POLARIMETRIC SPECKLE FILTERING

Transcription

1 $y $x r Ezt (, ) $z POLARIMETRIC SPECKLE FILTERING E. Pottier, L. Ferro-Famil (/)

2 SPECKLE FILTERING SPECKLE PHENOMENON E. Pottier, L. Ferro-Famil (/)

3 SPECKLE FILTERING OBSERVATION POINT SURFACE ROUGHNESS WAVELENGTH SCATTERING FROM DISTRIBUTED SCATTERERS COHERENT INTERFERENCES OF WAVES SCATTERED FROM MAN RANDOML DISTRIBUTED ELEMENTAR SCATTERERS INSIDE THE RESOLUTION CELL GRANULAR NOISE E. Pottier, L. Ferro-Famil (/) SPECKLE PHENOMENON

4 SPECKLE FILTERING SPECKLE PHENOMENON DISTORTION OF THE INTERPRETATION SPECKLE FILTERING HOMOGENEOUS AREA HETEROGENEOUS AREA SPECKLE REDUCTION (RADIOMETRIC RESOLUTION) E. Pottier, L. Ferro-Famil (/) DETAILS PRESERVATION (SPATIAL RESOLUTION)

5 SPECKLE FILTERING SPECKLE REDUCTION MULTI-LOOK SAR PROCESSING (BoxCar) Aeraging Amplitude / Intensity (Not complex images) of neighboring pixels Good Noise Smoothing Spatial Resolution Loss - blurring edges - erasing thin lines Loss of linear or point features E. Pottier, L. Ferro-Famil (/)

6 SPECKLE FILTERING LINEAR SPECKLE FILTERS Median Filter MAP Filter (Kuan) Gradient Filter Nagao Filter (Nagao) Sigma Filter (Lee) Frost Filter (Frost) Geometrical Filter (Crimmins) Morphological Filter (Safa, Flouzat).... Local Statistics Filter (Lee 8) E. Pottier, L. Ferro-Famil (/)

7 SPECKLE FILTERING SPECKLE : MULTIPLICATIVE NOISE MODEL «SPECKLE is a scattering phenomenon and not a noise. Howeer, from the image SAR processing point of ue, the speckle can be modeled as multiplicatie noise for extended target» (Lee, IGARSS-98) y y y y HH HV VV n HH n HV n VV x x x HH HV VV x x x HH HV VV n n n HH HV VV SCATTERING FIELD y y * NOISE REFLECTIVIT DENSIT A y y * INTENSIT AMPLITUDE E. Pottier, L. Ferro-Famil (/)

8 SPECKLE FILTERING HOMOGENEOUS AREA NUMBER OF ELEMENTAR SCATTERERS IS IMPORTANT CENTRAL LIMIT THEOREM n n I + jn Q n I,Q Ν (, CIRCULAR GAUSSIAN ) E E E ( I ) ( Q ) n E n ( I Q ) n n ( I ) ( Q ) n E n NOISE INTENSIT ( I ) ( Q ) n + n E( ) * n n E. Pottier, L. Ferro-Famil (/)

9 SPECKLE FILTERING HOMOGENEOUS AREA CONSTANT SPATIAL REFLECTIVIT ( ) E( ) E( ) E ( ) ar( ) ar( ) ar ( ) ( ) ar CV ar E ( ) CV ( ) CV CV CV ar E. Pottier, L. Ferro-Famil (/)

10 SPECKLE FILTERING HOMOGENEOUS AREA INTENSIT AMPLITUDE N LOOK CASE y y * A y y * N i i N LOOK A N i i P N N N N Γ ( N ) N ( / ) e DENSIT P ( A / ) N NA N N A Γ ( N ) N N e NA E( ) MEAN E( A ) N Γ ( N + Γ ( N ) ) ar( ) N VARIANCE ar( A ) N Γ ( N + N Γ ( N ) ) CV N N E. Pottier, L. Ferro-Famil (/) COEFFICIENT OF VARIATION CV NA NΓ ( N Γ ( N + ) ).5 N

11 SPECKLE FILTERING LOCAL STATISTICS LINEAR FILTER i, j ( ) + b i, j a b i, j ˆ ae + with: ν ν E Eν E ar( ) CV E + ( CV ) M.M.S.E ( a,b) \ min J ( a,b ) E ˆ i, j i, j J a ( ) + ab a + b E + E b ν J a a ν b J b b ν ar( ) ar( ) E. Pottier, L. Ferro-Famil (/)

12 SPECKLE FILTERING ˆ i, j E( ν ) + ( E( )) b i, j with: b ar( ) ν ar( ) ν CV CV and: CV E E ( CV CV ) E E ( CV ) CV ( CV + ) E ( CV CV ) b ν ar( ) ar( ) ν CV CV CV ν ( + CV ) ν E. Pottier, L. Ferro-Famil (/)

13 SPECKLE FILTERING or: ν E ( ν ) LOCAL STATISTICS LINEAR FILTER ˆ i, j E( ) + k ( E( )) i, j k ar( ) ar( ) CV CV CV [ ] [ + CV ar( ) + σ ] ar( ) E ( ) σ LOCAL STATISTICS E ( ), ar ( ) ( ) E E ( ) A PRIORI INFORMATION () σ ar CV N IMAGE NUMBER OF LOOK E. Pottier, L. Ferro-Famil (/)

14 POLSAR SPECKLE FILTERING VECTORIAL SPECKLE FILTER * T * T [ C] yy FILTER [$ C] xx $$ COVARIANCE MATRI LOPES - GOZE - NEZR - TOUZ (99-99) and SER (997) FILTERS, LEE FILTER (997) POLARIMETRIC SPECKLE FILTERING SHOULD FILTER ALL ELEMENTS OF THE COVARIANCE MATRI AVOIDING CROSS-TALK BETWEEN CHANNELS DUE TO THE FILTERING PROCESS PRESERVING POLARIMETRIC INFORMATION AND THE STATISTICAL CORRELATION BETWEEN THE CHANNELS PRESERVING SPATIAL RESOLUTION, FEATURES, EDGE SHARPNESS AND POINT TARGETS E. Pottier, L. Ferro-Famil (/)

15 POLSAR SPECKLE FILTERING ETENSION OF THE LOCAL STATISTIC LINEAR FILTER [ C] y y T* VECTORIZATION OF THE COVARIANCE MATRI HHHH * HVHV * HHVV HHHV HVHV * HVVV HHVV HVVV VVVV HHHH HHHV HHVV HVHV HVVV VVVV VECTORIAL MULTIPLICATIVE MODEL [ V ] E. Pottier, L. Ferro-Famil (/)

16 POLSAR SPECKLE FILTERING VECTORIAL MULTIPLICATIVE MODEL [ V ] HHHH HHHV HHVV HVHV HVVV VVVV HHHH HHHV HHVV HVHV HVVVV VVVV HHHH HHHV HHVV HVHV HVVV VVVV VECTORIAL LOCAL STATISTICS LINEAR FILTER [ A] E( ) [ B] ˆ + E. Pottier, L. Ferro-Famil (/)

17 POLSAR SPECKLE FILTERING M.M.S.E T ([ A][, B] )\ min J E ˆ E ( ˆ ) ( ˆ ) ([][] A, B ) [ ] * J J [ A] [ B] [ A] [ Id] [ B] E( [ V ]) [ B] co( ) E( [ V ]) T * co ( ) ˆ E ( ) [ k] ( E( ) ) [ k] co( ) E( [ V ]) T * co ( ) E. Pottier, L. Ferro-Famil (/)

18 POLSAR SPECKLE FILTERING VECTORIAL LOCAL STATISTICS LINEAR FILTER ˆ E ( ) [ k] ( E( ) ) [ k] co( ) E( [ V ]) T * co ( ) DERIVATION AND COMPUTATION OF THE COV() MATRI IS RATHER COMPLICATED (ILL-CONDITIONING) IN THE COVARIANCE MATRI, THE CO-POL INTENSITIES CHANNELS CAN BE MODELED AS MULTIPLICATIVE NOISE MODEL. BUT THE CROSS-POL (OFF-DIAGONAL) INTENSITIES CHANNELS ARE DIFFICULT TO DEFINE : NEITHER MULTIPLICATIVE NOR ADDITIVE E. Pottier, L. Ferro-Famil (/)

19 POLSAR SPECKLE FILTERING HHHH (Nwin 7) n HVHV (Nwin 7) n VVVV (Nwin 7) n ECART TPE ECART TPE /N.5.5 ECART TPE HHHV r (Nwin 7) HHHH.5 n 6 8 HHVV r (Nwin 7) HVHV.5 n 6 8 MOENNE HVVV r (Nwin 7) VVVV.5 n ECART TPE HHHV i (Nwin 7) HHHVr n ECART TPE HHVV i (Nwin 7) HHVVr n HVVV i (Nwin 7) HVVVr n ECART TPE HHHVi E. Pottier, L. Ferro-Famil (/).5 HHVVi HVVVi

20 POLSAR SPECKLE FILTERING POLARIMETRIC VECTORIAL SPECKLE FILTER [ ] C *T y y [ Ĉ] E [ C] ( ) k[ E( [ C] ) [ C] ] [ ] * T Ĉ xˆ xˆ SPAN IMAGE S + + S HHHH HVHV VVVV k ar ar ( S) CV ( S ) [ S CV + σ ] S S S S σ J.S. LEE Ŝ LINEAR SCALAR LEE FILTER E( S ) k[ E( S ) S ] S S S Homogeneous Areas ar S k Ŝ ( ) E( ) Highly Inhomogeneous Areas S S ( S) a ar( Ss ) k Ŝ SS ar REFINED FILTER E. Pottier, L. Ferro-Famil (/)

21 POLSAR SPECKLE FILTERING POLARIMETRIC VECTORIAL SPECKLE LEE FILTER [ Ĉ] E [ C] ( ) k[ E( [ C] ) [ C] ] EACH ELEMENT OF THE COVARIANCE MATRI IS FILTERED B THE SAME AMOUNT AVOIDING CROSS-TALK AND PRESERVING POLARIMETRIC INFORMATION AND CORRELATIONS SIMILAR TO THE MULTI LOOK PROCESSING B AVERAGING THE COVARIANCE MATRICES OF NEIGHBORING PIELS B WEIGHTING THE COVARIANCE MATRI OF THE CENTER PIEL OF THE SLIDING WINDOW WITH THE MEAN OF COVARIANCE MATRICES FROM SELECTED NEIGHBORING PIELS PRESERVING SPATIAL RESOLUTION, FEATURES, EDGES REFINED LEE FILTER E. Pottier, L. Ferro-Famil (/)

22 POLSAR SPECKLE FILTERING EDGE DIRECTED WINDOW LOCAL HETEROGENEIT & NOIS EDGE BOUDARIES DIRECTION DIRECTION DIRECTION DIRECTION THE EDGE DIRECTED WINDOWS ARE USED TO COMPUTE THE LOCAL MEAN AND VARIANCE DIRECTION 5 DIRECTION 6 DIRECTION 7 DIRECTION 8 POLARIMETRIC LEE FILTER [ Ĉ] E [ C] k ar ar ( ) k[ E( [ C] ) [ C] ] ( S) CVS σ ( ) [ S CV + σ ] S S FOR EACH PIEL, THE k VALUE IS COMPUTED IN AN EDGE DIRECTED WINDOW S S E. Pottier, L. Ferro-Famil (/)

23 POLSAR SPECKLE FILTERING OP-AIRFIELD L-BandL E. Pottier, L. Ferro-Famil (/)

24 POLSAR SPECKLE FILTERING POLARIMETRIC SPECKLE FILTERING IS NOT AN EACT SCIENCE SUBJECTIVE, IMAGE DEPENDENT Quantitatie Criteria (J.S. Lee - IGARSS 98) Speckle Reduction (E.N.L) Edge Sharpness Preseration Line and Point Target Contrast Preseration Retention of Mean Values in Homogeneous Regions Retention of Texture Information Retention of Polarimetric Information (co, cross-correlations) Computational Efficiency Implementation Complexity [ Ĉ] E [ C] ( ) k[ E( [ C] ) [ C] ] THE POLARIMETRIC SPECKLE LEE FILTER IS TODA A GOOD COMPROMISE E. Pottier, L. Ferro-Famil (/)

25 POLSAR SPECKLE FILTERING * T * T [ C] yy [$ C] xx $$ FILTER AVERAGING DATA SECOND ORDER STATISTICS COVARIANCE / COHERENC MATRICES SMOOTHING AVERAGING CONCEPT OF THE DISTRIBUTED TARGET E. Pottier, L. Ferro-Famil (/)

26 Questions? E. Pottier, L. Ferro-Famil (/)