Self Inducing Relational Distance and Its Application to Image Segmentation

We propose a new feature distance which is derived from an optimal relational graph matching criterion. Instead of defining an arbitrary similarity measure for grouping, we will use the criterion of reducing instability in the relational graph to induce a similarity measure. This similarity measure not only improves the stability of the matching, but more importantly, also captures the relative importance of relational similarity in the feature space for the purpose of grouping. We will call this similarity measure the self-induced relational distance. We demonstrate the distance measure on a brightness-texture feature space and apply it to the segmentation of complex natural images.

[1]  Azriel Rosenfeld,et al.  Scene Labeling by Relaxation Operations , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[2]  Harry G. Barrow,et al.  Subgraph Isomorphism, Matching Relational Structures and Maximal Cliques , 1976, Inf. Process. Lett..

[3]  Olivier D. Faugeras,et al.  Semantic Description of Aerial Images Using Stochastic Labeling , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[4]  King-Sun Fu,et al.  A distance measure between attributed relational graphs for pattern recognition , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[5]  Robert M. Haralick,et al.  A Metric for Comparing Relational Descriptions , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  R M Haralick,et al.  Relational matching. , 1994, Applied optics.

[7]  Kim L. Boyer,et al.  Structural Stereopsis for 3-D Vision , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[8]  Shinji Umeyama,et al.  An Eigendecomposition Approach to Weighted Graph Matching Problems , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  R. Brockett Least squares matching problems , 1989 .

[10]  Anil K. Jain,et al.  Unsupervised texture segmentation using Gabor filters , 1990, 1990 IEEE International Conference on Systems, Man, and Cybernetics Conference Proceedings.

[11]  P Perona,et al.  Preattentive texture discrimination with early vision mechanisms , 1990 .

[12]  H. C. Longuet-Higgins,et al.  An algorithm for associating the features of two images , 1991, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[13]  R. Brockett Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems , 1991 .

[14]  James R. Bergen,et al.  Texture Analysis: Representation and Matching , 1995, ICIAP.

[15]  B. S. Manjunath,et al.  Texture Features for Browsing and Retrieval of Image Data , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  Steven Gold,et al.  A Graduated Assignment Algorithm for Graph Matching , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  William J. Christmas,et al.  Probabilistic feature-labelling schemes: modelling compatibility coefficient distributions , 1996, Image Vis. Comput..

[18]  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.

[19]  Joachim M. Buhmann,et al.  Non-parametric similarity measures for unsupervised texture segmentation and image retrieval , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[20]  Joachim M. Buhmann,et al.  Pairwise Data Clustering by Deterministic Annealing , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[21]  Edwin R. Hancock,et al.  Structural Matching by Discrete Relaxation , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[22]  Jitendra Malik,et al.  Normalized cuts and image segmentation , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.