SIMULTANEOUS CALIBRATION OF MULTIPLE CAMERA HEADS WITH FIXED BASE CONSTRAINT

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1 SIMULTANEOUS CALIBRATION OF MULTIPLE CAMERA HEADS WITH FIXED BASE CONSTRAINT A. M. G. Tommselli, *, M. Glo, W. L. Bzn b,c, R. S. Ruy b,d, J. Mrcto Junior d São Pulo Stte University, Dept. of Crtogrphy, 96-9, Pres. Prudente, S.P., Brzil, (tomseli, glo@fct.unesp.br b Pos-Grdute Progrm in Crtogrphic Sciences (jrmrcto@gmil.com c Sntigo & Cintr Consultori (wim_bzn@msn.com d Engemp Geoinformção (roberto@engemp.com.br Commissions V I, IC WG V/I KEY WORDS: Dul hed cmers, cmer clibrtion, multi frme imges. ABSTRACT: Imge cquisition systems bsed on multi-hed rrngement of digitl cmers re ttrctive lterntives enbling lrger imging re when compred to single frme digitl cmer. Besides tht, cquisition of multiespectrl imgery is esier when independent cmers re used. Considering tht in multicmer systems the heds re tightly ttched to n externl mount, it cn be supposed tht reltive position orienttion between cmers re stble during imge cquisition. This work presents n pproch bsed on simultneous clibrtion of two or more cmers using constrints stting tht the reltive rottion mtrix the bse distnce between the cmers heds re stble. Experiments with imges cquired by n rrngement of two Hsselbld H3D cmers were ccomplished with terrestril clibrtion field. The experiments hve shown tht the clibrtion technique with RO constrints llows dvntges when compred to the pproch bsed on single cmer clibrtion.. INTRODUCTION Recent developments in the technology of opticl digitl sensor mde vilble digitl cmers with medium formt t resonble costs, when compred to high-end digitl photogrmmetric cmers. Due to this fvorble cost/benefit rtio, mny compnies hs been dpted professionl medium formt cmers for use in mpping generl photogrmmetric tsks (Hbib Morgn, 3; Roig et l, 6; Ruy et l, 7. When compred to clssic photogrmmetric film cmers (3x3cm formt, however, digitl medium formt cmers present smll ground coverge re. Modern photogrmmetric digitl cmers overcome this drwbck with distinct pproches: multiple liner pushbroom sensors (DLR HRSC, Leic ADS 4 or multiple frme cmer heds (Z/I DMC, Vexcel Ultrcm, DIMAC. Imge cquisition systems bsed on multi-hed rrngement of digitl cmers re ttrctive lterntives enbling lrger imging re when compred to single digitl frme cmer. Acquisition of multiespectrl imgery is fcilitted when considering independent cmers. Severl mnufctures re following this tendency, integrting individul cmers to produce high-resolution multiespectrl imges. Independent developers lso re integrting their own low cost systems with smll medium formt off-the-shelf cmers (Roig et l, 6; Ruy et l, 7. These imges cn be processed s units (Mostf Schwrz, or they cn registered mosicked to generte high resolution multispectrl imge. In ny cse, the knowledge of reltive orienttion between cmers is desirble. One strtegy is to directly mesure the coordintes of the perspective centers of ech individul cmer to determine indirectly the orienttion (rottion mtrix of these cmers by bundle block djustment (Doerstel et l.,. Another lterntive, presented in this pper, is the simultneous clibrtion of two or more cmers using constrints stting tht the reltive rottion mtrix the bse distnce between the cmers heds re stble. An dditionl constrint cn lso be introduced with the mesured length between the externl nodl points. This pproch is ssessed with close rnge imges some experiments re presented showing the fesibility dvntges of the process over the individul clibrtion of ech hed.. Cmer Clibrtion. BACKGROUND Cmer clibrtion ims t the determintion of set of IOP - inner orienttion prmeters (focl length, principl point coordintes lens distortion (Brown, 97; Merchnt, 979, Clrke Fryer, 998; Crmer, 4; Mikhil et l,. This process cn be crried out by severl methods: lbortory methods, like goniometer or multicolimtor; stellr field methods like mixed rnge field, convergent cmers self clibrting bundle djustment. In the field methods, imge observtions of points or liner fetures in severl imges re used to indirectly estimte the IOP by bundle djustment with Lest Squres Method. The mthemticl model used re the collinerity equtions with dditionl prmeters (Eq..

2 M F = x - x - Δx+ f F Q F = y - y - Δy + F = N f = Q where xf, yf re the imge coordintes; M, N, Q, Δx Δy re obtined by: m ij M m(x - X + m(y - Y + m3(z - Z N m(x - X + m(y - Y + m3(z - Z Q m3(x X + m3(y Y + m33(z Z Δx = δx + δx + δx r d re the rottion mtrix elements., Δy = δy + δy + δy ; r d In these equtions the rdil decentering lens distortion coefficients re given by Eq(s. ( (3 (Brown, 966: 4 δx = (K r + K r + K r...(x - x r 3 6 ( ( Previous works on stereo or multi-hed clibrtion usully do not tke dvntge of stbility constrints (Zhung, 995; Doerstel,. Considering tht in multicmer systems the heds re tightly ttched to n externl mount, it cn be supposed tht reltive position orienttion between cmers re stble during imge cquisition. As consequence, some dditionl constrints relted with this geometry cn be included in the clibrtion step, when using bundle djustment. The inclusion of these constrints in bundle djustment seems to be relevnt since the estimtion of reltive orienttion (RO prmeters from previous djusted block shows significnt devitions between different pir of imges, i.e., lrger physicl vritions thn the expected ones. In order to solve this problem, this work presents n pproch bsed on simultneous clibrtion of two or more cmers using constrints stting tht the reltive rottion mtrix the bse distnce between the cmers heds re stble. An dditionl constrint is lso introduced with the mesured length between the externl nodl points. 4 δy = (K r + K r + k r...(y - y r 3 where r is the rdil distnce relted to the principl point. δx = P [r + (x - x ] + P (x - x (y - y d δy = P (x - x (y - y + P [r + (y - y ] d 6 (3. Prmeter estimtion with Lest Squres Method Collinerity equtions combine djusted observtions (L unknowns (X in n implicit model, which cn be represented s F(L,X=, the linerized model tkes the following form (Mikhil Ackermn, 976: BV AX W (5 Affinity prmeters cn be estimted with Eq. (4 (Moniw, 97; Hbib e Morgn, 3. δx = A(x - x = A(y δy B(y - y - y where A B re the ffinity prmeters. The method of clibrtion using bundle djustment is bsed on the collinerity equtions (Eq. ( distortion models (Eq(s. (, (3 (4. In this method the exterior orienttion prmeters (EOP, interior orienttion prmeters (IOP object coordintes of photogrmmetric points re simultneously estimted from imge observtions some dditionl constrints. This method cn be used with no control points given minimum of seven constrints to define n object reference frme; this prticulr pproch is known s selfclibrting bundle djustment (Merchnt, 979. In this method liner dependence between prmeters rises when the cmer inclintion is ner zero the flight height hs little vrition. In these cses, focl length (f flight height (Z Z re not seprble the system eqution becme singulr or ill conditioned. Besides theses correltions, lso the coordintes of the principl point re highly correlted to the perspective center coordintes (x X; y Y. In order to cope with these dependences, severl methods were proposed like the mixed rnge method (Merchnt, 979 the convergent cmers method (Brown, 97. Multihed stereo cmer clibrtion (4 where A is the design mtrix relted to the prmeters, B is the design mtrix relted to the djusted observtions, V is the vector of residuls, X is the vector of corrections to the pproximted prmeters W is misclosure vector. Let us consider now set of constrints equtions tking the form:. The corresponding linerized equtions re: F ( L,X c c B V C C CX W where L c re pseudo-observtions, Bc is the design mtrix of functions Fc with respect to this pseudo-observtions, C is the design mtrix of functions Fc with respect to the prmeters W lso misclosure vector: W [ B( Lb L F( L,X ] W [ B ( L L F ( L,X c c c c c The vector of corrections to the pproximted prmeters is given by, which is updted with itertions: where - X=-[σˆ (N+N ] [σ (U+U ] c c N A (BQB A N C (B Q B C c c c c ] U A (BQB W (6 (7 U C (B Q B W' c c c c In cse the vlue of prmeter is previously known, with certin ccurcy, for exmple, the coordintes of control points, then weighted constrint cn be pplied.

3 3. RELATIVE ORIENTATION CONSTRAINTS AND GEOMETRY OF THE DUAL-HEAD SYSTEM As described in Section, the centrl point of this pper is concerned with the nlysis of the RO constrints pplied to dul-hed digitl imgery system, ssuming tht the system is physiclly stble during the imge cquisition flight mission. Before developing the proposed method, the geometry of the dul-hed system will be briefly described. 3. The geometry of dul-hed system: SAAPI The SAAPI system (Ruy et l, 7 is composed of two Hsselbld digitl cmers, positioned in convergent wy, s shown in Figure. The imges cn be cquired simultneously with fixed superposition. The elements Κ, Φ e Ω re the reltive orienttion (RO ngles, considering s reference the right cmer (C D is the Euclidin distnce between C C. The pproximted vlues of the ngles Ω, Φ e K re of -36º, º 8º, respectively. The RO elements cn be clculted s function of the exterior orienttion prmeters (EOP of both cmers by using: R RO R R where RRO re the RO mtrix, corresponding to the ngles K, Φ, Ω; R R re rottion mtrix for the cmers, respectively. Another element tht cn be considered s stble during the cquisition is the Euclidin distnce D between the perspective centers. This distnce cn be directly mesured, since the loction of the externl nodl points cn be obtined from the technicl dt provided by the cmer lens mnufctory (Figure.b. (8 3. Dul-hed clibrtion method In the proposed method, the bsic mthemticl model for clibrtion of the dul-hed system re the colinerity equtions (Eq. with dditionl prmeters the constrints equtions developed in this section. Let t R RO be the RO mtrix D t the squred distnce between the cmers perspective centers, for the instnt t, nlogously, for the instnt t+, t R RO Dt. As previously mentioned, it is resonble to consider the RO mtrix distnce between the perspective centers stble, lthough the orienttion of ech cmer chnges. Bsed on these ssumptions, the following equtions cn be written: with: (rr t R = (rr RO (r3r where t t+ RRO - RRO = (9 D D t t ( (t + rr + r3r3 (rr + rr + r3r3 (rr3 + rr3 + r3r33 + r r + r r (r r + r r + r r (r r + r r + r r r3r + r33r3 (r3r + r3r + r33r3 (r3r3 + r3r3 + r33r33 cmer r ij cmer, with i,j={,, 3}. re the elements of rottion mtrix for both Considering the Equtions (9 (, bsed on the EOP for both cmer in consecutive instnts, t t+, three linerly equtions cn be written: (t (t G = (rr r 3r3 - (rr r 3r3 = ( Externl projection of cmer nodl point Externl projection of cmer nodl point G = (r G = (r 3 3r 3r 3r 3r 33r3 33r3 (t - (r (t -(r 3r 3r 3r 3r 33r3 r3 33 (t = ( (t = (3 b Figure. PC s projected to the externl mount ( mesurements of the PC distnce (b. (t (t (t (t (t (t G = (X - X +(Y - Y +(Z - Z - 4 (t + (t + (t + (t + (t + (t + (X - X - (Y - Y - (Z - Z = (4 The direct mesurement of the physicl distnce mong PCs with pchymeter resulted in the observed vlue of, mm ± mm. Then, besides of the four constrint Eq(s ( to (4, one dditionl constrint eqution bsed in the mesured distnce cn be included. In fct, it s is importnt to mention tht the precision expressed in the mesured distnce is not relted to the pchymeter itself but minly by the projection of the PC to the externl mount. The mthemticl models corresponding to the mentioned constrints were implemented using the C/C++ lnguge on the CMC (Clibrtion of Multiple Cmers progrm (Ruy et l, 7. The flowchrt in the Figure shows the min process steps implemented bsed in the previous models.

4 Approximtes EO prmeters estimtion for ech imge Vector of prmeters (X 6m EOP (for m imges, IOP (up to prmeters 3j coordintes (X,Y,Z in object for j points. Block of imges Mesurement of coordintes in imge spce (with subpixel ccurcy Vector of observtions (L b Coordintes of n points mesured in m imges for these pirs. The group of 67 prmeters estimted in the Lest Squres Estimtion is composed by: 6 EOP for ech imge; IOP for ech cmer; 3 coordintes for ech point in the object spce (totl of 89 points. In this set of points, 7 were used s control points, 44 s check points the remining were considered photogrmmetric points. The priori vrince ws stted s.5e -5 mm, corresponding to strd devition of.5 pixel (.45mm in the imge coordintes. The imge coordintes were weighted depending on the type of mesurement:.5 pixel for circulr trgets pixel for the points mesured mnully. Control points respective strd devition for ech coordinte Adjustment by LSM - Lest Squre Method with constrints Mtrix vector cretion: A, B, W, P, C W ; P X W X X = X +X No All X i <ε? Yes X = X +X (Adjusted vector of prmeters - ΣX = σˆ (N + NC + P x (MVC of X Norml equtions N, U, N C e U C Figure. Flowchrt of the proposed method. Estimtion of corrections for the vector of prmeters X = (N+ N C+ P X - (U+ U C+ P X W X 4. EXPERIMENTS AND RESULTS ANALYSIS In order to ssess the proposed methodology, four experiments were crried out, without with RO constrints, with different weights for these constrints (Tble. Exp. RO Constrint s Vrition dmitted for RO ngulr elements Vrition dmitted in cmers bse distnce Constrint with distnce directly mesured A N B Y 3 mm N C Y 3 mm Y D Y mm N Tble - Chrcteristics of the four experiments crried out. In the experiments fourteen imges were used (seven of ech cmer resulting in 66 imge observtions (Figures 3b 3c corresponding to circulr trgets other distinguishble fetures (corners in the test field (Figure 3. The imge coordintes of circulr trgets were extrcted with subpixel ccurcy using n interctive tool tht computes the mss center fter utomtic threshold estimtion. The coordintes of other points like corners of pinted letters were extrcted mnully, thus, their ccurcy re of pixel level. Four exposure sttions were used in ech sttion 4 imges were tken ( for ech cmer, with the dul-mount being rotted by 9º. Due to the physicl dimensions of the test field to the cmer depth of field coverge ngle, in some imges few trgets were cquired. For this reson, only 4 imges from 9 originlly cquired could be used. From this group of 4 imges, 5 of ech cmer were tken t the sme instnt, then, constrints equtions cn be stted ( (b (c Figure 3. ( Test field distribution of imge points in imges tken with cmers (b (c. The weights in the pseudo-observtions of the constrints Eq(s. (, 3, were computed by covrince propgtion, bsed on the dmitted vritions for ech ngulr element. The smller re the dmitted vritions the higher re the weights in the constrints. A posteriori vrince 3,E-6,E-6,E-6,E+ (b ( A B C D Experiments (c Figure 4 Absolute vlue of residuls in the observtions for experiments A ( C (b, posteriori vrince for ll experiments (c (units re pixels. Figure 4 presents the bsolute vlues of residuls in the observtion fter lest squres djustment for experiments A

5 C the posteriori vrince (estimted for ll experiments. The experiment A is conventionl clibrtion with bundle djustment, with no constrints in the RO between cmers. In experiment C severl constrints were imposed, including the mesured distnce between perspective centers. In Figure 6.c the posteriori vrinces for ll the 4 experiments re presented. The increse in the posteriori vrince with the constrints is noticeble, it is higher s the constrints hve higher weight. Tble presents the estimted IOP their estimted strd devitions for the cmers used, in experiments A C. The units for the focl length principl point coordintes re mm pixels, respectively. f (mm x (mm y (mm K (mm - K (mm -4 K3 (mm -6 P (mm - P (mm - A B A CAMERA CAMERA CAMERA CAMERA ±.7 ±.6 ±.6 ±.6 (.93 pixel (.79 pixel (.8 pixel (.83 pixel -.73 ±.3 (.49 pixel -.45 ±.8 (.95 pixel -.846E-5 ±4.5E-7.7E-8 ±.E-9 5.E- ±.E-.595E-6 ±.6E E-6 ±.9E-6.89E-5 ±4.634E E-4 ±4.359E ±. (.9 pixel -.5 ±. (.34 pixel -.857E-5 ±3.7E-7.7E-8 ±.8E-9 5.E- ±.E E-7 ±.397E E-6 ±.593E-6.893E-5 ±.3E E-4 ±.559E ±.3 (.49 pixel -.98 ±.4 (.58 pixel -.868E-5 ±4.6E-7.78E-8 ±.37E-9 4.E- ±.E- 5.79E-7 ±.636E-6.748E-6 ±.9E-6.894E-4 ±4.5E E-5 ±4.E-5 C ±. (.3 pixel -.4 ±. (.8 pixel -.84E-5 ±3.8E-7.55E-8 ±.8E-9 5.E- ±.E- -.58E-6 ±.47E-6 -.5E-6 ±.564E E-5 ±.83E-5-9.E-5 ±.545E-5 Tble. Estimted IOP their estimted strd devitions for the two cmers, in experiments A C. Anlyzing Tble it cn be noted tht the estimted strd devitions of prmeters did not presented remrkble differences for the experiments A C for both cmers, except by the strd devition of the prmeter y for cmer, tht reduced.37 pixels from experiment A to C. It ws lso noted tht the estimted strd devitions of prmeters f, x y were slightly higher in experiment D. Due to lck of spce detils of these experiments re omitted in this pper. The discrepncies between IOPs of cmers, respectively, estimted in experiments B, C D, with respect to IOPs estimted in the experiment A, were computed. Anlyzing theses discrepncies, it cn be seen tht the discrepncies re lmost similr from experiments B C. Experiment D, however, exhibits different pttern, with some prmeters presenting discrepncies with different sense (f, y A, cmer ; K A of cmer. In these experiments (D the weight pplied to the constrints cn be considered high, becuse the vritions dmitted in the rottions re. This mens tht the weight to be used hve to be comptible with the uncertinty in the determintion of EOP, otherwise these constrints will ffect the estimted IOP. In order to ssess the influence of RO constrints in the EOP the strd devition for the experiments A C re shown in Figure 5. After prmeters estimtion, the Reltive Orienttion elements (ngles Κ, Φ Ω bse distnce cn be computed from the EOP of ech imge. Tble 3 presents the verge vlues strd devitions of these elements. ( (b Figure 5 - Estimted strd devitions of the prmeters k, φ, ω, X, Y Z in the experiments: ( A (without RO constrints ; (b C (with RO constrints. Ω Φ Κ Bse distnce A Averge -36º 4' 55'' -º 3' 8'' 79º 3' 5''.45 cm ±º ' 54'' ±º ' 44'' ±º ' 7'' ±.3478 cm B Averge -36º 4' 53'' -º 4' 54'' 79º 3' 4''.3cm ±º ' 3'' ±º ' '' ±º ' 38'' ±.6cm C Averge -36º 4' 33'' -º 4' 5'' 79º 3' 5''. cm ±º ' 5'' ±º ' 9'' ±º ' 37'' ±.7 cm D Averge -36º 45' 53'' -º 6' 7'' 79º 3' 7'' 9.556cm ±º ' '' ±º ' ' ±º ' '' ±.3cm Tble 3. Averge vlues strd devitions of RO elements, computed from EOP, for ech experiment. Tble 3 shows tht the RO elements were estimted ccordingly with the imposed constrints the dmitted vritions. Anlyzing Tble 3 it cn be noted tht there re vritions rounding to for the RO rottions 3.4 mm for the bse distnce. These vlues re, of course, due to the uncertinties in the indirect estimtion processes insted of physicl vritions itself. Introduction of RO constrints remedies this problem, s one cn se in Tble 3 (experiments B, C D. Imposing RO constrints leds to more consistent solution both for RO rottions bse distnce. A noticeble result chieved in the experiment B is relted to the bse distnce. The verge vlue computed from EOPs is.3mm, while the vlue mesured directly is.mm ( discrepncy of.7mm. Considering the uncertinness in the direct mesurement, it is resonble to stte tht the vlue estimted indirectly, by bundle djustment, is consistent with the direct mesurement, the estimtes cn

6 be considered ccurte. Due to this ccurcy, the introduction of the distnce directly mesured, s n dditionl constrint did not improve significntly the results, s one cn se in Tble 3 (experiment C. Figure 6 shows the RMS of the discrepncies between the field coordintes of check points its estimted vlues by bundle djustment for the four experiments. vritions due to vibrtions, temperture or mechnicl locking, or even to the uncertinty in the estimtion of the EOP prmeters, to which RO elements re functionlly relted. Experimentl work with higher dimensions test field, providing idel geometric conditions would be recommended. The sme pproch cn be used for multi-hed cmer clibrtion, which experimentl evlution is left s suggestion for future work. Also, the ssessment of these results with eril imges is topic for further reserch. 6. REFERENCES Figure 6. RMS of the discrepncies between the field coordintes of check points its estimted vlues. The nlysis of Figure 6 shows tht the discrepncies in the object spce coordintes increse proportionlly with weights in the constrints imposed to the RO elements. This increse is probbly due to error propgtion from estimted EOP IOP to the object spce. The RMSE of the discrepncies re similr in Experiments A to C. However, in the experiment D there is noticeble increse in the discrepncies in the coordintes of check points. The RMSE in the coordinte X in lmost twice in the experiment D when compred to experiment A. These experiments showed tht it is crucil to blnce the vlues to impose to the RO constrints. From the nlysis of experiments crried out with the existing dul-hed SAAPI system some conclusions cn be given: In generl, the RO constrints hve to be imposed with suitble weight. From our experiments, 3 for the rottions mm for the distnce re resonble ssumptions. The weight to be used in the pseudo-observtions hve to be estimted by covrince propgtion, since the ngulr elements of RO re not considered s prmeters in this pproch; Imposing RO constrints with high weights reflects negtively in the results: the residuls in the observtions re higher s well s the discrepncies in the check point coordintes; The estimted strd devitions of the EOP with RO constrints re slightly lower; however, the discrepncies in some check points, minly in the peripherl re of the test field re higher with the bundle djustment with RO constrints. 5. CONCLUSIONS In this pper method for dul-hed cmer clibrtion bsed on bundle djustment ws presented experimentlly ssessed. The method proposes the imposition of Reltive Orienttion constrints, which sttes tht orienttion between cmers distnce between perspective centers cn vry within certin vlues. The vritions to be dmitted were experimentlly ssessed it ws noted tht imposing constrints with higher weights could led to inccurte results. The vritions in the RO elements cn be credited to physicl Brown, D. C., 966. Decentering distortion of lenses. Photogrmmetric Engineering, 3(3, pp Brown, D., 97. Close-Rnge Cmer Clibrtion, Photogrmmetric Engineering, 37(8, p Clrke, T. A., Fryer, J. G., 998. The development of cmer clibrtion methods models. Photogrmmetric Record, 6(9, pp Crmer, M., 4. EuroSDR network on digitl cmer clibrtion. Institute of photogrmmetry, University of Stuttgrt, Finl Report, oct. 4. Disponível em: < jul. 7. Doerstel, C.; Zeitler, W.; Jcobsen, K.,. Geometric clibrtion of the DMC: method results. In: The Interntionl Archives for Photogrmmetry Remote Sensing, 34(, Denver, USA, pp ,. Hbib, A.; Morgn, M., 3. Automtic clibrtion of low-cost digitl cmers. Opticl Engineering, 4(4, pp Merchnt, D. C., 979. Anlyticl photogrmmetry: theory prctice. Notes Revised from Erlier Edition Printed in 973, The Ohio Stte University, Ohio Stte.. Mikhil, E. M.; Ackermn, F., 976. Observtions lest squres. New York: A Dun-Donnelley Publisher. Mikhil, E. M.; Bethel, J. S.; Mcglone, J. C.,. Introduction to modern photogrmmetry. New York: John Wiley & Sons,. Moniw, H., 97 Anlyticl cmer clibrtion for close-rnge photogrmmetry. Thesis, New Brunswick, Mster of Science, University of New Brunswick. Roig, J.; Wis, M.; Colomin, I., 6. On the geometric potentil of the NMC digitl cmer. In: Proceedings of the Interntionl Clibrtion Orienttion Workshop EuroCOW 6, 5-7 Jnury, Cstelldefels, Spin. Ruy, R. S.; Tommselli, A. G.; Hsegw, J. K.; Glo, M.; Imi, N. N.; Cmrgo, P. O., 7. SAAPI: lightweight irborne imge cquisition system: design preliminry tests. In: Proceedings of the 7th Geomtic Week High resolution sensors their pplictions, Brcelon, Spin. Zhung, H., 995. A self-clibrtion pproch to extrinsic prmeter estimtion of stereo cmers. Robotics Autonomous Systems, 5, pp Mostf, M. M. R.; Schwrz, K. P.,. A Multi-Sensor System for Airborne Imge Cpture Georeferencing. Photogrmmetric Engineering & Remote Sensing, 66(, pp ACKNOWLEDGEMENTS The uthors would like to cknowledge the support of CNPQ (Conselho Ncionl de Desenvolvimento Cientifico e Tecnológico, with Mster Scholrship Reserch Grnts (473/ /4-. The uthors re lso thnkful to FAPESP (Fundção de Ampro à Pesquis do Estdo de São Pulo to Engemp Geoinformção for providing the resources for imge cquisition.