MRF Energy Minimization for Unsupervised Image Segmentation

A Markov Random Field (MRF) model is proposed for unsupervised image segmentation in this paper. The theoretical framework is based on Bayesian estimation via the graph-cut energy optimization method. A Gaussian is used to model the density associated with each image segment (or class), and parameters are estimated with an expectation maximization (EM) algorithm. Here we use the perceptually uniform CIELAB color values instead of the RGB color. Graph cuts have emerged as a powerful optimization technique for minimizing MRF energy functions that arise in low-level vision problems. We adopt a new min-cut/max-flow algorithm which works several times faster than any of the other max-flow methods, which makes near real-time performance possible. Experimental results have been provided to illustrate the performance of our method.

[1]  Olga Veksler,et al.  Fast Approximate Energy Minimization via Graph Cuts , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[2]  Vladimir Kolmogorov,et al.  An experimental comparison of min-cut/max- flow algorithms for energy minimization in vision , 2001, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[3]  Richard A. Johnson,et al.  Applied Multivariate Statistical Analysis , 1983 .

[4]  David K. Smith Network Flows: Theory, Algorithms, and Applications , 1994 .

[5]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[6]  Gareth Funka-Lea,et al.  Graph Cuts and Efficient N-D Image Segmentation , 2006, International Journal of Computer Vision.

[7]  Fred S. Roberts,et al.  Applied Combinatorics , 1984 .

[8]  Zoltan Kato,et al.  A Markov random field image segmentation model for color textured images , 2006, Image Vis. Comput..

[9]  Ravindra K. Ahuja,et al.  Network Flows: Theory, Algorithms, and Applications , 1993 .

[10]  Jean Ponce,et al.  Computer Vision: A Modern Approach , 2002 .

[11]  David Alcaide López de Pablo,et al.  A network flow-based method to solve performance cost and makespan open-shop scheduling problems with time-windows , 2009, Eur. J. Oper. Res..

[12]  Geoffrey J. McLachlan,et al.  Maximum likelihood clustering via normal mixture models , 1996, Signal Process. Image Commun..

[13]  Richard Szeliski,et al.  A Comparative Study of Energy Minimization Methods for Markov Random Fields with Smoothness-Based Priors , 2008, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[14]  Noel Cressie,et al.  Conditional-mean least-squares fitting of Gaussian Markov random fields to Gaussian fields , 2008, Comput. Stat. Data Anal..

[15]  Yiu-ming Cheung,et al.  Maximum weighted likelihood via rival penalized EM for density mixture clustering with automatic model selection , 2005, IEEE Transactions on Knowledge and Data Engineering.

[16]  Vladimir Kolmogorov,et al.  An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision , 2004, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  Shankar M. Krishnan,et al.  Image segmentation using finite mixtures and spatial information , 2004, Image Vis. Comput..

[18]  Stan Z. Li,et al.  Markov Random Field Modeling in Computer Vision , 1995, Computer Science Workbench.

[19]  Claude Cariou,et al.  Unsupervised texture segmentation/classification using 2-D autoregressive modeling and the stochastic expectation-maximization algorithm , 2008, Pattern Recognit. Lett..

[20]  Richard Szeliski,et al.  A Comparative Study of Energy Minimization Methods for Markov Random Fields , 2006, ECCV.

[21]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .