Effect of control points distribution on the orthorectification accuracy of an Ikonos II image through rational polynomial functions

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1 Effect of cotrol poits distributio o the orthorectificatio accuracy of a Ikoos II image through ratioal polyomial fuctios Marcela do Valle Machado 1, Mauro Homem Atues 1 ad Paula Debiasi 1 1 Federal Rural Uiversity of Rio de Jaeiro, B4 465, km Seropédica - RJ, Brazil marcelamachado046@hotmail.com, mauroatues@ufrrj.br, paula@ufrrj.br Abstract This paper evaluated the orthorectificatio of a high resolutio image for distributio of poits betwee a flat ad a rugged area, usig the ratioal polyomial fuctios. A Ikoos II image was orthorectified usig a DEM from cotour maps ad poits obtaied i a orthophoto. Fifty-seve poits were collected over the etire image, from which 13 ad 8 cotrol poits were radomly selected from the flat ad rugged areas. Thirty poits from the etire area ad 15 poits radomly selected from these were also used i the orthorectificatio process for compariso purposes. The remaiig poits were used as check poits. The vector errors usig 30 or 15 poits had the same stadard deviatio ad errors icreased with altitude. From the flat area 8 or 13 poits yielded the same results ad vector errors icreased with terrai height. Whe poits were oly from the rugged area the average vector errors were smaller as compared with the poits oly from the flat area. A high correlatio betwee height ad vector errors was foud whe 30 poits all over the area were used. It is cocluded that the orthorectificatio usig the ratioal polyomial fuctios is sesible to groud height ad the poit distributio. Keywords: orthorectificatio, ratioal polyomial fuctios, Ikoos II. 1. Itroductio Several cartographic applicatios requires the image geometric correctio, i.e. to extract metric iformatio it is essetial the pre-processig of the image. The level of the geometric correctio depeds o the applicatio accuracy i use ad the orthorectificatio is the best recommeded techique. The orthorectificatio process uses the cetral perspective image to create a rectified image (vertical image corrected errors relative to the sesor attitude durig the image acquisitio) ad corrected of the relief displacemet due to the cetral projectio of image acquisitio. A Digital Elevatio Model (DEM) of the area of the image is eeded for the relief displacemet correctio. 269

2 Traditioal orthorectificatio ivolves the use of stereo pairs from which elevatio is extracted directly to be used for productio of DEMs. However the cost ad time of acquirig ad processig stereoimages may ot be justified if the purpose is to do orthorectificatio oly. Thus may researches were realized usig exteral elevatio iformatio for orthorectificatio of image (Behdiia, 2002; Mercer, et al., 2003; Upaka, et al., 2009). The mathematical models for image orthorectificatio ca be cosidered as the rigorous model ad geeralised model. The use of the rigorous model, or physical model, eeds the kowledge of the attitude parameters, calibratios ad sesor orbit. The mathematical fuctio of rigorous model is based o the colliearity equatios. However the use of the geeralised model is idepedet of the sesor parameters ad platform (Elashmawy et al., 2005). These models are vastly used whe the sesor parameters are uavailable (Okamoto et al., 1998; Di et al., 2003). The ratioal polyomial fuctio (RPF) ca be more appropriate for pushbroom sesors tha the rigorous model due the geometry of the images acquisitio (Fraser et al., 2006). The RPFs are established from the direct relatioship betwee the image ad terrai coordiates through coefficiets (Tao ad Hu, 2001). These equatios are showed at Equatio (1). p1( X, Y, Z ) r p2( X, Y, Z ) c p3( X p4( X, Y, Z, Y, Z ) ) (1) Where: r ad c are the image coordiates pixels, p 1 to p 4 are the polyomials ad X, Y ad Z are the groud coordiates. For the best performace of the RPF are recommeded the use of may ad good distributio groud cotrol poits (GCPs) (Tao ad Hu, 2001). The process of orthorectificatio usig RPF requires the use of Ratioal Polyomial Coefficiets (RPCs) i order to recostruct the object space from the image space. Basically two sources of RPCs ca be used i this process: estimatio from groud cotrol poits or ca be provided by the image producer (Tao ad Hu, 2001; Fraser et al., 2006). The first case is referred as terrai-depedet ad the secod as terrai idepedet (Fraser et al., 2006). Oe example of terraiidepedet RPCs is the set of coefficiets provided with the Ikoos II Ortho Kit. The terrai-depedet approach is of great iterest as the terrai-idepedet RPCs are ot available i may cases. However, a disadvatage of the terraidepedet approach is that the umber of cotrol poit teds to be large (Tao ad Hu, 2001). I order to provide a accuracy assessmet of the orthorectificatio of a Ikoos Geo image of oe meter resolutio usig the ratioal polyomial fuctios the experimets of this paper have bee desiged for the followig purposes: - to evaluate the ifluece of the umber of GCPs i the orthorectified image accuracy; - to evaluate the ifluece of the distributio of GCPs i the orthorectified image accuracy; - to evaluate the correlatio betwee the relief roughess ad the orthorectified image accuracy. 270

3 2. Material ad Methods The pa sharpeed Ikoos II Geo image from Seropédica-RJ-Brazil was used for the orthorectificatio tests usig the terrai-depedet approach. These tests were desiged to evaluate orthorectificatio accuracy o the same frame. The image covers a flat (below 50 meters) ad a rugged area (from 50 to 363 meters). The DEM used at orthorectificatio tests was geerated from cotour maps at the 1/10,000 scale ad poits obtaied from orthophotos with 1 meter pixel size. Fiftyseve poits were collected over the etire image. Thirty poits from the etire area were also used i the orthorectificatio process for compariso purposes. Figure (1) shows the distributio of the 15 GCPs from flat areas (triagles) ad the 15 GCPs from rugged area (squares). Figure 1: Groud Cotrol Poits distributio at flat ad rugged areas. Six orthoimages were geerated to evaluate the ifluece of the umber ad distributio of GCPs i the image orthorectified accuracy. From the fiftee GCPs of the flat area, 13 ad 8 cotrol poits were radomly selected ad two orthoimages were geerated with oly GCPs from flat area. The same procedure was performed with the poits from rugged area. Thirty poits from the etire area ad 15 poits radomly selected from these were also used i the orthorectificatio process for compariso purposes. The processig was carried out by usig the PCI Geomatica 9.0 software package. The orthoimages were produced usig the DEM ad the resamplig method was si(x)/x with a widow of sixtee by sixtee pixels (Touti, 2004). The 27 remaiig poits were used as check poits to calculate vector errors ad the Root Mea Square Error (RMSE). Figure (2) shows the 27 check poits used for the accuracy evaluatios of the orthoimages. Figure 2: Check poits distributio. 271

4 3. Results Six orthoimages were obtaied with a variable umber of GCPs. Table 1 shows the Root Mea Square Errors (RMSE) resultig from the discrepacies of 27 check poits used for the evaluatio of the six orthoimages. Table 1: RMSE (m) of check poits i the six orthoimages. Orthoimages with poits from Flat Area 13 GCPs 8 GCPs E N E N 24,30 28,02 22,72 28,35 Orthoimages with poits from Rugged Area 13 GCPs 8 GCPs E N E N 14,99 31,23 17,31 30,62 Orthoimage with All GCPs Orthoimage with Radom GCPs from the Etire Area 30 GCPs 15 GCPs E N E N 12,82 29,55 15,44 28,31 From the flat area 8 or 13 poits yielded practically the same results. Whe poits were oly from the rugged area the average vector errors were smaller as compared with the poits oly from the flat area. The use of a larger umber of GCPs, thirty poits, distributed across the etire image resulted i smaller RMSE values. The RMSEs were smaller eve whe oly fiftee GCPs distributed radomly were used. These results demostrate that the distributio of GCPs i the etire image is more importat tha the umber of GCPs used i the orthorectificatio process. To evaluate the correlatio betwee the relief roughess ad the orthorectified image accuracy the graphics of the Figures 3, 4 ad 5 have bee produced. These figures show that the vector errors icreased with the terrai height. Eve usig a smaller umber of GCPs produced similar same results. A high correlatio betwee height ad vector errors was foud whe 30 or 15 poits all over the area were used. 272

5 Error Vector (m) Flat Area R 2 = GCPs 30 8 GCPs Height (m) Figure 3: Error vector of check poits of the orthoimages geerated usig GCPs from the flat area. Error Vector (m) Rugged Area R² = 0, Height (m) 13 GCPs Figure 4: Error vector of check poits of the orthoimages geerated usig GCPs from the rugged area. Error Vector (m) Radom poits from etire area R² = 0, GCPs Height (m) Figure 5: Error vector of check poits of the orthoimages geerated usig radom GCPs. 4. Coclusios This paper provided a comparative evaluatio betwee six differet approaches i the processig of Ikoos II scee usig ratioal polyomial fuctios. The results allowed the followig coclusios: - Icreasig the umber of GCPs from eight to thirtee i a specific area or from fiftee to thirty i etire area made o sigificat differece i the quality of correctio results of the system tested; - The distributio of GCPs i the etire image has more ifluece o the accuracy of the orthoimage tha the umber of GCPs used; 273

6 - Vector errors icreased with terrai elevatio ad a high correlatio was foud betwee vector errors ad elevatio, except for the flat area where the height differece were o large; The high correlatio betwee vector errors ad height suggest the orthorectificatio process by ratioal polyomial fuctios is height depedet. Thus oe should be careful whe processig images with height differeces. It is recommeded that at least eight GCPs are used for better results i the orthorectificatio. It is also recommeded that the GCPs should be uiformly distributed over the image, ot oly horizotally but also i height, thus avoidig the cocetratio of GCPs oly o flat or rugged terrai areas. Ackowledgmets The authors ackowledge The Brazilia Istitute of Geography ad Statistics - IBGE for providig the orthophotos. Refereces Behdiia, B. (2002),"Geeratig Ortho image From Ikoos Data", Proceedigs of the 23rd Asia Coferece o Remote Sesig, Kathmadu, (173), Nepal. Di, K., Ma, R., Li, R. (2003), "Ratioal fuctios ad potetial for rigorous sesor model recovery". Photogrammetric Egieerig ad Remote Sesig, Vol. 69 (1): Elashmawy, N., Elmaadilli, Y., Barakat H. (2005), "Comparative aalysis ad evaluatio of various mathematical models for stereo IKONOS satellite images". I: FIG Workig meek 2005 ad iteratioal coferece o the global spacial data ifrastructutre,8, Proceedigs...,Cairo, Egito. Fraser, C. S.; Dial, G.; Grodecki, J. (2006), "Sesor orietatio via RPCs". ISPRS Joural of Photogrammetry ad Remote Sesig, Vol. 60 (3): Mercer, J.B., Alla, J., Glass, N., Rasmusse, J., Wollersheim, M. (2003), "Orthorectificatio of satellite images usig extreal DEMs from IFSAR". Proceedigs of Joit ISPRS Workshop o High Resolutio Mappig from Space, Haover, Germay, Commissio II, Workig Group II/2. Okamoto, A., Fraser, C., Hattoti, S., Hasegawa H. & Oo, T. (1998), "A alterative approach to the triagulatio of SPOT imagery". I: Iteratioal archives of Photogrammetry ad Remote Sesig, Vol. 32(4), Stuttgart, Tao, C.V.; Hu, Y. (2001), "A Comprehesive Study of the Ratioal Fuctio Model for Photogrammetric Processig". Photogrammetric Egieerig ad Remote Sesig, Vol. 67 (12): Touti, T. (2004), "Review article: Geometric processig of remote sesig images: models, algorithms ad methods". Iteratioal Joural of Remote Sesig, Vol. 25 (10): Upaka, R.; Kovitpogkajor, V.; Khaoubol, A. (2009), "Compariso of results orthorectificatio usig rigorous ad RPC models for WorldView-1 data". 30th Asia Coferece o Remote Sesig, Beijig, Chia. 274