Colm Lynch and Nicholas Devaney, "Registration for images in the presence of additive and multiplicative fixed-pattern noise," Appl. Opt. 57, 1824-1831 (2018)
Image registration under conditions of fixed-pattern noise is a difficult problem that has not been solved in the literature. While traditional registration methods are adequate for additive random noise, these are not suited to spatially invariant noise that is additive or multiplicative. We present a method for image registration using a difference operation in the frequency domain. Shift values are then computed by dividing by the object Fourier transform and inverse transforming. The method described is valid for both additive and multiplicative noise and determines shifts with sub-pixel accuracy. Additionally, minimal prior knowledge of the corrupting pattern is required. We compare our method with previous registration methods for varying amounts of noise. Results are presented for both simulated images and images recorded from a thermal camera with significant fixed-pattern noise.
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Mean-Absolute-Difference Comparisons of Registration Methods for Various Images with No FPNa
Image
Barb
0.049, 0.047
0.183, 0.971
4.096, 4.543
0.256, 0.159
Mand
0.044, 0.053
0.091, 3.418
3.820, 4.276
0.180, 0.212
Cam
0.052, 0.053
2.972, 0.516
3.843, 4.222
0.179, 0.176
USAF
0.040, 0.044
0.060, 0.047
4.048, 4.373
0.219, 0.283
MAD values are listed for each method for and shifts, respectively. The Barbara, Mandrill, Cameraman, and USAF test images are used. Registration methods tested are the proposed, PAC, DOCP, and phase-correlation methods. The maximum MAD values measured for the proposed method were Barb = 0.757, Mandrill = 0.759, Cameraman = 0.754, and USAF = 0.760.
Table 2.
Standard Deviation of Absolute Differences for Various Images with No FPNa
Image
Barb
0.039, 0.049
0.140, 0.292
5.127, 6.645
0.554, 0.184
Mand
0.038, 0.050
0.053, 1.967
4.947, 8.504
0.212, 0.222
Cam
0.044, 0.052
2.304, 0.155
4.734, 6.322
0.216, 0.219
USAF
0.035, 0.049
0.046, 0.022
4.804, 5.754
0.998, 2.166
Standard deviation values are listed for each method for and shifts, respectively. The associated MAD values are shown in Table 1.
Table 3.
Registration Results for Images with Additive Simulated Gaussian Term Using the Barbara Test Imagea
FWHM
25
0.0495
0.0491
0.693
0.550
4.285
4.993
50
0.0499
0.0493
0.716
0.617
4.282
4.972
75
0.0501
0.0494
0.725
0.636
4.285
4.977
100
0.0502
0.0495
0.717
0.693
4.283
4.978
MAD measured for increasing FWHM. The maximum amplitude of the Gaussian terms was fixed at 100, which corresponds to a peak-to-signal value of 0.922 at the image center. Higher precision is used for the proposed method to show an increasing MAD. The maximum MAD values recorded for increasing values of FWHM were 0.780, 0.799, 0.778, 0.778.
Table 4.
Standard Deviation of Absolute Differences for Images with Additive Gaussian FPNa
FWHM
25
0.0398
0.0501
0.503
0.219
5.209
7.384
50
0.0398
0.0503
0.517
0.224
5.211
7.366
75
0.0398
0.0502
0.528
0.226
5.216
7.385
100
0.0399
0.0504
0.517
0.221
5.215
7.390
Standard deviations here correspond to values presented in Table 3.
Table 5.
Registration Results for Images with Random Gaussian Noise and Additive FPN Watermarka
4
1
0.051
0.053
3.763
3.695
5.811
5.774
8
2
0.054
0.062
3.763
3.697
6.692
6.550
12
3
0.055
0.068
3.763
3.699
7.344
6.959
16
4
0.061
0.081
3.763
3.701
7.682
7.008
20
5
0.070
0.089
3.764
3.704
8.198
7.545
Watermark amplitude was fixed at 100. Additive random noise is normally distributed with mean and standard deviation . The Barbara image was used for testing. The largest values of MAD recorded for increasing and were 0.798, 0.804, 0.807, 0.928.
Table 6.
Standard Deviation of Absolute Difference for Images Corrupted by an Additive Watermark with Gaussian Noisea
Registration Results for Simulated Images Corrupted by a Multiplicative Fixed Pattern of Ones and Zerosa
0.025
0.043, 0.045
0.041, 0.053
1.611, 0.477
1.152, 0.380
0.050
0.045, 0.045
0.039, 0.041
1.684, 0.686
1.237, 0.648
0.100
0.056, 0.058
0.322, 0.498
1.877, 1.204
1.476, 1.148
0.200
0.073, 0.088
1.402, 0.791
2.228, 2.358
1.733, 1.786
0.300
0.089, 0.124
3.909, 4.524
2.446, 3.206
1.832, 1.959
0.400
0.153, 0.181
3.551, 3.427
2.664, 3.394
1.865, 1.983
MAD values measured for increasing value of [Eq. (30)]. The Barbara image was used for testing. Standard deviations for this set of data are denoted by . For increasing values of , the maximum MAD values recorded were 3.107, 0.806, 0.88, 0.934, 5.685.
Table 8.
Registration Results for Simulated Images with Saturated Columnsa
0.050
0.074, 0.080
0.073, 0.085
3.479, 0.555
1.970, 0.276
0.074
0.081, 0.088
0.080, 0.098
3.484, 0.549
1.969, 0.278
0.099
0.087, 0.100
0.084, 0.117
3.486, 0.546
1.970, 0.280
is a measure of saturated columns. The Barbara image was used for testing. The standard deviation of the absolute difference is shown for both the proposed and PAC methods, denoted by . The maximum MAD values recorded were 1.153, 1.664, 2.105 for an increasing value of .
Tables (8)
Table 1.
Mean-Absolute-Difference Comparisons of Registration Methods for Various Images with No FPNa
Image
Barb
0.049, 0.047
0.183, 0.971
4.096, 4.543
0.256, 0.159
Mand
0.044, 0.053
0.091, 3.418
3.820, 4.276
0.180, 0.212
Cam
0.052, 0.053
2.972, 0.516
3.843, 4.222
0.179, 0.176
USAF
0.040, 0.044
0.060, 0.047
4.048, 4.373
0.219, 0.283
MAD values are listed for each method for and shifts, respectively. The Barbara, Mandrill, Cameraman, and USAF test images are used. Registration methods tested are the proposed, PAC, DOCP, and phase-correlation methods. The maximum MAD values measured for the proposed method were Barb = 0.757, Mandrill = 0.759, Cameraman = 0.754, and USAF = 0.760.
Table 2.
Standard Deviation of Absolute Differences for Various Images with No FPNa
Image
Barb
0.039, 0.049
0.140, 0.292
5.127, 6.645
0.554, 0.184
Mand
0.038, 0.050
0.053, 1.967
4.947, 8.504
0.212, 0.222
Cam
0.044, 0.052
2.304, 0.155
4.734, 6.322
0.216, 0.219
USAF
0.035, 0.049
0.046, 0.022
4.804, 5.754
0.998, 2.166
Standard deviation values are listed for each method for and shifts, respectively. The associated MAD values are shown in Table 1.
Table 3.
Registration Results for Images with Additive Simulated Gaussian Term Using the Barbara Test Imagea
FWHM
25
0.0495
0.0491
0.693
0.550
4.285
4.993
50
0.0499
0.0493
0.716
0.617
4.282
4.972
75
0.0501
0.0494
0.725
0.636
4.285
4.977
100
0.0502
0.0495
0.717
0.693
4.283
4.978
MAD measured for increasing FWHM. The maximum amplitude of the Gaussian terms was fixed at 100, which corresponds to a peak-to-signal value of 0.922 at the image center. Higher precision is used for the proposed method to show an increasing MAD. The maximum MAD values recorded for increasing values of FWHM were 0.780, 0.799, 0.778, 0.778.
Table 4.
Standard Deviation of Absolute Differences for Images with Additive Gaussian FPNa
FWHM
25
0.0398
0.0501
0.503
0.219
5.209
7.384
50
0.0398
0.0503
0.517
0.224
5.211
7.366
75
0.0398
0.0502
0.528
0.226
5.216
7.385
100
0.0399
0.0504
0.517
0.221
5.215
7.390
Standard deviations here correspond to values presented in Table 3.
Table 5.
Registration Results for Images with Random Gaussian Noise and Additive FPN Watermarka
4
1
0.051
0.053
3.763
3.695
5.811
5.774
8
2
0.054
0.062
3.763
3.697
6.692
6.550
12
3
0.055
0.068
3.763
3.699
7.344
6.959
16
4
0.061
0.081
3.763
3.701
7.682
7.008
20
5
0.070
0.089
3.764
3.704
8.198
7.545
Watermark amplitude was fixed at 100. Additive random noise is normally distributed with mean and standard deviation . The Barbara image was used for testing. The largest values of MAD recorded for increasing and were 0.798, 0.804, 0.807, 0.928.
Table 6.
Standard Deviation of Absolute Difference for Images Corrupted by an Additive Watermark with Gaussian Noisea
Registration Results for Simulated Images Corrupted by a Multiplicative Fixed Pattern of Ones and Zerosa
0.025
0.043, 0.045
0.041, 0.053
1.611, 0.477
1.152, 0.380
0.050
0.045, 0.045
0.039, 0.041
1.684, 0.686
1.237, 0.648
0.100
0.056, 0.058
0.322, 0.498
1.877, 1.204
1.476, 1.148
0.200
0.073, 0.088
1.402, 0.791
2.228, 2.358
1.733, 1.786
0.300
0.089, 0.124
3.909, 4.524
2.446, 3.206
1.832, 1.959
0.400
0.153, 0.181
3.551, 3.427
2.664, 3.394
1.865, 1.983
MAD values measured for increasing value of [Eq. (30)]. The Barbara image was used for testing. Standard deviations for this set of data are denoted by . For increasing values of , the maximum MAD values recorded were 3.107, 0.806, 0.88, 0.934, 5.685.
Table 8.
Registration Results for Simulated Images with Saturated Columnsa
0.050
0.074, 0.080
0.073, 0.085
3.479, 0.555
1.970, 0.276
0.074
0.081, 0.088
0.080, 0.098
3.484, 0.549
1.969, 0.278
0.099
0.087, 0.100
0.084, 0.117
3.486, 0.546
1.970, 0.280
is a measure of saturated columns. The Barbara image was used for testing. The standard deviation of the absolute difference is shown for both the proposed and PAC methods, denoted by . The maximum MAD values recorded were 1.153, 1.664, 2.105 for an increasing value of .