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Transcript of Knut Conradsen 1, Allan A. Nielsen 1, Henning Skriver 2 and Jesper Schou 3 Technical University of...
![Page 1: Knut Conradsen 1, Allan A. Nielsen 1, Henning Skriver 2 and Jesper Schou 3 Technical University of Denmark 1 Informatics and Mathematical Modelling 2 Ørsted.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5518c5b1550346b31f8b5794/html5/thumbnails/1.jpg)
Knut Conradsen1, Allan A. Nielsen1, Henning Skriver2 and Jesper Schou3
Technical University of Denmark
1Informatics and Mathematical Modelling2Ørsted●DTU, Electromagnetics Section
33Shape
DSTL WS, 4-5 October 2006
Polarimetric SAR data and the Complex Wishart
Distribution
![Page 2: Knut Conradsen 1, Allan A. Nielsen 1, Henning Skriver 2 and Jesper Schou 3 Technical University of Denmark 1 Informatics and Mathematical Modelling 2 Ørsted.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5518c5b1550346b31f8b5794/html5/thumbnails/2.jpg)
• change detection
• edge detection
• segmentation
• speckle reduction
… applied to
![Page 3: Knut Conradsen 1, Allan A. Nielsen 1, Henning Skriver 2 and Jesper Schou 3 Technical University of Denmark 1 Informatics and Mathematical Modelling 2 Ørsted.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5518c5b1550346b31f8b5794/html5/thumbnails/3.jpg)
Synthetic aperture radar (SAR) is well suited for change detection, as it provides stable acquisition conditions, i.e., the acquisition is independent of weather and light conditions.
SAR is especially sensitive to geometrical structures, e.g., vegetation constituents (leaves, branches, trunks), buildings, towers, and other man-made structures.
The polarimetric SAR uses polarisation information to distinguish between different types of scattering for the different objects.
Introduction
![Page 4: Knut Conradsen 1, Allan A. Nielsen 1, Henning Skriver 2 and Jesper Schou 3 Technical University of Denmark 1 Informatics and Mathematical Modelling 2 Ørsted.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5518c5b1550346b31f8b5794/html5/thumbnails/4.jpg)
EMISAR
The Danish EMISAR, an airborne polarimetric and interferometric SAR (Lintz et al., IEEE Trans. Geosc. Rem. Sens., vol. 36, pp. 1852-1865, 1998).
![Page 5: Knut Conradsen 1, Allan A. Nielsen 1, Henning Skriver 2 and Jesper Schou 3 Technical University of Denmark 1 Informatics and Mathematical Modelling 2 Ørsted.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5518c5b1550346b31f8b5794/html5/thumbnails/5.jpg)
In the following an example of change detection by the Danish airborne polarimetric SAR, EMISAR, is shown, where acquisitions from two consecutive years are used. A new house is detected and the removal of a hedgerow is also detected. A special test statistics for polarimetric SAR data is used.
Change detection
![Page 6: Knut Conradsen 1, Allan A. Nielsen 1, Henning Skriver 2 and Jesper Schou 3 Technical University of Denmark 1 Informatics and Mathematical Modelling 2 Ørsted.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5518c5b1550346b31f8b5794/html5/thumbnails/6.jpg)
June 98
June 99
Two EMISAR polarimetric L-band images acquired over an agricultural test site, Foulum, in Denmark in June 1998 and June 1999, respectively.
![Page 7: Knut Conradsen 1, Allan A. Nielsen 1, Henning Skriver 2 and Jesper Schou 3 Technical University of Denmark 1 Informatics and Mathematical Modelling 2 Ørsted.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5518c5b1550346b31f8b5794/html5/thumbnails/7.jpg)
Polarimetric SAR - pdfs
Scattering matrix
SShh Shv
Svh Svv
Z Shh Shv Svv T
Covariance matrix
X ZZT*
ShhShh* ShhShv
* ShhSvv*
ShvShh* ShvShv
* ShvSvv*
SvvShh* SvvShv
* SvvSvv*
Complex Gaussian
Z NC(0,)
u(z) 1
p exp tr(1zz*T )
Complex Wishart Gamma
X WC(p,N,)
w(x) 1
p(N)N
xN p
exp tr( 1x)
I G(N,)
v(I) 1
(N)NI N1exp
I
![Page 8: Knut Conradsen 1, Allan A. Nielsen 1, Henning Skriver 2 and Jesper Schou 3 Technical University of Denmark 1 Informatics and Mathematical Modelling 2 Ørsted.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5518c5b1550346b31f8b5794/html5/thumbnails/8.jpg)
… for equality of two complex Wishart distributed matrices is the ratio
Equals 1 for equal matrices, small for “very unequal” matrices. With
Test statistic
![Page 9: Knut Conradsen 1, Allan A. Nielsen 1, Henning Skriver 2 and Jesper Schou 3 Technical University of Denmark 1 Informatics and Mathematical Modelling 2 Ørsted.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5518c5b1550346b31f8b5794/html5/thumbnails/9.jpg)
Probability for smaller value of
where
Test statistic
![Page 10: Knut Conradsen 1, Allan A. Nielsen 1, Henning Skriver 2 and Jesper Schou 3 Technical University of Denmark 1 Informatics and Mathematical Modelling 2 Ørsted.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5518c5b1550346b31f8b5794/html5/thumbnails/10.jpg)
For azimuthal symmetry and diagonal cases the test statistic and the probability measure are unchanged but and change.
Knut Conradsen, Allan Aasbjerg Nielsen, Jesper Schou and Henning Skriver (2003). A test statistic in the complex Wishart distribution and its application to change detection in polarimetric SAR data. IEEE Transactions on Geoscience and Remote Sensing 41(1), 4-19.
Test statistic
![Page 11: Knut Conradsen 1, Allan A. Nielsen 1, Henning Skriver 2 and Jesper Schou 3 Technical University of Denmark 1 Informatics and Mathematical Modelling 2 Ørsted.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5518c5b1550346b31f8b5794/html5/thumbnails/11.jpg)
June 98
June 99
Two EMISAR polarimetric L-band images acquired over an agricultural test site, Foulum, in Denmark in June 1998 and June 1999, respectively.
![Page 12: Knut Conradsen 1, Allan A. Nielsen 1, Henning Skriver 2 and Jesper Schou 3 Technical University of Denmark 1 Informatics and Mathematical Modelling 2 Ørsted.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5518c5b1550346b31f8b5794/html5/thumbnails/12.jpg)
June 98
TestStatistic(1/Q)
The Wishart test statistics applied to the two EMISAR polarimetric SAR images (Conradsen et al., IEEE TGARS, vol. 41, pp. 4-19, 2003).
![Page 13: Knut Conradsen 1, Allan A. Nielsen 1, Henning Skriver 2 and Jesper Schou 3 Technical University of Denmark 1 Informatics and Mathematical Modelling 2 Ørsted.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5518c5b1550346b31f8b5794/html5/thumbnails/13.jpg)
June 98
Teststatisticthresholded(1/Q)
Only extreme change events are shown due to a high threshold
![Page 14: Knut Conradsen 1, Allan A. Nielsen 1, Henning Skriver 2 and Jesper Schou 3 Technical University of Denmark 1 Informatics and Mathematical Modelling 2 Ørsted.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5518c5b1550346b31f8b5794/html5/thumbnails/14.jpg)
A new house is detected (red) and the removal of a hedgerowis detected (blue)
![Page 15: Knut Conradsen 1, Allan A. Nielsen 1, Henning Skriver 2 and Jesper Schou 3 Technical University of Denmark 1 Informatics and Mathematical Modelling 2 Ørsted.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5518c5b1550346b31f8b5794/html5/thumbnails/15.jpg)
Synthetic aperture radar (SAR) well suited for change detection: acquisition independent of weather and light conditions.
Airborne, but spaceborne Japanese ALOS with PALSAR in FY 2005 and Canadian Radarsat-2 late 2005.
SAR especially sensitive to geometrical structures buildings, towers, man-made structures.
Newly developed test statistic for polarimetric SAR data is used.
Example: new house and removal of hedge detected.
Conclusions, CD
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Rotate filter, calculate test statistic (low) andP-measure (high), store direction etc. if P “low enough”
Edge detection
![Page 17: Knut Conradsen 1, Allan A. Nielsen 1, Henning Skriver 2 and Jesper Schou 3 Technical University of Denmark 1 Informatics and Mathematical Modelling 2 Ørsted.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5518c5b1550346b31f8b5794/html5/thumbnails/17.jpg)
(A) winter wheat(B) spring barley(C) oats(D) peas
Edge detection
Span image, EMISAR L-band, May 1998
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L-band, May 98
(a) Diagonal(b) Azimuthal symmetry(c) Diagonal (L+C)(d) Ratio (HH)
Edge detection
(a) (b)
(c) (d)
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Diagonal Azimuthal symmetry
Segmentation
L-band, May 98
MOM method
![Page 20: Knut Conradsen 1, Allan A. Nielsen 1, Henning Skriver 2 and Jesper Schou 3 Technical University of Denmark 1 Informatics and Mathematical Modelling 2 Ørsted.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5518c5b1550346b31f8b5794/html5/thumbnails/20.jpg)
Speckle reduction
MRF, SACW, potential function
![Page 21: Knut Conradsen 1, Allan A. Nielsen 1, Henning Skriver 2 and Jesper Schou 3 Technical University of Denmark 1 Informatics and Mathematical Modelling 2 Ørsted.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5518c5b1550346b31f8b5794/html5/thumbnails/21.jpg)
A new test statistic for the equality of two matrices following the complex Wishart distribution is given with an asymptotic probability for obtaining a smaller value of the test statistic.
These measures are applied to segmentation, change detection and edge detection in polarimetric synthetic aperture radar data.
The new test statistic and the associated probability measure combines the full polarimetric signal in a unified way. As opposed to existing methods that deal with each polarization marginally in turn followed by some heuristic fusion step, this new test statistic allows for the full polarimetric information simultaneously.
Conclusions
![Page 22: Knut Conradsen 1, Allan A. Nielsen 1, Henning Skriver 2 and Jesper Schou 3 Technical University of Denmark 1 Informatics and Mathematical Modelling 2 Ørsted.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5518c5b1550346b31f8b5794/html5/thumbnails/22.jpg)
Jesper Schou and Henning Skriver (2001). Restoration of Polarimetric SAR Data Using Simulated Annealing. IEEE Transactions on Geoscience and Remote Sensing 39(9), 2005-2016.
Knut Conradsen, Allan A. Nielsen, Jesper Schou and Henning Skriver (2003). A test statistic in the complex Wishart distribution and its application to change detection in polarimetric SAR data. IEEE Transactions on Geoscience and Remote Sensing 41(1), 4-19.
Jesper Schou, Henning Skriver, Allan A. Nielsen and Knut Conradsen (2003). CFAR edge detector for polarimetric SAR images. IEEE Transactions on Geoscience and Remote Sensing 41(1), 20-32.
Henning Skriver, Allan A. Nielsen and Knut Conradsen (2003). Evaluation of the Wishart Test Statistic for Polarimetric SAR Data. International Geoscience and Remote Sensing Symposium, IGARSS 2003, Toulouse, France, 21-25 July 2003. Invited contribution.
Allan A. Nielsen, Knut Conradsen and Henning Skriver (2003). Polarimetric synthetic aperture radar data and the complex Wishart distribution. 13th Scandinavian Conference on Image Analysis, SCIA 2003, 1082-1089, Springer LNCS 2749. Göteborg, Sweden, 29 June-2 July 2003.
References
![Page 23: Knut Conradsen 1, Allan A. Nielsen 1, Henning Skriver 2 and Jesper Schou 3 Technical University of Denmark 1 Informatics and Mathematical Modelling 2 Ørsted.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5518c5b1550346b31f8b5794/html5/thumbnails/23.jpg)
Knut Conradsen1, Allan A. Nielsen1, Henning Skriver2 and Jesper Schou3
Technical University of Denmark
1Informatics and Mathematical Modelling2Ørsted●DTU, Electromagnetics Section
33Shape
DSTL WS, 4-5 October 2006
Polarimetric SAR data and the Complex Wishart
Distribution