Citation: |
[1] |
L. Ambrosio and S. Masnou, A direct variational approach to a problem arising in image reconstruction, Interfaces and Free Boundaries, 5 (2003), 63-81.doi: 10.4171/IFB/72. |
[2] |
L. Ambrosio and S. Masnou, On a variational problem arising in image reconstruction, In "Proc. Free Boundary Problems," volume 147 of Internat. Series of Num. Math., Basel, 2004. Birkhauser, 17-26. |
[3] |
G. Aubert and P. Kornprobst, "Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations," Second edition. With a foreword by Olivier Faugeras. Applied Mathematical Sciences, 147. Springer, New York, 2006. |
[4] |
E. Bae, J. Shi, and X. C. Tai, Graph cuts for curvature based image denoising, IEEE Trans. Image Process, 20(2011), 1199-1210.doi: 10.1109/TIP.2010.2090533. |
[5] |
P. Blomgren, P. Mulet, T. Chan and C. Wong, Total variation image restoration: Numerical methods and extensions, In "ICIP," pages 384-387, Santa Barbara, 1997.doi: 10.1109/ICIP.1997.632128. |
[6] |
C. Brito and K. Chen, Fast numerical algorithms for Euler's elastica inpainting model, Int. J. Modern Math., 5 (2010), 157-182. |
[7] |
C. Brito and K. Chen, Multigrid algorithm for high order denoising, SIAM J. Imaging Sci., 3 (2010), 363-389.doi: 10.1137/080737903. |
[8] |
A. Chambolle and P. Lions, Image recovery via total variation minimization and related problems, Numer. Math., 76 (1997), 167-188.doi: 10.1007/s002110050258. |
[9] |
T. Chan, G. Golub and P. Mulet, A nonlinear primal-dual method for total variation-based image restoration, SIAM J. Sci. Comp., 20 (1999), 1964-1977.doi: 10.1137/S1064827596299767. |
[10] |
T. Chan, S. Kang and J. Shen, Euler's elastica and curvature-based image inpainting, SIAM J. Appl. Math., 63 (2002), 564-592.doi: 10.1137/S0036139901390088. |
[11] |
T. Chan, M. Marquina and P. Mulet, High-order total variation-based image restoration, SIAM J. Sci. Comput., 22 (2000), 503-516.doi: 10.1137/S1064827598344169. |
[12] |
T. F. Chan and J. Shen, "Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods," Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2005.doi: 10.1137/1.9780898717877. |
[13] |
T. F. Chan, S. Esedo$\barg$lu and F. Park, A fourth order dual method for staircase reduction in texture extraction and image restoration problems, In "Proceedings of 2010 IEEE 17th Int. Conf. on Image Process," pages 4137-4140, Hong Kong, 2010.doi: 10.1109/ICIP.2010.5653199. |
[14] |
T. F. Chan, S. Esedo$\barg$lu, F. E. Park and A. M. Yip, Recent developments in total variation image restoration, In Nikos Paragios, Yunmei Chen, and Olivier Faugeras, Editors, Handbook of Mathematical Models in Computer Vision, pages 17-31. Springer, Berlin, 2005.doi: 10.1007/0-387-28831-7_2. |
[15] |
M. Elsey and S. Esedo$\barg$lu, Analogue of the total variation denoising model in the context of geometry processing, SIAM J. Imaging Sci., 7 (2009), 1549-1573.doi: 10.1137/080736612. |
[16] |
S. Esedo$\barg$lu and R. March, Segmentation with depth but without detecting junctions, Special issue on imaging science (Boston, MA, 2002). J. Math. Imaging and Vision, 18 (2003), 7-15.doi: 10.1023/A:1021837026373. |
[17] |
S. Esedo$\barg$lu and J. Shen, Digital inpainting based on the Mumford-Shah-Euler image model, European J. Appl. Math., 13 (2002), 353-370.doi: 10.1017/S0956792502004904. |
[18] |
J. B. Greer and A. L. Bertozzi, Traveling wave solutions of fourth order PDEs for image processing, SIAM J. Math. Anal., 36 (2004), 38-68.doi: 10.1137/S0036141003427373. |
[19] |
K. Ito and K. Kunisch, An active set strategy based on the augmented Lagrangian formulation for image restoration, RAIRO Math. Mod. and Num. Analysis, 33 (1999), 1-21.doi: 10.1051/m2an:1999102. |
[20] |
T. S. Lau and A. M. Yip, A fast method to segment images with additive intesity value, SIAM J. Imaging Sci., 5 (2012), 993-1021.doi: 10.1137/120863617. |
[21] |
Y. N. Law, H. K. Lee, C. Liu and A. M. Yip, A variational model for segmentation of overlapping objects with additive intensity value, IEEE Trans. Image Process., 20 (2011), 1495-1503.doi: 10.1109/TIP.2010.2095868. |
[22] |
M. Lysaker, A. Lundervold and X. C. Tai, Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time, IEEE Trans. Image Process., 12 (2003), 1579-1590.doi: 10.1109/TIP.2003.819229. |
[23] |
S. Masnou, Disocclusion: A variational approach using level lines, IEEE Trans. Image Process., 11 (2002), 68-76.doi: 10.1109/83.982815. |
[24] |
S. Masnou and J. M. Morel, Level lines based disocclusion, In "Proc. IEEE Int. Conf. on Image Process.," pages 259-263, Chicago, IL, 1998.doi: 10.1109/ICIP.1998.999016. |
[25] |
Y. Meyer, "Oscillating Patterns in Image Processing and Nonlinear Evolution Equations," The fifteenth Dean Jacqueline B. Lewis memorial lectures. University Lecture Series, 22. AMS, Providence, Rhode Island, 2001. |
[26] |
D. Mumford, Elastica and computer vision, Algebraic Geometry and its Applications, 491-506, Springer, New York, (1994). |
[27] |
M. Nitzberg and D. Mumford, The 2.1D sketch, In "Proc. of the 3rd Intl. Conf. on Computer Vision," pages 138-144, 1990. |
[28] |
M. Nitzberg, D. Mumford and T. Shiota, "Filtering, Segmentation, and Depth," Lecture Notes in Computer Science, 662. Springer-Verlag, New York, 1993.doi: 10.1007/3-540-56484-5. |
[29] |
L. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D, 60 (1992), 259-268.doi: 10.1016/0167-2789(92)90242-F. |
[30] |
P. Smereka, Semi-implicit level set methods for curvature and surface diffusion motion, J. Sci. Comput., 19 (2003), 439-456.doi: 10.1023/A:1025324613450. |
[31] |
D. M. Strong, P. Blomgren and T. F. Chan, Spatially adaptive local feature-driven total variation minimizing image restoration, In "Proceedings of The International Society of Photo-Optical Instrumentation Engineers: Statistical and Stochastic Methods in Image Processing II," 3167 (1997), 222-233.doi: 10.1117/12.279642. |
[32] |
X. C. Tai, J. Hahn, and G. J. Chung, A fast algorithm for Euler's elastica model using augmented Lagrangian method, SIAM J. Imaging Sci., 4 (2011), 313-344.doi: 10.1137/100803730. |
[33] |
C. Wu and X. C. Tai, Augmented Lagrangian method, dual methods, and split Bregman iteration for ROF, vectorial TV, and higher order models, SIAM J. Imaging Sci., 3 (2010), 300-339.doi: 10.1137/090767558. |
[34] |
Y. L. You and M. Kaveh, Fourth-order partial differential equations for noise removal, IEEE Trans. Image Process., 9 (2000), 1723-1730.doi: 10.1109/83.869184. |
[35] |
W. Zhu and T. Chan, A variational model for capturing illusory contours using curvature, J. Math. Imaging. Vis., 27 (2007), 29-40.doi: 10.1007/s10851-006-9695-8. |
[36] |
W. Zhu, T. Chan and S. Esedo\barglu, Segmentation with depth: A level set approach, SIAM J. Sci. Comput., 28 (2006), 1957-1973.doi: 10.1137/050622213. |
[37] |
W. Zhu and T. F. Chan, Image denoising using mean curvature of image surface, SIAM J. Imaging Sci., 5 (2012), 1-32.doi: 10.1137/110822268. |
[38] |
W. Zhu, X. C. Tai and T. F. Chan, Augmented Lagrangian method for a mean curvature based image denoising model, UCLA CAM Report, 12-02, 2012. |