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Extended sampling method for interior inverse scattering problems
Saturation-Value Total Variation model for chromatic aberration correction
1. | School of Mathematical Sciences, Tongji University, Shanghai, China |
2. | School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China |
3. | Department of Mathematics, The University of Hong Kong, Pokfulam, Hong Kong |
Chromatic aberration generally occurs in the regions of sharp edges in captured digital color images. The main aim of this paper is to propose and develop a novel Saturation-Value Total Variation (SVTV) model for chromatic aberration correction. In the proposed optimization model, there are three terms for the correction purpose. The SVTV regularization term is to model the target color image in HSV color space instead of RGB color space, and to avoid oscillations in the recovering process. In correction process, the gradient matching terms based on the green component are used to govern both red and blue components, and the intensity terms are employed to fit red, green and blue data components. The existence of the minimizer of the optimization model is analyzed and an efficient optimization algorithm is also developed for solving the resulting variational problem. Experimental results are presented to illustrate the effectiveness of the proposed model and to show that the correction results are better than those by using the other testing methods.
References:
[1] |
G. Aubert and P. Kornprobst, Mathematical Problems in Image Processing, Springer-Verlag, New York, 2002. |
[2] |
B. E. Bayer, Color Imaging Array, U.S. Patent No. 3971065, 1976. |
[3] |
T. E. Boult and G. Wolberg, Correcting chromatic aberrations using image warping, in Proceedings 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1992,684–687. |
[4] |
J. Chang, H. Kang and M. G. Kang,
Correction of axial and lateral chromatic aberration with false color filtering, IEEE Trans. Image Process., 22 (2013), 1186-1198.
doi: 10.1109/TIP.2012.2228489. |
[5] |
D. Gabay and B. Mercier,
A dual algorithm for the solution of nonlinear variational problems via finite element approximation, Comput. Math. Appl., 2 (1976), 17-40.
|
[6] |
N. A. Ibraheem, M. M. Hasan, R. Z. Khan and P. K. Mishra,
Understanding color models: A review, ARPN Journal of Science and Technology, 2 (2012), 265-275.
|
[7] |
Z. Jia, M. K. Ng and W. Wang,
Color image restoration by saturation-value (SV) total variation, SIAM J. Imaging Sci., 12 (2019), 972-1000.
doi: 10.1137/18M1230451. |
[8] |
S. B. Kang, Automatic removal of chromatic aberration from a single image, in 2007 IEEE Conference on Computer Vision and Pattern Recognition, 2007, 1–8. |
[9] |
H. Kang, S.-H. Lee, J. Chang and M. G. Kang,
Partial differential equation-based approach for removal of chromatic aberration with local characteristics, J. of Electronic Imaging, 19 (2010), 1-8.
|
[10] |
V. Kaufmann and R. Ladstädter, Elimination of color fringes in digital photographs caused by lateral chromatic aberration, in Proc. 20th Int. Comm. Int. Photogramm. Archit. Symp. Conf., Oct., 2005, 1–6. |
[11] |
H. K. Kelda and P. Kaur,
A review: Color models in image processing, Int. J. Computer Technology and Applications, 5 (2014), 319-322.
|
[12] |
B. Kim and R. Park, Automatic detection and correction of purple fringing using the gradient information and desaturation, in Proc. 16th Eur. Signal Process. Conf., Oct., 2008, 1–5. |
[13] |
R. Kimmel,
Demosaicing: Image reconstruction from color CCD samples, IEEE Trans. Image Process., 8 (1999), 1221-1228.
|
[14] |
H. Kour,
Analysis on image color model, International Journal of Advanced Research in Computer and Communication Engineering, 4 (2015), 1-3.
|
[15] |
P. B. Kruger, S. Mathews, K. R. Aggarwala and N. Sanchez,
Chromatic aberration and ocular focus: Fincham revisited, Vision Research, 33 (1993), 1397-1411.
doi: 10.1016/0042-6989(93)90046-Y. |
[16] |
J. Mallon and P. F. Whelan,
Calibration and removal of lateral chromatic aberration in images, Pattern Recognition Letters, 28 (2007), 125-135.
doi: 10.1016/j.patrec.2006.06.013. |
[17] |
D. H. Marimont and B. A. Wandell,
Matching color images: The effects of axial chromatic aberration, Journal of the Optical Society of America A, 11 (1994), 3113-3122.
doi: 10.1364/JOSAA.11.003113. |
[18] |
D. Martin, C. Fowlkes, D. Tal and J. Malik,
A Database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics, Proceedings of IEEE International Conference on Computer Vision (ICCV) 2001, 2 (2001), 416-423.
doi: 10.1109/ICCV.2001.937655. |
[19] |
P. Mouroulis and J. Macdonald, Geometrical Optics and Optical Design, 1$^{st}$ edition, Oxford U. Press, New York, 1997.
![]() |
[20] |
L. Pi, W. Wang and M. Ng,
A spatially variant total variational model for chromatic aberration correction, Journal of Visual Communication and Image Representation, 41 (2016), 296-304.
doi: 10.1016/j.jvcir.2016.10.009. |
[21] |
L. N. Thibos, A. Bradley, D. L. Still, X. Zhang and P. A. Howarth,
Theory and measurement of ocular chromatic aberration, Vision Research, 30 (1990), 33-49.
doi: 10.1016/0042-6989(90)90126-6. |
[22] |
R. G. Willson and S. A. Shafer,
Active lens control for high precision computer imaging, IEEE International Conference on Robotics and Automation, 3 (1991), 2063-2070.
doi: 10.1109/ROBOT.1991.131931. |
[23] |
X. Zhang and B. A. Wandell,
A spatial extension of CIELAB for digital color-image reproduction, Journal of the Society for Information Display, 5 (1997), 61-63.
doi: 10.1889/1.1985127. |
show all references
References:
[1] |
G. Aubert and P. Kornprobst, Mathematical Problems in Image Processing, Springer-Verlag, New York, 2002. |
[2] |
B. E. Bayer, Color Imaging Array, U.S. Patent No. 3971065, 1976. |
[3] |
T. E. Boult and G. Wolberg, Correcting chromatic aberrations using image warping, in Proceedings 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1992,684–687. |
[4] |
J. Chang, H. Kang and M. G. Kang,
Correction of axial and lateral chromatic aberration with false color filtering, IEEE Trans. Image Process., 22 (2013), 1186-1198.
doi: 10.1109/TIP.2012.2228489. |
[5] |
D. Gabay and B. Mercier,
A dual algorithm for the solution of nonlinear variational problems via finite element approximation, Comput. Math. Appl., 2 (1976), 17-40.
|
[6] |
N. A. Ibraheem, M. M. Hasan, R. Z. Khan and P. K. Mishra,
Understanding color models: A review, ARPN Journal of Science and Technology, 2 (2012), 265-275.
|
[7] |
Z. Jia, M. K. Ng and W. Wang,
Color image restoration by saturation-value (SV) total variation, SIAM J. Imaging Sci., 12 (2019), 972-1000.
doi: 10.1137/18M1230451. |
[8] |
S. B. Kang, Automatic removal of chromatic aberration from a single image, in 2007 IEEE Conference on Computer Vision and Pattern Recognition, 2007, 1–8. |
[9] |
H. Kang, S.-H. Lee, J. Chang and M. G. Kang,
Partial differential equation-based approach for removal of chromatic aberration with local characteristics, J. of Electronic Imaging, 19 (2010), 1-8.
|
[10] |
V. Kaufmann and R. Ladstädter, Elimination of color fringes in digital photographs caused by lateral chromatic aberration, in Proc. 20th Int. Comm. Int. Photogramm. Archit. Symp. Conf., Oct., 2005, 1–6. |
[11] |
H. K. Kelda and P. Kaur,
A review: Color models in image processing, Int. J. Computer Technology and Applications, 5 (2014), 319-322.
|
[12] |
B. Kim and R. Park, Automatic detection and correction of purple fringing using the gradient information and desaturation, in Proc. 16th Eur. Signal Process. Conf., Oct., 2008, 1–5. |
[13] |
R. Kimmel,
Demosaicing: Image reconstruction from color CCD samples, IEEE Trans. Image Process., 8 (1999), 1221-1228.
|
[14] |
H. Kour,
Analysis on image color model, International Journal of Advanced Research in Computer and Communication Engineering, 4 (2015), 1-3.
|
[15] |
P. B. Kruger, S. Mathews, K. R. Aggarwala and N. Sanchez,
Chromatic aberration and ocular focus: Fincham revisited, Vision Research, 33 (1993), 1397-1411.
doi: 10.1016/0042-6989(93)90046-Y. |
[16] |
J. Mallon and P. F. Whelan,
Calibration and removal of lateral chromatic aberration in images, Pattern Recognition Letters, 28 (2007), 125-135.
doi: 10.1016/j.patrec.2006.06.013. |
[17] |
D. H. Marimont and B. A. Wandell,
Matching color images: The effects of axial chromatic aberration, Journal of the Optical Society of America A, 11 (1994), 3113-3122.
doi: 10.1364/JOSAA.11.003113. |
[18] |
D. Martin, C. Fowlkes, D. Tal and J. Malik,
A Database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics, Proceedings of IEEE International Conference on Computer Vision (ICCV) 2001, 2 (2001), 416-423.
doi: 10.1109/ICCV.2001.937655. |
[19] |
P. Mouroulis and J. Macdonald, Geometrical Optics and Optical Design, 1$^{st}$ edition, Oxford U. Press, New York, 1997.
![]() |
[20] |
L. Pi, W. Wang and M. Ng,
A spatially variant total variational model for chromatic aberration correction, Journal of Visual Communication and Image Representation, 41 (2016), 296-304.
doi: 10.1016/j.jvcir.2016.10.009. |
[21] |
L. N. Thibos, A. Bradley, D. L. Still, X. Zhang and P. A. Howarth,
Theory and measurement of ocular chromatic aberration, Vision Research, 30 (1990), 33-49.
doi: 10.1016/0042-6989(90)90126-6. |
[22] |
R. G. Willson and S. A. Shafer,
Active lens control for high precision computer imaging, IEEE International Conference on Robotics and Automation, 3 (1991), 2063-2070.
doi: 10.1109/ROBOT.1991.131931. |
[23] |
X. Zhang and B. A. Wandell,
A spatial extension of CIELAB for digital color-image reproduction, Journal of the Society for Information Display, 5 (1997), 61-63.
doi: 10.1889/1.1985127. |











Figure | method | PSNR | SSIM | SCIELAB Error |
1 by TV-CAC | 26.8443 | 0.9745 | 76557 | |
27.5209 | 0.9763 | 69818 | ||
28.3432 | 0.9784 | 60924 | ||
28.8332 | 0.9796 | 55742 | ||
28.6660 | 0.9793 | 56195 | ||
27.9948 | 0.9778 | 58992 | ||
1 by SVTV-CAC | 28.9121 | 0.9739 | 62781 | |
30.6855 | 0.9793 | 44484 | ||
32.1152 | 0.9824 | 33414 | ||
30.4036 | 0.9809 | 38666 | ||
28.7030 | 0.9774 | 47549 | ||
27.8225 | 0.9744 | 56347 | ||
2 by TV-CAC | 26.3643 | 0.9764 | 132157 | |
26.4490 | 0.9764 | 129911 | ||
26.5936 | 0.9766 | 125456 | ||
26.7426 | 0.9765 | 120319 | ||
26.8504 | 0.9761 | 115719 | ||
26.8937 | 0.9750 | 111624 | ||
26.8625 | 0.9735 | 108241 | ||
26.7493 | 0.9712 | 104724 | ||
26.5678 | 0.9685 | 102599 | ||
2 by SVTV-CAC | 27.5949 | 0.9683 | 39666 | |
28.0019 | 0.9724 | 33962 | ||
28.4454 | 0.9743 | 34005 | ||
28.3332 | 0.9738 | 35153 | ||
27.5742 | 0.9693 | 40700 | ||
26.4950 | 0.9604 | 47721 |
Figure | method | PSNR | SSIM | SCIELAB Error |
1 by TV-CAC | 26.8443 | 0.9745 | 76557 | |
27.5209 | 0.9763 | 69818 | ||
28.3432 | 0.9784 | 60924 | ||
28.8332 | 0.9796 | 55742 | ||
28.6660 | 0.9793 | 56195 | ||
27.9948 | 0.9778 | 58992 | ||
1 by SVTV-CAC | 28.9121 | 0.9739 | 62781 | |
30.6855 | 0.9793 | 44484 | ||
32.1152 | 0.9824 | 33414 | ||
30.4036 | 0.9809 | 38666 | ||
28.7030 | 0.9774 | 47549 | ||
27.8225 | 0.9744 | 56347 | ||
2 by TV-CAC | 26.3643 | 0.9764 | 132157 | |
26.4490 | 0.9764 | 129911 | ||
26.5936 | 0.9766 | 125456 | ||
26.7426 | 0.9765 | 120319 | ||
26.8504 | 0.9761 | 115719 | ||
26.8937 | 0.9750 | 111624 | ||
26.8625 | 0.9735 | 108241 | ||
26.7493 | 0.9712 | 104724 | ||
26.5678 | 0.9685 | 102599 | ||
2 by SVTV-CAC | 27.5949 | 0.9683 | 39666 | |
28.0019 | 0.9724 | 33962 | ||
28.4454 | 0.9743 | 34005 | ||
28.3332 | 0.9738 | 35153 | ||
27.5742 | 0.9693 | 40700 | ||
26.4950 | 0.9604 | 47721 |
Figure | method | PSNR | SSIM | SCIELAB Error |
5 | PDE | 21.0142 | 0.9076 | 52054 |
TV | 22.9057 | 0.9587 | 54186 | |
SVTV | 26.1505 | 0.9644 | 32019 | |
6 | PDE | 27.2024 | 0.9531 | 24001 |
TV | 26.6299 | 0.9603 | 50560 | |
SVTV | 27.8191 | 0.9611 | 21604 | |
7 | PDE | 25.5506 | 0.9533 | 29722 |
TV | 27.4673 | 0.9762 | 39483 | |
SVTV | 28.2084 | 0.9776 | 18815 | |
8 | PDE | 24.9437 | 0.9389 | 27986 |
TV | 27.4506 | 0.9787 | 65008 | |
SVTV | 30.0501 | 0.9835 | 9287 | |
9 | PDE | 35.9356 | 0.9864 | 6197 |
TV | 35.4925 | 0.9883 | 6444 | |
SVTV | 36.3883 | 0.9892 | 4130 |
Figure | method | PSNR | SSIM | SCIELAB Error |
5 | PDE | 21.0142 | 0.9076 | 52054 |
TV | 22.9057 | 0.9587 | 54186 | |
SVTV | 26.1505 | 0.9644 | 32019 | |
6 | PDE | 27.2024 | 0.9531 | 24001 |
TV | 26.6299 | 0.9603 | 50560 | |
SVTV | 27.8191 | 0.9611 | 21604 | |
7 | PDE | 25.5506 | 0.9533 | 29722 |
TV | 27.4673 | 0.9762 | 39483 | |
SVTV | 28.2084 | 0.9776 | 18815 | |
8 | PDE | 24.9437 | 0.9389 | 27986 |
TV | 27.4506 | 0.9787 | 65008 | |
SVTV | 30.0501 | 0.9835 | 9287 | |
9 | PDE | 35.9356 | 0.9864 | 6197 |
TV | 35.4925 | 0.9883 | 6444 | |
SVTV | 36.3883 | 0.9892 | 4130 |
Figure | method | PSNR | SSIM | SCIELAB Error |
10 | CM1 | 26.2709 | 0.8654 | 18085 |
CM2 | 24.9585 | 0.8485 | 23807 | |
CM3 | 28.2337 | 0.8956 | 13936 | |
PM | 26.3282 | 0.8559 | 15946 | |
SVTV | 31.5037 | 0.9450 | 6768 |
Figure | method | PSNR | SSIM | SCIELAB Error |
10 | CM1 | 26.2709 | 0.8654 | 18085 |
CM2 | 24.9585 | 0.8485 | 23807 | |
CM3 | 28.2337 | 0.8956 | 13936 | |
PM | 26.3282 | 0.8559 | 15946 | |
SVTV | 31.5037 | 0.9450 | 6768 |
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