Abstract
Most image labeling problems such as segmentation and image reconstruction are fundamentally ill-posed and suffer from ambiguities and noise. Higher-order image priors encode high-level structural dependencies between pixels and are key to overcoming these problems. However, in general these priors lead to computationally intractable models. This paper addresses the problem of discovering compact representations of higher-order priors which allow efficient inference. We propose a framework for solving this problem that uses a recently proposed representation of higher-order functions which are encoded as lower envelopes of linear functions. Maximum a Posterior inference on our learned models reduces to minimizing a pairwise function of discrete variables. We show that our framework can learn a compact representation that approximates a low curvature shape prior and demonstrate its effectiveness in solving shape inpainting and image segmentation problems.
A. Shekhovtsov was supported by EU project FP7-ICT-247870 NIFTi.
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Shekhovtsov, A., Kohli, P., Rother, C.: Curvature prior for MRF-based segmentation and shape inpainting. Tech. rep., research Report CTU–CMP–2011–11, Czech Technical University (2011)
Barnes, C., Shechtman, E., Finkelstein, A., Goldman, D.B.: Patchmatch: a randomized correspondence algorithm for structural image editing. ACM Trans. Graph. 28(3) (2009)
Bertozzi, A., Esedoglu, S., Gillette, A.: Inpainting of binary images using the Cahn-Hilliard equation. IP 16 (2007)
Boykov, Y., Jolly, P.: Interactive graph cuts for optimal boundary & region segmentation of objects in N-D images. In: ICCV (2001)
Bredies, K., Pock, T., Wirth, B.: Convex relaxation of a class of vertex penalizing functionals (preprint)
Chan, T.F., Shen, J.: Non-texture inpainting by curvature-driven diffusions (CDD). JVCIR 12 (2001)
El-Zehiry, N.Y., Grady, L.: Fast global optimization of curvature. In: CVPR (2010)
Esedoglu, S., March, R.: Segmentation with depth but without detecting junctions. JMIV 18 (2003)
Goldluecke, B., Cremers, D.: Introducing total curvature for image processing. In: ICCV (2011)
Gupta, R., Diwan, A.A., Sarawagi, S.: Efficient inference with cardinality-based clique potentials. In: ICML (2007)
Hinton, G.E.: Products of experts. In: ICANN (1999)
Kohli, P., Kumar, M.: Energy minimization for linear envelope MRFs. In: CVPR (2010)
Kohli, P., Ladicky, L., Torr, P.: Robust higher order potentials for enforcing label consistency. IJCV 82 (2009)
Kolmogorov, V., Zabin, R.: What energy functions can be minimized via graph cuts? PAMI 26 (2004)
Komodakis, N., Paragios, N.: Beyond pairwise energies: Efficient optimization for higher-order MRFs. In: CVPR (2009)
Nowozin, S., Lampert, C.: Global connectivity potentials for random field models. In: CVPR (2009)
Ramalingam, S., Kohli, P., Alahari, K., Torr, P.: Exact inference in multi-label CRFs with higher order cliques. In: CVPR (2008)
Roth, S., Black, M.: Fields of experts. IJCV 82 (2009)
Rother, C., Kohli, P., Feng, W., Jia, J.: Minimizing sparse higher order energy functions of discrete variables. In: CVPR (2009)
Schoenemann, T., Kahl, F., Cremers, D.: Curvature regularity for region-based image segmentation and inpainting: A linear programming relaxation. In: ICCV (2009)
Schoenemann, T., Kahl, F., Masnou, S., Cremers, D.: A linear framework for region-based image segmentation and inpainting involving curvature penalization. CoRR abs/1102.3830 (2011)
Schoenemann, T., Kuang, Y., Kahl, F.: Curvature Regularity for Multi-label Problems - Standard and Customized Linear Programming. In: Boykov, Y., Kahl, F., Lempitsky, V., Schmidt, F.R. (eds.) EMMCVPR 2011. LNCS, vol. 6819, pp. 163–176. Springer, Heidelberg (2011)
Schoenemann, T., Masnou, S., Cremers, D.: The elastic ratio: Introducing curvature into ratio-based image segmentation. IEEE Transactions on Image Processing 20(9), 2565–2581 (2011)
Strandmark, P., Kahl, F.: Curvature Regularization for Curves and Surfaces in a Global Optimization Framework. In: Boykov, Y., Kahl, F., Lempitsky, V., Schmidt, F.R. (eds.) EMMCVPR 2011. LNCS, vol. 6819, pp. 205–218. Springer, Heidelberg (2011)
Tarlow, D., Zemel, R., Frey, B.: Flexible priors for exemplar-based clustering. In: UAI (2008)
Vicente, S., Kolmogorov, V., Rother, C.: Joint optimization of segmentation and appearance models. In: ICCV (2009)
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Shekhovtsov, A., Kohli, P., Rother, C. (2012). Curvature Prior for MRF-Based Segmentation and Shape Inpainting. In: Pinz, A., Pock, T., Bischof, H., Leberl, F. (eds) Pattern Recognition. DAGM/OAGM 2012. Lecture Notes in Computer Science, vol 7476. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32717-9_5
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