Saturation-Value Total Variation model for chromatic aberration correction

Wei Wang; Ling Pi; Michael K. Ng

doi:10.3934/ipi.2020034

Article Contents

2020, Volume 14, Issue 4: 733-755. Doi: 10.3934/ipi.2020034

This issue Previous Article Extended sampling method for interior inverse scattering problems Next Article

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

^* Corresponding author: Ling Pi
^* Corresponding author: Ling Pi

Received: September 2019

Revised: February 2020

Published: May 2020

Wei Wang is supported by Natural Science Foundation of Shanghai and Fundamental Research Funds for the Central Universities of China (22120180255, 22120180067), Michael K. Ng is supported in part by the HKRGC GRF 12306616, 12200317, 12300218 and 12300519

Abstract / Introduction Full Text(HTML) Figure(11) / Table(3) Related Papers Cited by

Abstract

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.

Keywords:

Mathematics Subject Classification: Primary: 65J22, 65K10, 68U10; Secondary: 65K15.

Citation:

Full Text(HTML)

Figure 1. First row: The ground-truth image; Second row: the CA image; Third row: the CA correction image by using the local PDE method [9]; Forth row: the CA correction image by using the TV method [20] with $ \mu = 45 $; Fifth row: the CA corrected image by using the proposed method with $ \mu = 20 $. Note that the intensity values of red, green and blue colors are shown in line profile images

Download: Full-size image PowerPoint slide

Figure 2. First row: The ground-truth image; Second row: the CA image; Third row: the CA correction image by using the local PDE method [9]; Forth row: the CA correction image by using the TV method $ \mu = 45 $ [20]; Fifth row: the CA corrected image by using the proposed method $ \mu = 20 $. Note that the intensity values of red, green and blue colors are shown in line profile images

Download: Full-size image PowerPoint slide

Figure 3. First row: CA image, Ground-truth, zooming parts; First column (except first row): the restored results by using TV-CAC model with $ \mu = 5, 10, 15, 20, 25 $; Second column (except first row): the restored results by using SVTV-CAC model with $ \mu = 5, 10, 15, 20, 25 $; Third column (except first row): zooming parts of the restored results by using TV-CAC model; Forth column (except first row): zooming parts of the restored results by using SVTV-CAC model

Download: Full-size image PowerPoint slide

Figure 4. Measure distribution

Download: Full-size image PowerPoint slide

Figure 5. From left to right: ground-truth image, CA image, the restored results by using PDE model, the restored results by using TV-CAC model $ \mu = 1 $, the restored results by using SVTV-CAC model $ \mu = 20 $. Second row: the corresponding zooming parts. Third row: S-CIELAB color error distribution

Download: Full-size image PowerPoint slide

Figure 6. From left to right: ground-truth image, CA image, the restored results by using PDE model, the restored results by using TV-CAC model $ \mu = 1 $, the restored results by using SVTV-CAC model $ \mu = 10 $. Second row: the corresponding zooming parts. Third row: S-CIELAB color error distribution

Download: Full-size image PowerPoint slide

Figure 7. From left to right: ground-truth image, CA image, the restored results by using PDE model, the restored results by using TV-CAC model $ \mu = 5 $, the restored results by using SVTV-CAC model $ \mu = 15 $. Second row: the corresponding zooming parts. Third row: S-CIELAB color error distribution

Download: Full-size image PowerPoint slide

Figure 8. From left to right: ground-truth image, CA image, the restored results by using PDE model, the restored results by using TV-CAC model $ \mu = 0.5 $, the restored results by using SVTV-CAC model $ \mu = 15 $. Second row: the corresponding zooming parts. Third row: S-CIELAB color error distribution

Download: Full-size image PowerPoint slide

Figure 9. From left to right: ground-truth image, CA image, the restored results by using PDE model, the restored results by using TV-CAC model $ \mu = 1 $, the restored results by using SVTV-CAC model $ \mu = 20 $. Second row: the corresponding zooming parts. Third row: S-CIELAB color error distribution

Download: Full-size image PowerPoint slide

Figure 10. First row: ground-truth image and CA image; Second row: the restored results by using GW and LC1 respectively; Third row: the restored results by using LC2, FCF and SVTV-CAC respectively

Download: Full-size image PowerPoint slide

Figure 11. First row: original real world image and zooming part; Second row: the restored results by using GW and LC1 respectively; Third row: the restored results by using LC2, and FCF respectively; Fourth row: the restored result by using SVTV-CAC

Download: Full-size image PowerPoint slide

Table 1. Measure values with respect to $ \mu $

Figure	method	PSNR	SSIM	SCIELAB Error
1 by TV-CAC	$ \mu = 30 $	26.8443	0.9745	76557
	$ \mu = 35 $	27.5209	0.9763	69818
	$ \mu = 40 $	28.3432	0.9784	60924
	$ \mu = 45 $	28.8332	0.9796	55742
	$ \mu = 50 $	28.6660	0.9793	56195
	$ \mu = 55 $	27.9948	0.9778	58992
1 by SVTV-CAC	$ \mu = 10 $	28.9121	0.9739	62781
	$ \mu = 15 $	30.6855	0.9793	44484
	$ \mu = 20 $	32.1152	0.9824	33414
	$ \mu = 25 $	30.4036	0.9809	38666
	$ \mu = 30 $	28.7030	0.9774	47549
	$ \mu = 35 $	27.8225	0.9744	56347
2 by TV-CAC	$ \mu = 25 $	26.3643	0.9764	132157
	$ \mu = 30 $	26.4490	0.9764	129911
	$ \mu = 35 $	26.5936	0.9766	125456
	$ \mu = 40 $	26.7426	0.9765	120319
	$ \mu = 45 $	26.8504	0.9761	115719
	$ \mu = 50 $	26.8937	0.9750	111624
	$ \mu = 55 $	26.8625	0.9735	108241
	$ \mu = 60 $	26.7493	0.9712	104724
	$ \mu = 65 $	26.5678	0.9685	102599
2 by SVTV-CAC	$ \mu = 10 $	27.5949	0.9683	39666
	$ \mu = 15 $	28.0019	0.9724	33962
	$ \mu = 20 $	28.4454	0.9743	34005
	$ \mu = 25 $	28.3332	0.9738	35153
	$ \mu = 30 $	27.5742	0.9693	40700
	$ \mu = 35 $	26.4950	0.9604	47721

| Show Table

DownLoad: CSV

Table 2. Measure values of different models

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

| Show Table

DownLoad: CSV

Table 3. Measure values of different models

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

| Show Table

DownLoad: CSV

Related Papers

Cited by

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.