Sylvain Faisan,*
Christian Heinrich,
François Rousseau,
Alex Lallement,
and Jihad Zallat
Laboratoire des Sciences de l’Image, de l’Informatique et de la Télédétection (LSIIT)—UMR 7005 CNRS, University of Strasbourg Pôle API, Boulevard Sébastien Brant, B.P. 10413, 67412 Illkirch Cedex, France
Sylvain Faisan, Christian Heinrich, François Rousseau, Alex Lallement, and Jihad Zallat, "Joint filtering estimation of Stokes vector images based on a nonlocal means approach," J. Opt. Soc. Am. A 29, 2028-2037 (2012)
Conventional estimation techniques of Stokes images from observed radiance images through different polarization filters suffer from noise contamination that hampers correct interpretation or even leads to unphysical estimated signatures. This paper presents an efficient restoration technique based on nonlocal means, permitting accurate estimation of smoothly variable polarization signatures in the Stokes image while preserving sharp transitions. The method is assessed on simulated data as well as on real images.
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PSNR and Stokes Vector Estimation Error Obtained with the Five Different Methods and for Different Variances of Noisea
PSNR
0.001
24.09
24.17
24.81
30.81
43.49
0.002
21.08
21.16
21.86
28.40
40.33
0.005
17.12
17.21
17.98
25.26
35.85
0.01
14.08
14.15
15.02
23.02
32.31
0.02
11.07
11.13
12.15
20.50
29.06
0.05
7.09
7.14
8.46
16.97
25.24
Stokes Vector Estimation Error
0.001
5.09
4.94
4.67
2.35
0.54
0.002
7.20
6.98
6.55
3.12
0.79
0.005
11.34
10.95
10.22
4.44
1.31
0.01
16.09
15.47
14.32
5.60
1.95
0.02
22.76
21.73
19.86
7.44
2.86
0.05
36.02
33.86
30.06
10.97
4.35
Bold values correspond to the best results.
Table 2.
PSNR and Stokes Vector Estimation Error Obtained with Four Simplified Versions of the Proposed Approach (, , , and ) and with the Proposed Approach for Different Variances of Noisea
PSNR
0.001
40.24
40.68
38.98
37.41
43.49
0.002
37.23
37.57
36.17
35.06
40.33
0.005
33.00
33.24
32.26
31.44
35.85
0.01
29.85
30.41
29.62
28.89
32.31
0.02
26.92
27.80
27.25
26.66
29.06
0.05
23.18
24.54
24.39
24.12
25.24
Stokes Vector Estimation Error
0.001
0.79
0.76
0.91
1.08
0.54
0.002
1.13
1.08
1.24
1.40
0.79
0.005
1.82
1.74
1.93
2.10
1.31
0.01
2.59
2.41
2.61
2.83
1.95
0.02
3.64
3.25
3.43
3.65
2.86
0.05
5.57
4.70
4.75
4.88
4.35
Bold values correspond to the best results (without considering the proposed approach , which provides always the best results).
Table 3.
PSNR and Stokes Vector Estimation Error Obtained with the GF- and MF-Based Approaches and with the Proposed Approach () for Different Variances of Noisea
GF
MF
PSNR
0.001
27.00 (0.5)
31.04 ()
43.49
0.002
25.06 (0.6)
29.38 ()
40.33
0.005
22.86 (0.7)
26.77 ()
35.85
0.01
21.39 (0.9)
24.57 ()
32.31
0.02
20.12 (1.2)
22.52 ()
29.06
0.05
18.61 (1.7)
19.57 ()
25.24
Stokes Vector Estimation Error
0.001
3.44 (0.5)
1.98 ()
0.54
0.002
4.15 (0.6)
2.43 ()
0.79
0.005
5.27 (0.8)
3.35 ()
1.31
0.01
6.16 (1.1)
4.28 ()
1.95
0.02
7.02 (1.4)
5.50 ()
2.86
0.05
8.29 (1.9)
7.49 ()
4.35
For each case, only the best result is given as well as the corresponding setting in parentheses (filter size for MF and standard deviation for GF).
Table 4.
PSNR and Stokes Vector Estimation Error Obtained with Two Simplified Versions of the Proposed Approach (NLMPI, NLMPROJ) and with the Proposed Approach for Different Variances of Noise
NLMPI
NLMPROJ
PSNR
0.001
41.55
41.63
43.49
0.002
38.30
38.36
40.33
0.005
33.97
34.18
35.85
0.01
30.65
30.79
32.31
0.02
27.52
27.63
29.06
0.05
23.77
23.88
25.24
Stokes Vector Estimation Error
0.001
0.67
0.66
0.54
0.002
1.00
0.97
0.79
0.005
1.61
1.57
1.31
0.01
2.36
2.31
1.95
0.02
3.41
3.34
2.86
0.05
5.19
5.08
4.35
Tables (4)
Table 1.
PSNR and Stokes Vector Estimation Error Obtained with the Five Different Methods and for Different Variances of Noisea
PSNR
0.001
24.09
24.17
24.81
30.81
43.49
0.002
21.08
21.16
21.86
28.40
40.33
0.005
17.12
17.21
17.98
25.26
35.85
0.01
14.08
14.15
15.02
23.02
32.31
0.02
11.07
11.13
12.15
20.50
29.06
0.05
7.09
7.14
8.46
16.97
25.24
Stokes Vector Estimation Error
0.001
5.09
4.94
4.67
2.35
0.54
0.002
7.20
6.98
6.55
3.12
0.79
0.005
11.34
10.95
10.22
4.44
1.31
0.01
16.09
15.47
14.32
5.60
1.95
0.02
22.76
21.73
19.86
7.44
2.86
0.05
36.02
33.86
30.06
10.97
4.35
Bold values correspond to the best results.
Table 2.
PSNR and Stokes Vector Estimation Error Obtained with Four Simplified Versions of the Proposed Approach (, , , and ) and with the Proposed Approach for Different Variances of Noisea
PSNR
0.001
40.24
40.68
38.98
37.41
43.49
0.002
37.23
37.57
36.17
35.06
40.33
0.005
33.00
33.24
32.26
31.44
35.85
0.01
29.85
30.41
29.62
28.89
32.31
0.02
26.92
27.80
27.25
26.66
29.06
0.05
23.18
24.54
24.39
24.12
25.24
Stokes Vector Estimation Error
0.001
0.79
0.76
0.91
1.08
0.54
0.002
1.13
1.08
1.24
1.40
0.79
0.005
1.82
1.74
1.93
2.10
1.31
0.01
2.59
2.41
2.61
2.83
1.95
0.02
3.64
3.25
3.43
3.65
2.86
0.05
5.57
4.70
4.75
4.88
4.35
Bold values correspond to the best results (without considering the proposed approach , which provides always the best results).
Table 3.
PSNR and Stokes Vector Estimation Error Obtained with the GF- and MF-Based Approaches and with the Proposed Approach () for Different Variances of Noisea
GF
MF
PSNR
0.001
27.00 (0.5)
31.04 ()
43.49
0.002
25.06 (0.6)
29.38 ()
40.33
0.005
22.86 (0.7)
26.77 ()
35.85
0.01
21.39 (0.9)
24.57 ()
32.31
0.02
20.12 (1.2)
22.52 ()
29.06
0.05
18.61 (1.7)
19.57 ()
25.24
Stokes Vector Estimation Error
0.001
3.44 (0.5)
1.98 ()
0.54
0.002
4.15 (0.6)
2.43 ()
0.79
0.005
5.27 (0.8)
3.35 ()
1.31
0.01
6.16 (1.1)
4.28 ()
1.95
0.02
7.02 (1.4)
5.50 ()
2.86
0.05
8.29 (1.9)
7.49 ()
4.35
For each case, only the best result is given as well as the corresponding setting in parentheses (filter size for MF and standard deviation for GF).
Table 4.
PSNR and Stokes Vector Estimation Error Obtained with Two Simplified Versions of the Proposed Approach (NLMPI, NLMPROJ) and with the Proposed Approach for Different Variances of Noise