled reference. Then, the frst GCP s ID s set up and the GCP s collected on the nadr mage as precsely as possble. Later, the backward mage was labeled workng and the nadr mage was labeled reference. When the same ID of the GCP was typed n for the backward mage, the georeferencng nformaton of the GCP was automatcally taken from the prevous entry. The only mssng part was the pxel and the lne coordnates of the GCP on the backward mage. The Orthoengne module can estmate the possble locaton of the GCP by usng an automatc correlaton feature avalable n the GCP collecton wndows. Therefore, there s no need to search for the correspondng GCP locaton on the backward mage. The automatc correlaton gudes the user to locate the possble locaton of the GCP on the backward mage. But, the user must verfy the estmated postons and adjust them before acceptng the GCP on the backward mage (Orthoengne user gude, 003). Afterwards, the GCP locaton s fxed and the GCP s accepted. Ths stereo GCP collecton process was therefore repeated for the avalable 77 GCPs. The postons of the GCPs were located on both mages as precsely as possble. Then, the overall root mean square error (RMSE) of the stereo model was automatcally computed for the nadr and backward mages by the software. 73
94 Among the avalable 77 GCPs, frst, the evenly dstrbuted 8 were selected as GCPs and the remanng 69 were released as CPs. Therefore, the rectfcaton process was started usng 8 GCPs. Then, the the number of GCPs was ncreased to 16, 4 and 3 respectvely to assess the effect of the number of GCPs on DEM accuracy of the ASTER magery. Durng the process, 8, 16, 4 and 3 numbers of GCPs were named as set 1,, 3, and 4, respectvely. The number of CPs used for the sets, 3, and 4 were 61, 53, and 45, respectvely. Fgure 5.3 llustrates four sets of GCPs and CPs. Later, the bundle adjustment was carred out for all the sets by usng the model calculatons menu. The bundle adjustment s smply referred to the computaton of the unknowns of the stereo model. It s a method used to calculate the poston and the orentaton of the sensor at the tme when the mage was taken (Orthoengne user gude, 003). The results of the bundle adjustment for the sets, namely the resduals or the RMS errors of the GCPs and CPs, help determne the results and the qualty of the stereo model. The RMSE values of the GCPs and the check ponts are gven n Appendx E. 74
95 (A) (B) (C) (D) Fgure 5.3 Four sets of GCPs and CPs. The red ponts ndcate the locaton of the GCPs, whereas the yellow ponts ndcate the locaton of the CPs. The dstrbuton of (A) 8 GCPs, (B) 16 GCPs, (C) 4 GCPs, and (D) 3 GCPs. 75
96 5..3 DEM Generaton The Orthoengne module can generate DEMs from varous nput sources such as rasters, vectors, ponts or stereo mages. The DEM generaton usng the stereo mages has an addtonal ntal stage pror to the DEM generaton that s the eppolar mages must be generated from the nput stereo mage pars. The eppolar mages are stereo pars that are reprojected so that the left and rght mages have a common orentaton. Therefore, the matchng features between the two mages appear only along a common x axs. Because the eppolar mages ncrease the speed of the correlaton process and reduce the possblty of ncorrect matches (Orthoengne user gude, 003) they are necessary pror to DEM generaton n the Orthoengne module. To generate the eppolar mages, the nadr mage was selected as the left mage and the backward mage was selected as the rght mage. The down sample factor, whch s the number of pxels and lnes used to calculate for one eppolar mage, was selected as 1 to retan the orgnal pxel sze of the nput mages. Then, the eppolar mages were generated successfully n a mnute. Fgure 5.4 llustrates the generated left and rght eppolar mages for GCP set. 76
97 (a) (b) Fgure 5.4 The eppolar mages that are generated from the (a) nadr and (b) backward mages. Once the eppolar mages were generated, the DEMs were extracted for all GCP sets usng the DEM from Stereo segment. To do that, the generated eppolar mages were selected as nput mages. The program requres the estmated mnmum and maxmum elevaton values for the terran wthn the area covered by the stereo par. These values are used to estmate the search area for the correlaton stage and t s recommended that ncreasng the range between the estmated mnmum and maxmum elevatons for the terran reduces the falure areas (Orthoengne user gude, 003). The estmated mnmum and maxmum elevatons for the area was taken from the Shuttle Radar Topography Msson (SRTM)  90 m resoluton data. Ths data has been released to the publc wth free of charge and t was drectly downloaded from the World Wde Web (Web 6). The mnmum and maxmum elevaton values that were estmated from the SRTM data for the study area were 700 m and 1900 m, respectvely. A 500 m cushon on each sde of the elevaton range was gven n order to reduce the falure areas n the generated 77
98 DEMs (Hurtado, 00). Thus, the mnmum and maxmum elevaton values determned for the study area were 00 m and 400 m, respectvely. The Orthoengne module performs mage matchng based on a herarchcal mage matchng approach. Ths approach ntegrates a pyramd of reduced resoluton mages that are generated from the eppolar mages. In the frst part of the approach, very coarse versons of the eppolar mages were tred to be matched. Ths allows the matchng of certan features whch forms the bass for the subsequent correlaton attempts. The next correlaton attempts were performed on hgher resoluton versons of the mages. Fnally, the correlaton was performed on full resoluton eppolar mages, whch provdes the hghest precson for the terran n the generated DEM (Orthoengne user gude, 003). The level of the correlaton pyramd can be manpulated by usng the DEM Detal parameter whch determnes how precsely the terran s represented n the generated DEM. Three types of DEM detals (hgh, medum and low) can be selected. The Low detal means that the correlaton process stops at the hgher (coarser) level of the mage pyramd and the detal levels of the generated DEMs are low. Smlarly, the Medum detal means that the correlaton process stops at the average level of the mage pyramd and the detal levels of the generated DEMs are moderate. The Hgh detal means that the correlaton process contnues untl the full resoluton mage matchng s fnshed and the level of the detals of the generated DEMs s hgh. In the present case, all three possble choces were selected and performed separately. It was found that, the best results were obtaned usng the Medum detal soluton and ths DEM detal was selected for all the sets of GCPs. The last mportant factor that affects the DEM accuracy s the Pxel Samplng Interval. Ths parameter controls the sze of the output pxel n the generated DEMs. The pxel samplng nterval can be selected as 1,, 78
99 4, 8, 16 and 3. The hgher the number of the pxel samplng nterval, the larger the pxel sze of the output DEM s and the faster the DEM s generated. Fgure 5.5 llustrates the condton of the pxel samplng nterval of. Because the ASTER mages have a moderate resoluton n the present case the pxel samplng nterval of was selected (Orthoengne user gude, 003). (a) eppolar mage (b) pxel samplng of (c) Output DEM Fgure 5.5 The llustraton of the pxel samplng ntervals In addton to the above explaned parameters, the values for the falure and background were used as 100 and 150, respectvely. The channel type for the output DEM was selected as 3 bts for all sets and the fll holes and flter box was also selected to enhance the output qualty of the DEMs. The fll holes and flter parameter nterpolates the faled areas and flters the elevaton values automatcally. After assgnng the values for all parameters requred to generate a DEM, the eppolar DEMs were extracted for the above mentoned four sets of GCPs. The matchng pxel postons extracted from the two eppolar mages were used to calculate the 3D coordnate postons of the pxels by usng the computed mathematcal model. At ths stage, the generated DEMs were not the fnal DEMs and they are called eppolar DEMs because they are nether georeferenced nor free from errors (Fgure 5.6). 79
100 The nformaton report of the eppolar DEM generaton processes and the elevaton RMS errors related to the GCPs and the CPs for all sets are gven n Appendx F. Fgure 5.6 (A) The eppolar mage of the nadr mage of ASTER, (B) the stereo extracted eppolar DEM usng GCP set, (C) mage matchng falure over Lake Mogan, and (D) multple blunders occurred durng mage matchng. 80
101 5..4 Postprocessng and Geocodng the Generated DEM Next, a postprocessng operaton was appled on the generated eppolar DEMs n order to remove the errors ntroduced durng DEM generaton (Fgure 5.6 CD). The man reason for applyng a postprocessng operaton was to smooth out the falure areas and blunders exstng n the eppolar DEMs. The Orthoengne module provdes the specalzed manually edtng features that nclude the creaton of masks and replacng the elevaton values under these masks wth the userdefned or average values. It also provdes powerful flterng and nterpolaton features and specfc tool strateges for common errors encountered durng the DEM generaton. These tools equalze the pxel values over lakes, compensate for forests and urban areas, neutralze for cloudcovered areas and deals wth nose. As mentoned earler, the falure and background values were assgned and 150 pror to the DEM generaton. However, t was observed that several falure areas on the generated eppolar DEMs contaned the value of Intally, a correcton procedure was appled to the generated eppolar DEMs to assgn all falure areas to 100 and the background value to Ths operaton was accomplshed at these steps: Frst, a unque value 00 was assgned as the new background value. Then, all other 100 and 150 values were automatcally selected and 100 was assgned. Fnally, the correct background value 150 were reassgned to the pxels whch have 00 values. After fnshng these steps, all falure and background values were assgned 100 and correctly. Later, the falure areas were examned by swtchng back and forth between the mage channel and the eppolar DEM. Several scattered falure areas were observed over Lake Mogan (Fgure 5.6C) and small 81
102 water bodes. Therefore, the lake correcton was performed. The falure area over the Lake Mogan was masked. The masked regon was extended on the border by one pxel usng the erode holes command n order to be sure that all falure values are ncluded wthn the masked area. Then, for all DEM pxels wthn the masked area, the elevaton value of 973 m, whch was taken from the vector data, was assgned as the new elevaton value. Later, the blunders were vsually located, masked and an elevaton of 100 was assgned to them. The vsual nspecton and edtng step was the most tedous and tme consumng step because the blunders were randomly dstrbuted all around the DEM wth varyng szes (Fgure 5.6D). Subsequently, all falure areas were masked and ther regons were ncreased by one pxel. The faled values were then replaced wth the values calculated from the vald pxels surroundng the faled pxels usng the nterpolate command. Ths command uses an estmate weghted dstance calculated from the neghborng vald pxels of the faled pxels and only applcable for small areas contanng less than 00 pxels (Orthoengne user gude, 003). Fnally, the nose removal strategy suggested by the Orthoengne user gude manual was appled on the eppolar DEMs. Two flters were used by the Nose removal algorthm to dentfy the faled pxel values (Orthoengne user gude, 003). The frst flter calculates the average and the varance of the eght elevaton values mmedately surroundng each pxel, excludng the faled and background pxels. If the center pxel s more than two standard devatons away from the average, t s replaced wth the average value. The second flter counts the number of faled values mmedately surroundng the pxel beng analyzed. If fve or more faled pxels border the center pxel, then the center pxel s set to a faled value. After detectng the faled pxels by the nose removal algorthm, they were nterpolated from the surroundng vald pxels. Fnally, a Gaussan smoothng flter, whch calculates the weghted sum of all pxels n a three 8
103 by three kernel and assgns the value to the center pxel n the kernel, was appled to the eppolar DEMs for twce. After performng the postprocessng operaton, the eppolar DEMs were purfed from the falure areas and blunders. Next the eppolar DEMs were geocoded n a projecton system. In order to that the geocode extracted eppolar DEM menu was used. Now, the postprocessed eppolar DEMs were selected as the nput DEMs. The output pxel sze remaned as 30 m and the DEMs were geocoded to Unversal Transverse Mercator (UTM) zone 36 and row S on WGS 84 ellpsod. Next, the accuraces of the generated DEMs were determned Evaluaton of the DEMs In order to assess the accuraces of the generated DEMs, a btmap whch covers the regon of the reference DEM, was generated by usng the Focus Module. Later, ths btmap was used to mask out the regon for whch reference data were not avalable for the generated DEMs. After performng the maskng operaton, the DEMs were ready for performng varous accuracy analyses. The elevaton dfferences between the generated DEMs and the reference DEM can be computed n several ways. The frst one s to export both the generated and the reference DEM elevatons n a text fle and than calculate the dfferences between the two by usng a commercal software such as SPSS or Mcrosoft EXCEL. But, handlng of approxmately. mllon elevaton ponts would be qute hard for such software. In addton, ths method would be tme consumng and may not be useful. In the present case the accuracy assessment was carred out usng the IMAGESUB command of the Focus Module. Ths command automatcally calculates the dfferences between the two nput DEMs and produces a resultng dfference DEM. Next, the standard devaton (bas) of the elevaton dfference values were automatcally 83
104 computed from the dfference DEM values wthn usng Focus module. The comparson between the reference DEM and the generated DEMs were performed twce. Frst, the reference DEM was compared wth the DEMs whch are not postprocessed (notedted DEM). The second comparson was carred out after the DEMs were postprocessed (edted DEM). The comparson of the two dfferent results gave an opportunty to assess the mportance of the postprocessng operaton. The hstograms of the dfferences between the DEMs and the results of the comparson are gven n Appendx G. In order to assess the accuraces of the generated DEMs based on the slopes, the reference dgtal slope map was produced from the reference DEM. The dgtal slope map was generated automatcally by usng the SLP command of the Focus Module. Ths command calculates the slopes usng a plane formed by the vector connectng the left and rght neghbours and the vector connectng the upper and lower neghbours of a pxel (Orthoengne user gude, 003). Fnally, masks were generated from the dgtal slope map for every 10 degree nterval by usng the THR command of the Focus Module and these masks were used to evaluate the accuraces of the generated DEMs based on the slopes. To compute the accuraces based on land cover types, the raw mage had to be orthorectfed and vsually classfed. Therefore, the Nadr mage was orthorectfed usng the Orthoengne module and the best GCP confguraton of set. The nadr mage was preferred due to ts strong mage geometry relatve to the backward mage. For performng the orthorectfcaton the generated DEM wth GCP set was used as the source DEM. Because the pxel sze of the generated DEM was 30 m, the output pxel sze of the orthophotos was also set to 30 m. The projecton nformaton of the output orthorectfed mages were defned as UTM zone 36 and row S on WGS 84 ellpsod, whch s dentcal to the projecton 84
105 nformaton of the DEMs generated. Next, the area covered by the reference DEM was vsually classfed from the orthorectfed mage nto fve man land cover types (water, urban, forest, mountanous and others) usng the Focus Module. Then for each class, the prevously generated btmaps for each class were used to assess the accuraces of the DEMs based on land cover types. 5.3 The Assessment of the ASTER DEMs The Results of the Least Squares Bundle Adjustment As mentoned n the prevous part, DEMs were generated usng four dfferent sets of GCPs that are 8, 16, 4, and 3. For each set, the remanng ponts out of 77 GCPs were used as CPs for each set. Table 5.6 summarzes the results of the RMSE for each set of control and check ponts. Table 5.6 The Results of the least squares adjustment for the four sets of GCPs. Results of GCPs RMS Error (m) LSA CPs X Y XY Z Set Set Set Set
106 The results gven n the Table 5.6 were computed by takng the average of the nadr and backward RMSE values. The ndvdual RMS errors of the nadr and the backward mages are gven n Appendx H. As can be seen n Table 5.6, for all sets, the GCP RMSE values were found to be less than 1 pxel n both planmetry and elevaton. Surprsngly, the best total planmetrc accuracy was obtaned as ± 6.90 m (0.46 pxels) wth 8 GCPs. On the other hand, the RMS error ncreased to m (0.7 pxels) for 16 GCPs and became stable for 4 GCPs and 3 GCPs as m (0.76 pxels). If we look at the trends ndvdually for X and Y drectons, smlar to the total error results, the best accuracy was acheved usng set 1 both n X and Y drecton. However, one mportant pont s that a systematc ncrease n X drecton can be easly observed for sets, 3 and 4 wth respect to set 1. The Y drecton RMS errors demonstrate small dfferences between each other wth a narrow range of 5.5 m (0.35 pxels) to 6.15 m (0.41 pxels). The 5 m RMSE dfference between set 1 and the other sets mght have been caused by the less number of GCPs used n the frst set. Besdes, no logcal explanaton could be made about the remarkably hgh planmetrc accuracy of the set 1. The total RMS error values for the GCPs and CPs are llustrated n Fgure 5.7. Despte the extreme accuracy acheved for the GCPs wth less than half a pxel sze usng set 1, the results proved that the RMSE of CPs for set 1 are not affected from that hgh accuracy. Furthermore, all sets demonstrate good coherency and consstency n planmetrc accuracy for the CPs. The RMSE values for sets 1 and are the same and equal to 1.15 m (0.81 pxels). The RMSE values for CPs decreased to m (0.77 pxels) for set 3 and m (0.76 pxels) for set 4. Therefore, the best planmetrc accuracy for CPs was provded by the set 4. 86
107 RMSE (m) GCPs C. Ponts 0 Set 1 Set Set 3 Set 4 Fgure 5.7 The planmetrc total RMS error values for the GCPs and CPs for all sets The assessment of the elevatons of the ponts, for all sets, s also mportant as the elevaton RMS errors may gve ntal sgns of the overall DEM accuracy. The best elevaton RMSE for both GCPs and CPs was computed for set as m (0.79 pxels) and 5.90 m (0.39 pxels), respectvely. An rregular trend of the accuracy was observed for both GCPs and CPs n the elevaton accuracy. Ths rregular trend s llustrated graphcally n Fgure 5.8. Unfortunately, no logcal explanaton can be made about ths trend for the elevaton accuracy of the GCPs. The GCP elevaton accuracy for sets and 4, and sets 1 and 3 show smlar results. However, for all sets, the elevaton RMS error values for the CPs were relatvely better than the elevaton RMS error values of the GCPs. The RMS errors were approxmately half a pxel sze and vared between 5.90 m (0.39 pxels) and 8.90 m (0.59 pxels). One pont to note s that, for all sets, the RMSE values for GCPs and CPs were found to be less than one pxel sze n both planmetry and elevaton. 87
108 RMSE (m) GCPs C. Ponts 0 Set 1 Set Set 3 Set 4 Fgure 5.8 The elevaton RMS error values for the GCPs and check ponts for all sets In addton to the assessment of the RMSE values, the maxmum errors of the least squares adjustment were also evaluated. The assessment of the maxmum errors gve ndcatons of the stablty of the model used for the least squares adjustment (Toutn, 004). For four sets, the results of the maxmum errors computed for the GCPs and CPs are gven n Table 5.7. As can be seen n Table 5.7, the maxmum errors refer to the GCPs wth the hghest total error. Smlar to the planmetrc RMSE results, for GCPs the best maxmum planmetrc error was computed for set 1. However, ths good result was not sgnfcant because the maxmum error for CPs was around two pxels. It s obvous that, for all sets, the total planmetrc errors were hghly affected from the errors n X drecton as when compared wth Y drecton; the errors n X drecton are remarkably hgh. It s also clear that all planmetrc errors were better than the sze of two pxels. For elevaton the maxmum error values were better for sets 1 and than the 88
109 Results of LSA Set 1 Set Set 3 Set 4 Table 5.7 The maxmum errors computed for all sets. GCPs Maxmum Error (m) CPs X Y XY Z sets 3 and 4. Unfortunately, the reason for ths nearly 10 m elevaton dfference between the sets cannot be explaned The Assessment of the DEMs The results of the ntal DEM evaluaton were obtaned from the CPs. The best accuracy of 5.9 m (0.39 pxels) was computed usng set. The summary of the results for each set s gven n Table 5.6. In fact, the fnal accuracy obtaned from the 61 CPs was excellent and was close to one thrd of a pxel sze of the ASTER magery. However, because ths accuracy was obtaned usng only 61 ponts, t mght not reflect the overall DEM accuracy. To assess the accuraces of the DEMs, frst, the DEMs generated for all sets were evaluated wthout applyng any postprocessng operaton except for the correctons appled over water bodes. The results obtaned from the statstcal evaluatons are gven n Table 5.8. The accuracy assessment was performed by comparng the reference DEM wth each of the stereo extracted DEMs usng,171,664 ponts. 89
110 Table 5.8 The results of the DEMs generated wthout postprocessng. Set ID Before Postprocessng (m) Bas Mn. Error Max. Error The accuraces for the generated DEMs were m for set 1, m for set, 18.8 m for set 3 and m for set 4. It s clear that, the computed accuraces for approxmately. mllon ponts were or 3 tmes hgher than the accuraces computed for the CPs. Ths confrms that, the computed accuraces usng CPs are almost trval and do not reflect the actual DEM accuracy. It s also mportant to evaluate the mnmum and maxmum errors of the generated DEMs. The mnmum errors around 350 m and the maxmum errors around 1050 m of the generated DEMs demonstrate that the DEMs contan serous local errors. These errors mght be occurred from the ncorrectly computed matchng ponts durng mage matchng process. Further nvestgaton was carred out to fnd the total number and the locatons of these blunders. In ths study, the elevaton ponts whch le outsde the regon of 3σ and +3σ were defned as blunders. The results of the nvestgaton for each DEM generated are gven n Table 5.9. Table 5.9 The total number of the blunders detected n the generated DEMs Set Before Postprocessng (m) Total Percentage ID Bas Mn. Bound Max. Bound Number ( )
111 As can be seen n Table 5.9, for each set, more than ponts fell outsde the 3σ and +3σ range. Actually, the percentage of the blunders occurred n the DEMs were less than %1 of all the ponts. However, these blunders must be located and removed before performng any knd of subsequent process. After the vsual nvestgaton of the locatons of the blunders, t was observed that the blunders mostly occurred n the mountanous areas. However, t was also observed that even n the flat areas some localzed blunders were present. Two of the common blunders are llustrated n Fgure 5.9. Next, the DEMs were postprocessed usng both the manual and the automatc methods provded by the Orthoengne module of PCI Geomatca. The results obtaned from the statstcal evaluatons are gven n Table Fgure 5.9 The blunders occurred after generatng the DEM. 91
112 Table 5.10 The results of the DEMs generated after postprocessng. Set ID After Postprocessng(m) Bas Mn. Error Max. Error As can be seen n Table 5.10, the accuraces after the postprocessng were m, m, 1.36 m and 1.09 m for set 1, set, set 3 and set 4, respectvely. Despte the accuracy acheved usng CPs dd not reflect the overall DEM accuracy; the trend found usng CPs may reflect the trend of the fnal accuracy of the output DEMs. The mnmum and maxmum errors ensure that consderable number of the erroneous elevaton values was removed through postprocessng. The resultng scenes after the postprocessng stage for the blunders removal are llustrated n Fgure Fgure 5.10 The resultng scenes after applyng postprocessng. 9
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