Abstract
In this paper we generalize the recently proposed graduated non-convexity and concavity procedure (GNCCP) to approximately solve the maximum a posteriori (MAP) inference problem with the Markov random field (MRF). Unlike the commonly used graph cuts or loopy brief propagation, the GNCCP based MAP algorithm is widely applicable to any types of graphical models with any types of potentials, and is very easy to use in practice. Our preliminary experimental comparisons witness its state-of-the-art performance.
This work was supported by the National Science Foundation of China(61375005).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Boykov, Y., Veksler, O., Zabih, R.: Fast approximate energy minimization via graph cuts. IEEE Transactions on Pattern Analysis and Machine Intelligence 23(11), 1222–1239 (2001)
Cour, T., Shi, J.: Solving markov random fields with spectral relaxation. Journal of Machine Learning Research - Proceedings Track, 75–82 (2007)
Frank, M., Wolfe, P.: An algorithm for quadratic programming. Naval Research Logistics Quarterly 3(1-2), 95–110 (1956)
Freeman, W., Pasztor, E., Carmichael, O.: Learning low-level vision. International Journal of Computer Vision 40(1), 25–47 (2000)
Leordeanu, M., Herbert, M., Sukthankar, R.: An integer projected fixed point method for graph matching and map inference. In: NIPS (2009)
Liu, Z.Y., Qiao, H.: Gnccp - graduated nonconvexity and concavity procedure. IEEE Transactions on Pattern Analysis and Machine Intelligence (2014), doi:10.1109/TPAMI.2013.223
Liu, Z.Y., Qiao, H., Xu, L.: An extended path following algorithm for graph matching problem. IEEE Transactions on Pattern Analysis and Machine Intelligence 34(7), 1451–1456 (2012)
Liu, Z.Y., Qiao, H., Yang, X., Hoi, C.S.: Graph matching by simplified convex-concave relaxation procedure. International Journal of Computer Vision (2014), doi:10.1007/s11263–014–0707–7
Liu, Z.Y., Qiao, H.: A convex-concave relaxation procedure based subgraph matching algorithm. Journal of Machine Learing Research: W&CP 25, 237–252 (2012)
Murphy, K.P., Weiss, Y., Jordan, M.I.: Loopy belief propagation for approximate inference: An empirical study. In: Uncertainty in Artificial Intelligence (1999)
Ravikumar, P., Lafferty, J.D.: Quadratic programming relaxations for metric labeling and markov random field map estimation. In: ICML, pp. 737–744 (2006)
Szeliski, R., Zabih, R., Scharstein, D., Veksler, O., Kolmogorov, V., Agarwala, A., Tappen, M., Rother, C.: A comparative study of energy minimization methods for markov random fields with smoothness-based priors. IEEE Transactions on Pattern Analysis and Machine Intelligence 30(6), 1068–1080 (2008)
Tappen, M.F., Freeman, W.T.: Comparison of graph cuts with belief propagation for stereo, using identical mrf parameters. In: Proceedings of the Ninth IEEE International Conference on Computer Vision, pp. 900–906. IEEE (2003)
Zaslavskiy, M., Bach, F., Vert, J.P.: A path following algorithm for the graph matching problem. IEEE Transactions on Pattern Analysis and Machine Intelligence 31(12), 2227–2242 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Liu, ZY., Qiao, H., Su, JH. (2014). MAP Inference with MRF by Graduated Non-Convexity and Concavity Procedure. In: Loo, C.K., Yap, K.S., Wong, K.W., Teoh, A., Huang, K. (eds) Neural Information Processing. ICONIP 2014. Lecture Notes in Computer Science, vol 8835. Springer, Cham. https://doi.org/10.1007/978-3-319-12640-1_49
Download citation
DOI: https://doi.org/10.1007/978-3-319-12640-1_49
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-12639-5
Online ISBN: 978-3-319-12640-1
eBook Packages: Computer ScienceComputer Science (R0)