Jan 19, ‘11

Block Adjustment Block Adjustment of of Cartosat-I Stereo Data Using RPCsCartosat-I Stereo Data Using RPCs

MURALI MOHANMURALI MOHAN

mohan@mobiterrasolutions.commohan@mobiterrasolutions.com

MOBITERRASOLUTIONS (INDIA) PRIVATE LIMITED

5

BIE (Bisector Elevation Angle)

15.5

26

Bis

ecto

r

0

0

norm

al

640

0

Ang

le o

f ass

ymet

ry (

A)

= 1

0.5

0

About About MMOOBITERRABITERRA

Incorporated in 2010; Located at Hyderabad

Solution Provider

Focus on Algorithms & Custom Solutions

Surveying, Photogrammetry, Remote sensing

Developed 2 products for Land Resurvey

TerraForma: TerraForma: Tool for land resurvey under NLRMPTool 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

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

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Scope of the PresentationScope 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

Cartosat-ICartosat-I

5

BIE (Bisector Elevation Angle)

15.5

26

Bis

ecto

r

0

0

norm

al

640

0

Ang

le o

f ass

ymet

ry (

A)

= 1

0.5

0

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 Height Sensitivity

7

Raw Product Accuracy Raw Product Accuracy

Residuals at Check points in X,Y,Z without using GCPs

-400

-200

0

200

400

600

800

1000

1200

Point-Id

Res

idua

l Err

or (m

)

Residual Error (X)

Residual Error (Y)

Residual Error (Z)

21 23 24 31 39 40 41 42 43

Residuals at Check points in X,Y,Z without using GCPs

-400

-200

0

200

400

600

800

1000

1200

Point-Id

Res

idua

l Err

or (m

)

Residual Error (X)

Residual Error (Y)

Residual Error (Z)

21 23 24 31 39 40 41 42 43

X-error = 61 mX-error = 61 m

Y-error = 314 mY-error = 314 m

Z-error = 1049 mZ-error = 1049 m

Error Vector (1000X)

8

rn = P1(X, Y, Z) / P2(X, Y, Z)

c n = P3(X, Y, Z) / P4(X, Y, Z)

Where P1 = a a00 + a1Z + a2Y + a3X + a4ZY + a5ZX + a6YX + a7Z2 + a8Y

2+ a9X2 + a10ZXY

+ a11Z2Y + a12Z

2X + a13 Y2Z + a14Y

2X+ a15ZX2 + a16 YX2 + a17Z

3 + a18Y3 + a19Z

3

X,Y,Z : Ground coordinates; a0….a19 : Polynomial Coefficients

rn & c n : Normalized row and column indices in image space

Rational Polynomial Coefficients (RPCs): Rational Polynomial Coefficients (RPCs): User-sideUser-side

LINE_OFF: +5999.97 pixelsSAMP_OFF: +6000.00 pixelsLAT_OFF: +31.71550742 degreesLONG_OFF: +79.04313203 degreesHEIGHT_OFF: +4249.995 metersLINE_SCALE: +6099.98 pixelsSAMP_SCALE: +6100.00 pixelsLAT_SCALE: +0.17195169 degreesLONG_SCALE: +0.19526625 degreesHEIGHT_SCALE: +1349.999 metersLINE_NUM_COEFF_1: +4.832002101528874E-04LINE_NUM_COEFF_2: -2.494192583363085E-01LINE_NUM_COEFF_3: -1.203624337000269E+00LINE_NUM_COEFF_4: +4.784735738655975E-02LINE_NUM_COEFF_5: +2.436545448722357E-02LINE_NUM_COEFF_6: -3.398996506834039E-03LINE_NUM_COEFF_7: -1.734635182453075E-02

…SAMP_DEN_COEFF_1:

+1.000000000000000E+00SAMP_DEN_COEFF_2: -7.503988256474431E-03SAMP_DEN_COEFF_3: -5.702810235082488E-02

.,

SAMP_DEN_COEFF_11: +8.960493156727774E-08SAMP_DEN_COEFF_12: -1.233706699756710E-07SAMP_DEN_COEFF_13:

+6.362072176937147E-07SAMP_DEN_COEFF_14: -3.936217087164640E-08SAMP_DEN_COEFF_15: -1.245484072673269E-06SAMP_DEN_COEFF_16:

+6.296562904257587E-08SAMP_DEN_COEFF_17: -1.244273828362835E-07SAMP_DEN_COEFF_18: -3.913700126388425E-07SAMP_DEN_COEFF_19: -4.839891323942274E-07SAMP_DEN_COEFF_20: -3.835211837080171E-08

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BUNDLE ADJUSTMENTBUNDLE 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 pointsRFMsetTiePointsFile(“TiePoints.dat”);

RFM->PerformBundleAdjustment(0); //For Biasor

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

Test Results:Test Results:Plan Error: Single Stereo PairPlan Error: Single Stereo Pair

Latitude

Longitude

Height Error: Height Error: Single stereo pairSingle stereo pair

Test2: Two Stereo Pairs Test2: Two Stereo Pairs

Control Configurations for the BlockControl Configurations for the Block

Error in LongitudeError 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

Error in LatitudeError 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

Height ErrorHeight 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

Height ErrorHeight 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

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SUMMARYSUMMARY 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

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Mobiterra Solutions (India) Private Limitedwww.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