Region competition: unifying snakes, region growing, energy/Bayes/MDL for multi-band image segmentation

We present a novel statistical and variational approach to image segmentation based on a new algorithm named region competition. This algorithm is derived by minimizing a generalized Bayes/MDL (Minimum Description Length) criterion using the variational principle. We show that existing techniques in early vision such as, snake/balloon models, region growing, and Bayes/MDL are addressing different aspects of the same problem and they can be unified within a common statistical framework which combines their advantages. We analyze how to optimize the precision of the resulting boundary location by studying the statistical properties of the region competition algorithm and discuss what are good initial conditions for the algorithm. Our method is generalized to color and texture segmentation and is demonstrated on grey level images, color images and texture images.<<ETX>>

[1]  Michael D. Greenberg,et al.  Foundations of Applied Mathematics , 1978 .

[2]  J. Rissanen,et al.  Modeling By Shortest Data Description* , 1978, Autom..

[3]  Azriel Rosenfeld,et al.  Compact Region Extraction Using Weighted Pixel Linking in a Pyramid , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[4]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  Roland Wilson,et al.  The Uncertainty Principle in Image Processing , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  M. Gage,et al.  The heat equation shrinking convex plane curves , 1986 .

[7]  R. Hathaway.  Another interpretation of the EM algorithm for mixture distributions , 1986 .

[8]  John F. Canny,et al.  A Computational Approach to Edge Detection , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[9]  Andrew Blake,et al.  Visual Reconstruction , 1987, Deep Learning for EEG-Based Brain–Computer Interfaces.

[10]  Azriel Rosenfeld,et al.  O(log n) bimodality analysis , 1989, Pattern Recognit..

[11]  D. Mumford,et al.  Optimal approximations by piecewise smooth functions and associated variational problems , 1989 .

[12]  Laurent D. Cohen,et al.  A finite element method applied to new active contour models and 3D reconstruction from cross sections , 1990, [1990] Proceedings Third International Conference on Computer Vision.

[13]  Ruzena Bajcsy,et al.  Segmentation as the search for the best description of the image in terms of primitives , 1990, [1990] Proceedings Third International Conference on Computer Vision.

[14]  Donald Geman,et al.  Boundary Detection by Constrained Optimization , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  Kenneth Keeler,et al.  Map representations and coding-based priors for segmentation , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[16]  Laurent D. Cohen,et al.  On active contour models and balloons , 1991, CVGIP Image Underst..

[17]  Glenn Healey,et al.  Segmenting images using normalized color , 1992, IEEE Trans. Syst. Man Cybern..

[18]  K. Sung.  A Vector Signal Processing Approach to Color , 1992 .

[19]  Farzin Mokhtarian,et al.  A Theory of Multiscale, Curvature-Based Shape Representation for Planar Curves , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[20]  James S. Duncan,et al.  Deformable boundary finding influenced by region homogeneity , 1994, 1994 Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[21]  Gang Xu,et al.  Robust active contours with insensitive parameters , 1994, Pattern Recognit..

[22]  Rolf Adams,et al.  Seeded Region Growing , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[23]  Tapas Kanungo,et al.  A fast algorithm for MDL-based multi-band image segmentation , 1994, 1994 Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[24]  Jean-Michel Morel,et al.  Variational methods in image segmentation , 1995 .

[25]  Song-Chun Zhu,et al.  FRAME: filters, random fields, and minimax entropy towards a unified theory for texture modeling , 1996, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition.