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

• change detection

• edge detection

• segmentation

• speckle reduction

… applied to

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

EMISAR

The Danish EMISAR, an airborne polarimetric and interferometric SAR (Lintz et al., IEEE Trans. Geosc. Rem. Sens., vol. 36, pp. 1852-1865, 1998).

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

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.

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

… for equality of two complex Wishart distributed matrices is the ratio

Equals 1 for equal matrices, small for “very unequal” matrices. With

Test statistic

Probability for smaller value of

where

Test statistic

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

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.

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).

June 98

Teststatisticthresholded(1/Q)

Only extreme change events are shown due to a high threshold

A new house is detected (red) and the removal of a hedgerowis detected (blue)

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

Rotate filter, calculate test statistic (low) andP-measure (high), store direction etc. if P “low enough”

Edge detection

(A) winter wheat(B) spring barley(C) oats(D) peas

Edge detection

Span image, EMISAR L-band, May 1998

L-band, May 98

(a) Diagonal(b) Azimuthal symmetry(c) Diagonal (L+C)(d) Ratio (HH)

Edge detection

(a) (b)

(c) (d)

Diagonal Azimuthal symmetry

Segmentation

L-band, May 98

MOM method

Speckle reduction

MRF, SACW, potential function

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

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

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