An Integrated Semantically Correct 2.5D Object Oriented TIN. Andreas Koch

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1 An Integrated Semantcally Correct 2.5D Object Orented TIN Andreas Koch Unverstät Hannover Insttut für Photogrammetre und GeoInformaton

2 Contents Introducton Integraton of a DTM and 2D GIS data Semantcs n the context of terran modellng The approach Examples Conclusons Unverstät Hannover Insttut für Photogrammetre und GeoInformaton

3 Data Integraton Introducton Aggregaton of data from dfferent data sources to obtan a homogeneous data set Integraton 2D DLM DTM 3D DLM geometry semantc Hake et al., 2002: Kartographe Unverstät Hannover Insttut für Photogrammetre und GeoInformaton

4 Integraton of DTM and 2D GIS data Example data ATKIS Bass-DLM ATKIS DGM 5 Rver Lake Road Path Dgtal Terran Model 2.5D Ponts wth coordnates XYZ Structure elements (break lnes, sngle heghts,...) GIS vector data 2D Ponts, lnes, areas Attrbutes on functon and dmenson of the objects Unverstät Hannover Insttut für Photogrammetre und GeoInformaton

5 Problem Integraton of DTM and 2D GIS data Inconsstences between the data - Data acquston methods - Data modellng - Tme shft between acqurng the data Unverstät Hannover Insttut für Photogrammetre und GeoInformaton

6 Problem Integraton of DTM and 2D GIS data Inconsstences between the data - Data acquston methods - Data modellng - Tme shft between acqurng the data Result Integrated TIN Semantcally ncorrect Unverstät Hannover Insttut für Photogrammetre und GeoInformaton

7 Problem Integraton of DTM and 2D GIS data Inconsstences between the data - Data acquston methods - Data modellng - Tme shft between acqurng the data Result Integrated TIN Semantcally ncorrect The am Re-establshment of the semantcally correctness Unverstät Hannover Insttut für Photogrammetre und GeoInformaton

8 Semantcs n the context of terran modellng Object characterstcs Horzontal plane Increasng terran Sloped and curved areas Maxmum slopes and curvatures Decreasng nveau and ncreasng terran Unverstät Hannover Insttut für Photogrammetre und GeoInformaton

9 Semantcs n the context of terran modellng Lake Local TIN wth horzontal trangles Terran hgher than lake heght Rver Object wth tlted planes; local TIN nsde Terran hgher than local rver heght Road / Path Object wth tlted planes; local TIN nsde Lmted slope and curvature Unverstät Hannover Insttut für Photogrammetre und GeoInformaton

10 Input data DTM GIS objects The approach Preprocessng Ponts Pontswth wthunknown (XY)Z (XY)Z coordnates coordnates DTM-TIN GIS-TIN Pont nterpolaton Bufferng lne objects Basc observatons Observaton constrants Inequalty constrants Integrated TIN Semantcally correct Output data Optmsaton Integraton Inequalty constraned least-squares-adjustment Based on a TIN Unverstät Hannover Insttut für Photogrammetre und GeoInformaton

11 Input data DTM GIS objects The approach Preprocessng Ponts Pontswth wthunknown (XY)Z (XY)Z coordnates coordnates DTM-TIN GIS-TIN Pont nterpolaton Bufferng lne objects Basc observatons Observaton constrants Inequalty constrants Integrated TIN Semantcally correct Output data Optmsaton Integraton Inequalty constraned least-squares-adjustment Based on a TIN Unverstät Hannover Insttut für Photogrammetre und GeoInformaton

12 Input data DTM GIS objects The approach Preprocessng Ponts Pontswth wthunknown (XY)Z (XY)Z coordnates coordnates DTM-TIN GIS-TIN Pont nterpolaton Bufferng lne objects Basc observatons Observaton constrants Inequalty constrants Integrated TIN Semantcally correct Output data Optmsaton Integraton Inequalty constraned least-squares-adjustment Based on a TIN Unverstät Hannover Insttut für Photogrammetre und GeoInformaton

13 Input data DTM GIS objects The approach Preprocessng Ponts Pontswth wthunknown (XY)Z (XY)Z coordnates coordnates DTM-TIN GIS-TIN Pont nterpolaton Bufferng lne objects Basc observatons Observaton constrants Inequalty constrants Integrated TIN Semantcally correct Output data Optmsaton Integraton Inequalty constraned least-squares-adjustment Based on a TIN Unverstät Hannover Insttut für Photogrammetre und GeoInformaton

14 Optmsaton Unverstät Hannover Insttut für Photogrammetre und GeoInformaton Inequalty constraned least-squares-adjustment - Functonal model - Transformaton nto the Lnear Complementary Problem (LCP) - Soluton usng the Lemke-Algorthm (Pvotng method) = c * c c v v x A A l l b x H * - Stochastc model = l c l c ll Σ 0 0 Σ Σ 0 b z x H * = + ( ) T r T z z z = z z 0

15 Equatons and nequatons Lake - Observatons v = Z lake Z v = X X Ẑ lake v = Y Y X Y v = Z lake Z ( ) X Y - Inequatons Z lake Z j < 0 Ẑ Unverstät Hannover Insttut für Photogrammetre und GeoInformaton

16 Road Parameters Equatons and nequatons X Y ab 0 0 Ẑ XYZ plane a 0a1a2 Ẑ plane Unverstät Hannover Insttut für Photogrammetre und GeoInformaton

17 Equatons and nequatons Road Observatons t t Z a Y X a a v + + = a a a Y ab X 0 0 ( ) ( ) X Y ab Y Y X Y ab X X t t = = plane Z Z v = Ẑ plane ( ) t t plane Y X Z Z v = j Z Z v = Ẑ j Ẑ Unverstät Hannover Insttut für Photogrammetre und GeoInformaton

18 Equatons and nequatons Road Inequatons s max Z Z S j j Ẑ ds max Z Z S j j Z j Z S jk k Ẑ j S = S j j t t t t ( X Y X Y ) j j Ẑ k Unverstät Hannover Insttut für Photogrammetre und GeoInformaton

19 Integraton Startpont P 1 Area of consderaton Ponts of ntersecton S 1 and S 2 Integraton of object geometry between S 1 and S 2 Heght nterpolaton Polygon trangulaton Unverstät Hannover Insttut für Photogrammetre und GeoInformaton

20 Integraton Optmsaton of the shape of the trangle - Edge flp S 2 s next startpont Crossng the same trangle a second tme - Dfferent area of consderaton Unverstät Hannover Insttut für Photogrammetre und GeoInformaton

21 Examples Synthetc data Road Identcal weghts s Max 0,1 ds Max 0,2 Hgh weghts: Horzontal cross profles & planes s Max 0,1 ds Max 0,2 Unverstät Hannover Insttut für Photogrammetre und GeoInformaton

22 Examples Synthetc data Road Identcal weghts s Max 0,03 ds Max 0,06 Hgh weghts: Horzontal cross profles & planes s Max 0,03 ds Max 0,06 Unverstät Hannover Insttut für Photogrammetre und GeoInformaton

23 Examples Synthetc data Road Hgh weghts: Horzontal cross profles & planes Ponts of center axs s Max 0,1 ds Max 0,2 Hgh weghts: Horzontal cross profles & planes Ponts of center axs s Max 0,03 ds Max 0,06 Unverstät Hannover Insttut für Photogrammetre und GeoInformaton

24 Examples Weghts Z nsde lake 1,00 XY object 0,04 Z object 1,00 Semantcally correct not correct Unverstät Hannover Insttut für Photogrammetre und GeoInformaton

25 Examples Resduals v Z 0 v Z > 0 v XY Unverstät Hannover Insttut für Photogrammetre und GeoInformaton

26 Examples Resduals Resduals [m] Heghts nsde lakes Heghts of borderng polygons Planmetrc coordnates of borderng polygon ponts Unverstät Hannover Insttut für Photogrammetre und GeoInformaton

27 Conclusons An approach was presented whch produces an ntegrated semantcally correct TIN - Optmsaton and Integraton - Usng objects wth mplct heght nformaton - Changng the heghts and the planmetrc postons of the objects Approach s a further development of a method changng only the heghts The results are satsfyng Unverstät Hannover Insttut für Photogrammetre und GeoInformaton

28 The end Thank you for your attenton! Unverstät Hannover Insttut für Photogrammetre und GeoInformaton

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