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Block Adjustment of Cartosat-I Stereo Data Using RPCs

This presentation discusses the algorithm development for block adjustment of Cartosat-I stereo data using Rational Polynomial Coefficients (RPCs). It includes information on space resection, space intersection, motivation, experimental results, and future work. The presentation also mentions the accuracy of the raw product and the corrections made with refined RPCs.

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Block Adjustment of Cartosat-I Stereo Data Using RPCs

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  1. Bisector normal 0 0 26 0 5 Angle of assymetry (A) = 10.5 0 15.5 BIE (Bisector Elevation Angle) 0 64 Block Adjustment of Cartosat-I Stereo Data Using RPCs MURALI MOHAN mohan@mobiterrasolutions.com MOBITERRA SOLUTIONS (INDIA) PRIVATE LIMITED Jan 19, ‘11

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

  6. Bisector normal 0 0 26 0 5 Angle of assymetry (A) = 10.5 0 15.5 BIE (Bisector Elevation Angle) 0 64 Cartosat-I Height Sensitivity 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

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

  8. rn = P1(X, Y, Z) / P2(X, Y, Z) c n = P3(X, Y, Z) / P4(X, Y, Z) Where P1 = a0 + a1Z + a2Y + a3X + a4ZY + a5ZX + a6YX + a7Z2 + a8Y2+ a9X2 + a10ZXY + a11Z2Y + a12Z2X + a13Y2Z + a14Y2X+ a15ZX2 + a16YX2 + a17Z3 + a18Y3 + a19Z3 X,Y,Z : Ground coordinates; a0….a19 : Polynomial Coefficients rn & c n : Normalized row and column indices in image space Rational Polynomial Coefficients (RPCs): User-side … 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 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

  9. 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. SUMMARY • Library of tools developed • Ground to Image function • Image to Ground function • Stereo intersection function • 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. 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 Mobiterra Solutions (India) Private Limited www.mobiterrasolutions.comPhone: +91 99852 93505 Email: mohan@mobiterrasolutions.com

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