DIGITAL STEREO-ORTHOPHOTOS OF ARCHAEOLOGICAL SITES FROM SMALL FORMAT AERIAL PHOTOGRAPHS. iluis, leirac,

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1 DIGITAL STEREO-ORTHOPHOTOS OF ARCHAEOLOGICAL SITES FROM SMALL FORMAT AERIAL PHOTOGRAPHS M. Jáuregui *, L. Jáuregui *, L. Chcón, J. Vílchez Photogrmmetr Institute, Engineerring Fcult, Universidd de Los Andes, Av Tulio Febres, Mérid 511 (mnuel, iluis, leirc, Commission V, WG V/4 KEY WORDS: Photogrmmetr, rcheolog, restitution, orthoimge, DTEM, pixel ABSTRACT: The digitl orthophoto is vluble tool for representing n object on orthogonl projection t known scle, due to the reltion between its reltivel low production cost nd the photogrphic detil representtion in its true position. When this orthophoto is ccompnied b its mte imge, nmed stereomte, its dvntges rises significntl, becuse the observtion cn be performed in 3D. Along the production process of the digitl orthophoto the mte imge cn be produced with minimum of dditionl processing. From the DEM, the prllxes for ech imge point, nd the pixel position for ech point of the mte imge re computed in reference coordinte sstem. Finll resmpling is performed on the mte imge in order to complete the imge from visul point of view. Tht is wh we thought to use the stereo-orthophoto to fcilitte the stud of n rcheologicl site b rcheologists becuse the sme llows, not onl the observtion, but lso the nnottion of themtic observtions resulting from field surves. (directl in orthogonl position when done on the orthophoto) The prcticl exmple on this pper hs been done in the old mission town of Sn Antonio de Mucuño, which ws founded in 162 nd bndoned in the erl ninet centur. The onl w to obtin the imges over the town, ws using smll formt eril photogrphs (SFAP), tken from smll irplne. The SFAP is relible tool to interpret rcheologicl sites 1. INTRODUCTION In eril photogrmmetr commonl it hs been used the 23 x 23 mm. photogrph, s stndrd formt for the tking of eril photogrphs. In prllel w, the film formts of 35 mm nd 7 mm, known s Smll formt Aeril Photogrph (SFAP) lso hve been used. Nevertheless, these smll formts hve not been widel ccepted for photogrmmetric surves due to the non metric chrcteristics of those cmers. Its min ppliction hs been in the field of photointerprettion. At present, the digitl methods hve permitted the determintion of the externl nd internl orienttion prmeters of the cmer in simple form, expnding the potentil of use of the SFAP in photogrmmetric surves in zones of smll extension, when compl the following conditions: i) The re is it sufficientl smll so tht photogrmmetric surve using stndrd formt, re not competitive economicll. ii) The re is sufficientl lrge so tht topogrphicl surve is not competitive economicll. This pper shows procedure used for the genertion of digitl stereo-orthophoto from SFAP in n rcheologicl site of difficult ccess, where is not possible to tke stndrd formt photogrphs to n ppropritel scle. This work is prt of crtogrphic documenttion project of this site. The digitl stereo-orthophoto consists of n orthophoto nd n ssocite imge or stereomte contining the corresponding prllxes in order to chieve the stereoscopic vision. The orthophoto nd stereomte re produced in digitl form. The digitl orthophoto is generted from the geometric informtion of the Digitl Terrin Elevtion Model (DTEM) of the re, nd of the rdiometric informtion of the originl imge, ppling the colinerit equtions nd resmpling procedures to the rdiometric vlues of the originl imge. The digitl stereomte is generted dding the prllxes to the points imge in the digitl orthophoto. These prllxes re clculted from the heights resulting from intersection of the DTEM with the plne of reference, ssuming n pproprite reltion between photogrphic bse nd point height (B/H). The stereo-imges re useful in the representtion of the plnimetric informtion of the re, nd in the photointerprettion of the zone. 2. PROCEDURE The procedure scheme used for the genertion of the stereoorthophoto is shown in the figure 1. Ech stge of the procedure is explined briefl in the next sections. 1

2 Correspondence between digitl imge nd photogrphic imge Determintion of the inner prmeters of the cmer Reltion between digitl nd fiducil coordinte sstems Projection of the DTEM to the fiducil coordinte sstem Trnsformtion of the DTEM coordintes from the fiducil sstem to the digitl sstem Correspondence betwen the DTEM resolution nd the digitl imge resolution. Determintion of the gr levels for ech bnd of the orthophoto. Computing the horizontl prlxes of the DTEM. 2.2 Determintion of the internl prmeters of photogrphic cmer From the terrin coordintes of the control points nd its coordintes in the photogrphic imge, the internl prmeters of cmer using the procedure of Liner Direct Trnsformtion (DLT) (Gml, 22) re determined. Hving the prmeters f x, f, x o, o,, the coordintes of the control points of the photogrphic imge in the fiducil sstem re computed. 2.3 Trnsformtion of the DTEM from the terrin sstem to the fiducil sstem The DTEM nodes re projected to the nlogicl imge sstem b mens of the colinerit equtions. This is performed in two phses: First, the prmeters of trnsformtion between the terrin sstem nd the fiducil sstem re determined using the control points. Second, with these prmeters the coordintes of the nodes DTEM re trnsformed to the fiducil sstem. The representtion of ground point on the negtive plne of the imge is done b mens of the projective line tht strts from the point, pssing through the projection centre O up to its intersection with this negtive plne, s shown in the Figure 2.. The length of the line L is determined from the ltimetric informtion provided b the DTEM. The projective line is represented b the colinerit equtions (Eq 1). x = k* A c T X Xo * Y Yo Z Z o (1) Trnsformtion of the DTEM subcells to the stereomte. Determintion of the gr tone for ech stereomte bnd. Figure 1. Procedure scheme where x,, -c = imge point coordintes referenced in the fiducil sstem. c = principl distnce of the cmer X, Y, Z = point coordintes in the terrin sstem X,Y,Z = coordintes of projection centre O referenced in the terrin sstem k = scle fctor between the vector l nd the vector L for ech point A= rottion mtrix defined b the ngles ω, ϕ nd κ round the X, Y nd Z, respectivel z Z Y 2.1 Correspondence between the digitl imge nd photogrphic imge The reltionship between the digitl imge coordintes nd the nlogicl imge is determined from the clibrtion results of the scnner used. Digitl imge coordintes re referenced to coordintes sstem of the scnner, corresponding with its columns nd rows. The nlogicl imge coordintes re referenced to n orthogonl xes sstem (x,). The reltionship between the digitl imge nd photogrphic imge is estblished through n ffine trnsformtion, thus obtining the coordintes of the control points in the sstem of photogrph. Z Y O c Z O X P XO Y O x X l p L P Y P Figure 2. Reconstruction of projective r x X 2

3 The Eq. 2 cn be expressed s the Eq. 2 nd 3, where ij re the mtrix elements. The Eq. 3 nd 4 re rigorous nd not liner in terms of ll six prmeters unknowns X,Y,Z, ω, ϕ, κ. x c c = = X) + X ) + X) + X ) Y ) + Y ) + Y ) + Y ) Z) Z ) 32 Z) Z ) 2.4 Trnsformtion of the DTEM from the fiducil sstem to the digitl imge sstem The coordintes of the DETM nodes re trnsformed from the fiducil sstem to the digitl imge sstem through n ffine trnsformtion. 2.5 Correspondence between the DTEM resolution nd the digitl imge In the stge 2.4, the position of ech DTEM cell referenced to the fiducil sstem, is determined in the digitl imge sstem. As the size of the DTEM cells re greter thn the pixels of the digitl imge, the cells must be divided in subcells whose heights re unknown. The geometric correspondence between ech subcell of the DTEM nd the digitl imge cn be determined in two ws: i) using the colinerit equtions or, ii) using projective trnsformtion. In the first one, it is needed to know the coordinte Z of ech subcell, which is given onl for the cell nodes of the DTEM. This mens tht it would be necessr to generte new DTEM to the resolution of the digitl imge. This involves gret volume of clcultion nd informtion to store. In the second w, it is not needed the coordinte Z of the subcell, since ech subcell is projected directl on the digitl imge, considering ech DTEM cell s plne surfce (Figure 3) (Juregui, 2). (2) (3) The projective trnsformtion of ech DTEM subcell on the digitl imge cn be expressed in the Eq. 4. x i = + 1 X i + 2 Y i + 3 X i Y i i = b + b 1 X i + b 2 Y i + b 3 X i Y i (4) where x i, i = DTEM nodes coordinte referenced to the digitl imge sstem X i,y i =DTEM nodes coordinte referenced to the terrin sstem, 1, 2, 3, b, b 1, b 2, b 3 = prmeters of the projective trnsformtion. The prmeters of the projective trnsformtion re determined from the coordintes of ll four nodes of ech DETM cell. Then, the coordintes Xi, Yi of ech subcell node re trnsformed to the digitl imge. 2.6 Determintion of the gre levels of the color orthophoto bnds The color imge is seprted into the red, green nd blue bnds. For ech bnd, the gre tone is ssigned to ech subcell of the DTEM tht hs been projected on the digitl imge in the step 2.5. In generl, the DTEM subcells projected on the digitl imge do not coincide precisel with n pixel. Commonl, it exists prtil overlpping on severl pixels. For this reson it is necessr to relize n interpoltion of the gre tone, from the pixel vlues of the digitl imge covered b the subcell, to obtin the gre vlue of ech subcell. The interpoltion methods commonl used re closest neighbour, proportionl res, significnt res mong others. Imge pixel Projected DTEM subcell O Digitl imge Figure. 4. Projection of the DTEM subcell on the digitl imge Cell Subcell 2.7 Determintion of the horizontl prllxes of the DTEM nodes DTEM cell Cell nodes Z The horizontl prllxes of ech DTEM node re determined in the terrin sstem respect to the reference plne. The referenced plne is the one tht contins the miniml Z vlue of DTEM. With these prllxes nd n ppropritel photogrphic bse the coordintes of ech DTEM node re trnsformed to the stereomte sstem, involving onl scle fctor long the direction of the X xis in the two sstems. The horizontl prllxes Px for ech DTEM node re determined b the Eq. 5: DTEM subcell Px j = H j B / (Z R - H j ) (5) Figure 3. Projection nd densifiction of the DTEM 3

4 where H j = height difference from ech node (Hp) to the reference plne. The reference plne height (H R ) is tken s the lowest DTEM height. Then H j = Hp j - H R Z R = reltive height flight, determined s the difference between height centre projection Z O H R. B = photogrphic bse of the stereoimgen (B=Z R /5 gurntee n dequte stereoscopic vision) deformtion of the stereomte subcell width.. Therefore, to generte the stereomte imge, it is necessr to hve n rr of pixels to the sme resolution s those of the ortofoto. It hppens then, tht in row of the stereomte the number of pixels is different thn in its corresponding row in the ortofoto, see figure 6. Then, correspondence is estblished between the stereomte cells nd the stereomte imge pixels, in order to ssign the respective tone. The coordintes X of ech DTEM node in the stereomte sstem is determined b the Eq. 6: X j = X j + Px j (6) where X j : coordinte in the X xis of the node j in the stereomte sstem X j : coordinte in the X xis if the node j in the terrin sstem Px j : horizontl prllx of the node j Stereomte cells Stereomte pixels Figure. 6. Liner interpoltion of the stereomte pixels 2.8 Trnsformtion of the DTEM subcells to the estereomte. The position of the DTEM nodes in the terrin sstem nd in the stereomte sstem llows to determine the prmeters of projective trnsformtion between both sstems. From them, the position of ech DETM subcell is determined in the stereomte, generting n rr with the sme number of subcells but of different sizes nd forms (Figure 5). Obviousl, ech deformed subcell hs ssocited the gre tone corresponding pixel in the orthophoto. DTEM cell = Orthophoto cell Cell Regulr subcells DTEM cell + prlx = Stereomte cell Deformed cell 2. APPLICATION The procedure ws used on the ncient town of Sn Antonio of Mucuño, locted in the Stte Merid, Venezuel, of mountinous relief. The SFAP re selected b two resons: i) budget reduced to relize the surve of the zone, disbling the photogrmmetric surve in stndrd formt, nd ii) topogrphic surve of the re, mde six ers behind, llowed to compre it with the surve obtined through eril photogrph using SFAP. From the beginning, it ws considered to tke the photogrphs, hving the control points previousl mrked on the re. Nineteen ground control points were mesured, which were used s control points for the restitution of the eril photogrphs. These points were signlised on the ground with two white concentric circles before the flight. The result is tht the points pper s white circles clerl defined in the photogrph. It ws used n Hssebld 553 cmer (formt 7 mm) with n lens of f = 4 mm, mounted in specil support coupled to the bggge porthole of Cessn 182 plne. Over the re were relized three flight psses, with heights between 8 nd 1 feet bove the se level. Deformed subcells Figure 5. Correspondence between DTEM nd stereomte. 2.9 Determintion of the gre levels of the stereomte color bnds The stereomte imgen is creted from the digitl orthophoto rdiometric vlues. There is geometric vrition between the orthophoto nd the stereomte number of pixels, due to Figure 7. DTEM perspective view of ppliction re 4

5 The photogrphic scle is 1:3. The re is the verge heights rnging between 12 m nd 2 m bove se level, generting lrge relief displcements. The DETM ws generted from the photogrmmetric restitution, with contour intervls of 2 m (Figure 7). The size grid ws 2 m. The eril photogrph ws scnned with n opticl resolution of 12 dpi. The results of the ffine trnsformtion, performed to determine the prmeters of correspondence between the digitl imge (rows nd columns) nd the photogrphic imge (sstem of photogrph in millimeters) re shown in the Tble 1. The internl cmer prmeters obtined through DLT re shown in the Tble 2. Tble 2. Internl cmer prmeters obtined b DLT f x (mm) f (mm) Skew X (mm) Y (mm) 39,66 4, The orienttion prmeters determined using the coordintes of ll seven control points in both fiducil sstem nd terrin sstem nd the Eq 3 nd 4, re shown in the Tble 3. From these prmeters, the DETM nodes were projected on the photogrphic imge using the Eq. 3 nd 4, obtining the rectified imge show in the Fig. 13. The stereomte corresponding is presented in the Fig. 12. Finll, the Figure 11 is n ngliph mde with both imges. Tble 1. Affine trnsformtion from digitl imge to photogrphic imge Control points Digitl imge sstem (pixels) Anlogic imge sstem (mm) x x = , 1 = , 3 = , b = , b 1 = , b 2 = Figure 11. Digitl nplph of the site. Tble 3. Coordintes of control points in fiducil sstem fter colinerit trnsformtion Control points Fiducil sstem Terrin sstem Discrepnces x (mm) (mm) X(m) Y(m) Z(m) x (mm) (mm) RMSEX = ±.37 mm, RMSEY = ±.27 mm Exterior orienttion vlues X O = m ±.11 m κ = rd ±.4 rd Y O = m ±.11 m ϕ = rd ±.59 rd Z O = m ±.2 m ω= rd ±.11 rd Rottion mtrix A = =

6 Figure 12. Digitl Stereomte Figure 13. Digitl orthophoto with restitution superimposed Conclusions The photogrmmetric flight relized over Mucuño, though mde in experimentl form, nd therefore without hving mjor gurntee of success, contributed providing lot of informtion on the generl chrcteristics of the re, s well s from the methodologicl point of view. It cn be stted tht the eril photogrph of smll formt constitutes vluble instrument for the surves of rcheologicl sites.. Juregui M., 2. Digitl orthophoto genertion. The Interntionl Archives of the Photogrmmetr, Remote Sensing nd Sptil Informtion Sciences. Amsterdm, The Netherlnds. The stereo-ortofoto llows for three-dimensionl observtion of n re in stud. Annottions cn be mde directl on the ortofoto s if it ws ver detiled mp of the re. This procedure ws relized in n re of mountinous relief, producing stisfctor results which shows the potentil of use. Acknowledgements This pper is the result of project sponsored b the Consejo de Desrrollo Científico Humnístico Tecnológico (CDCHT) of Universidd de Los Andes. This support is grtefull knowledged. References nd/or Selected Bibliogrph Gml, H., 22 Retrievl of the Clibrtion Mtrix from the 3-D Projective Cmer Model. Proceedings of the 15 th Interntionl Conference on Vision Interfse. Clgr, Cnd. 6