LINEAR FEATURE DETECTION IN SAR IMAGES

Transcription

1 iitl-h. '^r^^-' LINEAR FEATURE DETECTION IN SAR IMAGES Ph. COURMONTAGNE L2MP UMR CNRS 6137 / ISEM L2MP UMR 6137

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3 INTRODUCTION Ship wakes in Synthetic Aperture Radar (SAR) images Detection using Radon transform (DEANS, 1983) Straight line Radon transform Peak or trough SAR images affected by speckle Detection wedding between the Radon transform and a filtering method 9th ASAP Workshop 13/14 March /17

4 CONTENTS Radon transform discrete form Stochastic matched filtering method Interpolation-filtering method theory and subimage processing Experimental results on SAR images comparison with the classical approach 9th ASAP Workshop 13/14 March /17

5 3 LINEAR FEATURE DETECTION IN SAR IMAGES THE RADON TRANSFORM Consider an image I, with dimensions The Radon transform where MI2 of this image is: (xe, y^) Z and ^ e [0; n] Problems : - new pixel coordinates in Computation of the new pixel values - pixels localized at the edge in (surrounding points) Edge effect size of the image in : 9th ASAP Workshop 13/14 March /17 M xm I{xs: B) ^ I{x& COS 0 He sin 9, XQ sin 9 -hys cos 0) yg = -M/2 R^t 5Rfl^/.0*^,- ''' Ue ^ye h < ri 9 n ;7T^? >,- ^' v li * V ". ^ _. V ^jf _,.r' \ - -'. V < ':, _^ C. '.' \ -^ _, ' y' _\ 5" V" en M M V2 ".V.' ' \ ^. ',' 1^ _,._ ^^. vt j-o V - ' ^^ '(^ ^^r., - 1 V * ' i-',\ _.i \ ^h h ^,»- \ '.-_.-= : '- \ ' ' ^ ' \ u \ V2.7;

6 STOCHASTIC MATCHED FILTERING METHOD Consider the stationary noise-corrupted signal defined over D : where signal S{x,y) and noise B{x,y) are assumed to be independent. Observed signal expansion: Z{x,y) = S{x,y) + B{x,y) Z{x,y) -^2 *n(a;,?/) n=l : deterministic and linearly independent basis functions where: Q : number of basis functions retained for the expansion uncorrelated random variables defined by Zfi // Z{x,y)^n{x,y)dxdy 9th ASAP Workshop 13/14 March /17

7 Determination of functions ^n{x, y) Making sure n are uncorrelated Optimization of the signal to noise ratio K expressed as a Rayleigh quotient K will be maximized if ^n{x, y) are solutions of: jj Tss{^-x',y-y')^n{x\y')dx'dy =\n 11 TBB{X-x,y-y')^n{x',y')dx'dy' where ^ss and ^BB are the covariances of the signal and of the noise Determination of functions *n{x,y) * {x,y)= // YBB[x-x',y-y')^n{x\y')dx'dy' Signal to noise ratio of the component of : number Q of basis functions such as Ag>l 9th ASAP Workshop 13/14 March /17 n th Z(x,y) -4X ^s 2 ''n ^B

8 INTERPOLATION-FILTERING METHOD Basic idea Observed signal signal Z{x, y) ^n{x,y) Ki^.y) Zn and andq Mx,y) ^^Zn'^iix-.y) n=l Observed signal expansion and restoration using interpolated functions *»(^,y) Defaults: heavy CPU budget and memory problems new formulation using the discrete cosine transform 9th ASAP Workshop 13/14 March /17

9 Z{x, y) interpolation-filtering using DCT, with D = [-T; T] Functions DCT coefficients *n(a:, y) <l *n(x,?/) Z{x, y) Z{x,y) ^ss ^BB an yp,q ^p,q dk,i ^\^ll,q ^%l,p,q ^n{x, y) <J=^ *n(x,y)<^=^ 'n 1 T Z{x, y) '\ r Nf Nf Nf A'/ Af/ Nf Nf p^o q=0 Q Nf Signal of interest restoration in 3fJ e Nf Nf Zeixe^ye) = >. >.t'fc^^cos I r^i^ 1 cos 2T fc=0 /=o 9th ASAP Workshop 13/14 March /17 2T

10 Subimage processing Assumption: Z{x,ij) is stationary necessity of a subimage processing Edge effect overlapping between adjacent subimages: (/- A^ cos ^ + sin 6* and h = N sin e sin 9 + cos 0 Smoothing effect when Q is the same for the whole image minimization of the mean square error to find 9th ASAP Workshop 13/14 March /17 Q for each subimage Q Nf Nf 1 ^-=-?- + iek-ax)ee(/5m)

11 EXPERIMENTAL RESULTS SIR-C/X-SAR image moving ship dark turbulent wake (17 miles) 256 gray levels (0: black, 255: white) Image size: 698 X 698 Variation coefficient: Z>0 Difficulty: dark patches in the upper right corresponding to smooth area of low wind 9th ASAP Workshop 13/14 March /17

12 Signal and noise auto-correlation functions a priori knowledge of the signal and the noise auto-correlation functions determination of normalized auto-correlation models Signal auto-correlation function 9th ASAP Workshop 13/14 March /17 Noise auto-correlation function

13 Interpolation-filtering of the SIR-C/X-SAR image 1 r r Rotation angle: CO XO ^ - K)0 Number Q of basis functions: approximately 13 for the wake ~ 0 > near 1 for the rest of the image loo > - - loo 200 V - Image size: 973 X ' Variation coefficient: _i 1 j C0 -ECC -lo) 0 ico SIR-C/X-SAR image in reference system 5R 35 9th ASAP Workshop 13/14 March /17

14 Radon domain displayed as image <^ Angles -30CO Angles -90CO -fioco -SKO '3JD 'lod D 'DD «0 Projections Our processing Trough corresponding to the wake localized near 9th ASAP Workshop 13/14 March /17 5r Projections Classical processing

15 Radon domain displayed as graph 6000 xlo^ Amplitude ' Amplitude -MOO -aooo Angles Our processing Angles Classical processing No ambiguity about the presence of a ship wake with our processing detection by simply using a threshold contrarily to classical approach 9th ASAP Workshop 13/14 March /17

16 Reconstructed image using the transform domain Inverse Radon transform applied to the transform domain raised to the power of 3 -S^l fu -3ni?» SfO 3in 21X1 I5D -im 15(1 lua ICO IK «30] -im -jro -ifyi CPH mi iro Our processing Variation coefficient: Classical processing Variation coefficient: th ASAP Workshop 13/14 March /17

17 ANOTHER SAR IMAGE ERS SAR image ship pixels replaced by mean background dark turbulent wake 256 gray levels (0: black, 255: white) Image size: 325 X 325 Difficulty: dark patch near the wake (slick oil) 9th ASAP Workshop 13/14 March /17

18 ]000 LINEAR FEATURE DETECTION IN SAR IMAGES Radon domain displayed as image f ma Qi Angles n m I Qi Angles * 1 10O3 M ^M-^m ^M-m> ^M^}m ^M-m> 140 H-soco m * ' ^ ^' ' '' ' -20} -t50 -TO) ffi 'DD 'K??00 Projections Our processing?» '150 -K -SD 0 a ^w»?:c Projections Classical processing ^ -60DD -TODD Trough corresponding to the wake localized near 115^ 9th ASAP Workshop 13/14 March /17

19 CONCLUSION New processing for ship wakes detection SAR image Radon transform original contribution: taking into account the speckle for image interpolation Better detection with lower probability of false alarm or no detection Future work: extension of this method to the localized Radon transform 9th ASAP Workshop 13/14 March /17