1. Jan 19, ‘11 Block Adjustment of Cartosat-I Stereo Data Using RPCs MURALI MOHAN mohan@mobiterrasolutions.com M O BITERRA SOLUTIONS (INDIA) PRIVATE LIMITED

2. About M O BITERRA  Incorporated in 2010; Located at Hyderabad  Solution Provider  Focus on Algorithms & Custom Solutions  Surveying, Photogrammetry, Remote sensing  Developed 2 products for Land Resurvey

3. TerraForma: Tool for land resurvey under NLRMP Hybrid techniques (aerial orthophoto / satellite orthoimage, Total Station data, or any combination) Pure Ground Surveys (Total Station) Project structure for different phases of resurvey Output as ESRI’s shapefile in WGS84/UTM

4. TerraTippan: Converts Land Tippans into ESRI’s Shape Files

5. 5 Scope of the Presentation 1.Algorithm Development for Block Adjustment Cartosat-I, RPCs Space Resection, Space Intersection, Block Adjustment Motivation 2.Experimental Results Scene level, Block-level 3.Summary & Future work

6. 6 Cartosat-I Change in elevation associated with a pixel of height parallax dh/dp = GSD/{[tan(A+C/2) – (A-C/2)] * Sin(BIE)} = 4.1 m Height Sensitivity

7. 7 Raw Product Accuracy Raw Product Accuracy X-error = 61 m Y-error = 314 m Z-error = 1049 m Error Vector (1000X)

8. 8 r n = P 1 (X, Y, Z) / P 2 (X, Y, Z) c n = P 3 (X, Y, Z) / P 4 (X, Y, Z) a 0 Where P 1 = a 0 + a 1 Z + a 2 Y + a 3 X + a 4 ZY + a 5 ZX + a 6 YX + a 7 Z 2 + a 8 Y 2 + a 9 X 2 + a 10 ZXY + a 11 Z 2 Y + a 12 Z 2 X + a 13 Y 2 Z + a 14 Y 2 X+ a 15 ZX 2 + a 16 YX 2 + a 17 Z 3 + a 18 Y 3 + a 19 Z 3 X,Y,Z : Ground coordinates; a 0 ….a 19 : Polynomial Coefficients r n & c n : Normalized row and column indices in image space Rational Polynomial Coefficients (RPCs): User-side LINE_OFF: +5999.97 pixels SAMP_OFF: +6000.00 pixels LAT_OFF: +31.71550742 degrees LONG_OFF: +79.04313203 degrees HEIGHT_OFF: +4249.995 meters LINE_SCALE: +6099.98 pixels SAMP_SCALE: +6100.00 pixels LAT_SCALE: +0.17195169 degrees LONG_SCALE: +0.19526625 degrees HEIGHT_SCALE: +1349.999 meters LINE_NUM_COEFF_1: +4.832002101528874E-04 LINE_NUM_COEFF_2: -2.494192583363085E-01 LINE_NUM_COEFF_3: -1.203624337000269E+00 LINE_NUM_COEFF_4: +4.784735738655975E-02 LINE_NUM_COEFF_5: +2.436545448722357E-02 LINE_NUM_COEFF_6: -3.398996506834039E-03 LINE_NUM_COEFF_7: -1.734635182453075E-02 … SAMP_DEN_COEFF_1: +1.000000000000000E+00 SAMP_DEN_COEFF_2: -7.503988256474431E-03 SAMP_DEN_COEFF_3: -5.702810235082488E-02., SAMP_DEN_COEFF_11: +8.960493156727774E-08 SAMP_DEN_COEFF_12: -1.233706699756710E-07 SAMP_DEN_COEFF_13: +6.362072176937147E-07 SAMP_DEN_COEFF_14: -3.936217087164640E-08 SAMP_DEN_COEFF_15: -1.245484072673269E-06 SAMP_DEN_COEFF_16: +6.296562904257587E-08 SAMP_DEN_COEFF_17: -1.244273828362835E-07 SAMP_DEN_COEFF_18: -3.913700126388425E-07 SAMP_DEN_COEFF_19: -4.839891323942274E-07 SAMP_DEN_COEFF_20: -3.835211837080171E-08

9. 9 BUNDLE ADJUSTMENT BUNDLE ADJUSTMENT Input: RPCs, GCPs, Tie Points RFM= new RPC_Process; RFM  setTotalBlockImages(N);// reads the Block details RFM  setIndex_Value(0); RFM-  Read_File("image1.RPC");// reads all the RPC files.. RFM  setIndex_Value(N); RFM-> Read_File("imageN.RPC"); RFM  setGCPFile(“GCP.dat");// reads the Control and Tie points RFM  setTiePointsFile(“TiePoints.dat”); RFM->PerformBundleAdjustment(0); //For Bias or RFM->PerformBundleAdjustment(1); //For Affine //To apply the corrected RPCs RFM  setIndex_Value(1); //Using the 1st image RFM  Apply_G2I( Longitude, Latitude, Height, line,pixel); // Ground to Image transformation Delete RFM; Output: Corrections to each image, Refined RPCs

10. Test Results: Plan Error: Single Stereo Pair Latitude Longitude

11. Height Error: Single stereo pair

12. Test2: Two Stereo Pairs

13. Control Configurations for the Block

14. Error in Longitude GCP in Left Pair GCP in Right Pair GCPS in Common Area GCPs in Left, Right Pairs and Common Area X-axis: Point Id. Y-axis: Error in Degrees

15. Error in Latitude GCP in Left Pair GCP in Right Pair GCPS in Common Area GCPs in Left, Right Pairs and Common Area X-axis: Point Id. Y-axis: Error in Degrees

16. Height Error GCP in Left Pair GCP in Right Pair GCPS in Common Area GCPs in Left, Right Pairs and Common Area X-axis: Point Id. Y-axis: Error in in Metres

17. Height Error GCP in Left Pair GCP in Right Pair GCPS in Common Area GCPs in Left, Right Pairs and Common Area X-axis: Point Id. Y-axis: Error in in Metres

18. 18 SUMMARY  Library of tools developed 1.Ground to Image function 2.Image to Ground function 3.Stereo intersection function 4.Bundle adjustment  Tested on two data sets; Carto data amenable for block adjustment with minimum control  Generic enough & adoptable to other sensors  To be expanded for DEM and ortho generation

19. 19 Mobiterra Solutions (India) Private Limited www.mobiterrasolutions.com Phone: +91 99852 93505 Email: mohan@mobiterrasolutions.com References 1.Grodecki, J., and Dial, G., 2001, IKONOS Geometric Accuracy, Proceedings of Joint ISPRS Workshop on High Resolution Mapping from space, 19-21 September, pp. 77-86 2. Dial, G., and Grodecki, J., 2002, Block Adjustment with Rational Polynomial Camera Models, ACSM-ASPRS 2002 Annual Conference Proceedings 3. Lillesand, T.M., Kiefer R.W., and Chipman J.W., 2004, Remote Sensing and Image Interpretation, John wiley & Sons, Inc. 4. Vincent Tao, C., and Yong Hu, “ A comprehensive study of the Rational function model for photogrammetric processing”, PERS, Vol 67, No. 12, Dec 2001, PP 1347-1357 5. Wolf, P.R., 1983, Elements of Photogrammetry, Mc Graw- Hill, Inc. 6. Rao B.S., Murali Mohan, K. Kalyanaraman and K. Radhakrishnan, 2006, International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol. 36, Part 4, on CD-ROM. Also in Vol. XXXVI, Part-IVB, pp. 1026- 1029 7.Vincent Tao & Hu, 2001, A comprehensive Study of the Rational Function Model for Photogrammetric Processing, Photogrammetric Engineering & Remote Sensing, Vol 67, No.12 December 2001, pp 1347-1357