Abstract
Image matting and segmentation are two closely related topics that concern extracting the foreground and background of an image. While the methods based on global optimization are popular in both fields, the cost functions and the optimization methods have been developed independently due to the different interests of the fields: graph cuts optimize combinatorial functions yielding hard segments, and closed-form matting minimizes quadratic functions yielding soft matte.
In this paper, we note that these seemingly different costs can be represented in very similar convex forms, and suggest a generalized framework based on convex optimization, which reveals a new insight. For the optimization, a primal-dual interior point method is adopted. Under the new perspective, two novel formulations are presented showing how we can improve the state-of-the-art segmentation and matting methods. We believe that this will pave the way for more sophisticated formulations in the future.
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References
Argyriou, A., Evgeniou, T., Pontil, M.: Multi-task feature learning. In: Advances in Neural Information Processing Systems, vol. 19 (2007)
Bhusnurmath, A., Taylor, C.J.: Graph cuts via l\(_{\mbox{1}}\) norm minimization. IEEE Trans. PAMI 30, 1866–1871 (2008)
Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, New York (2004)
Buatois, L., Caumon, G., Levy, B.: Concurrent number cruncher: an efficient sparse linear solver on the GPU. In: High Performance Computation Conference (2007)
Boykov, Y., Veksler, O., Zabih, R.: Fast approximate energy minimization via graph cuts. IEEE Trans. PAMI 23, 2001 (1999)
Ford, L.R., Fulkerson, D.R.: Maximal flow through a network. Canad. J. Math. 8, 399–404 (1956)
Fu, H., Ng, M.K., Nikolova, M., Barlow, J.L.: Efficient minimization methods of mixed l2-l1 and l1-l1 norms for image restoration. SIAM J. Sci. Comput. 27 (2006)
Goldberg, A.V., Tarjan, R.E.: A new approach to the maximum flow problem. In: Eighteenth Annual ACM Symposium on Theory of Computing, pp. 136–146 (1986)
Grady, L.: Random walks for image segmentation. IEEE Trans. PAMI 28(11), 1768–1783 (2006)
Greig, D.M., Porteous, B.T., Seheult, A.H.: Exact maximum a posteriori estimation for binary images. Journal of the Royal Statistical Society (1989)
Gulshan, V., Rother, C., Criminisi, A., Blake, A., Zisserman, A.: Geodesic star convexity for interactive image segmentation. In: CVPR (2010)
He, K., Sun, J., Tang, X.: Fast matting using large kernel matting laplacian matrices. In: CVPR (2010)
Kim, S., Koh, K., Lustig, M., Boyd, S., Gorinevsky, D.: An interior-point method for large-scale l1-regularized least squares. IEEE Journal of Selected Topics in Signal Processing 1, 606–617 (2007)
Lempitsky, V., Kohli, P., Rother, C., Sharp, T.: Image segmentation with a bounding box prior. In: CVPR (2009)
Levin, A., Lischinski, D., Weiss, Y.: A closed-form solution to natural image matting. IEEE Trans. PAMI (2008)
Martin, D., Fowlkes, C., Tal, D., Malik, J.: A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In: ICCV (2001)
Rhemann, C., Rother, C., Gelautz, M.: Improving color modeling for alpha matting. In: BMVC (2008)
Rhemann, C., Rother, C., Rav-Acha, A., Sharp, T.: High resolution matting via interactive trimap segmentation. In: CVPR, pp. 1–8 (2008)
Rhemann, C., Rother, C., Wang, J., Gelautz, M., Kohli, P., Rott, P.: A perceptually motivated online benchmark for image matting. In: CVPR, pp. 1826–1833 (2009)
Rother, C.: Grabcut dataset, http://tinyurl.com/grabcut
Rother, C., Kolmogorov, V., Blake, A.: “GrabCut”: interactive foreground extraction using iterated graph cuts. ACM Trans. Graphics 23, 309–314 (2004)
Singaraju, D., Rother, C., Rhemann, C.: New appearance models for natural image matting. In: CVPR, pp. 659–666 (2009)
Singaraju, D., Vidal, R.: Interactive image matting for multiple layers. In: CVPR (2008)
Sinop, A.K., Grady, L.: A seeded image segmentation framework unifying graph cuts and random walker which yields a new algorithm. In: ICCV, pp. 1–8 (2007)
Vicente, S., Kolmogorov, V., Rother, C.: Graph cut based image segmentation with connectivity priors. In: ICCV (2008)
Wang, J., Cohen, M.F.: Image and video matting: a survey. Foundations and Trends in Computer Graphics and Vision 3, 97–175 (2007)
Wang, J., Cohen, M.F.: Optimized color sampling for robust matting. In: CVPR, pp. 1–8 (2007)
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Park, Y., Yoo, S.I. (2011). A Convex Image Segmentation: Extending Graph Cuts and Closed-Form Matting. In: Kimmel, R., Klette, R., Sugimoto, A. (eds) Computer Vision – ACCV 2010. ACCV 2010. Lecture Notes in Computer Science, vol 6494. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19318-7_28
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DOI: https://doi.org/10.1007/978-3-642-19318-7_28
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