An expectation-maximisation framework for segmentation and grouping

Abstract This paper casts the problem of perceptual grouping into an evidence combining setting using the apparatus of the EM algorithm. We are concerned with recovering a perceptual arrangement graph for line-segments using evidence provided by a raw perceptual grouping field. The perceptual grouping process is posed as one of pairwise relational clustering. The task is to assign line-segments (or other image tokens) to clusters in which there is strong relational affinity between token pairs. The parameters of our model are the cluster memberships and the pairwise affinities or link-weights for the nodes of a perceptual relation graph. Commencing from a simple probability distribution for these parameters, we show how they may be estimated using the apparatus of the EM algorithm. The new method is demonstrated on line-segment grouping problems where it is shown to outperform a non-iterative eigenclustering method.

[1]  Geoffrey E. Hinton,et al.  SMEM Algorithm for Mixture Models , 1998, Neural Computation.

[2]  Jorma Rissanen,et al.  Stochastic Complexity in Statistical Inquiry , 1989, World Scientific Series in Computer Science.

[3]  Yair Weiss,et al.  Segmentation using eigenvectors: a unifying view , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[4]  Jitendra Malik,et al.  Normalized Cuts and Image Segmentation , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  Pietro Perona,et al.  A Factorization Approach to Grouping , 1998, ECCV.

[6]  José M. N. Leitão,et al.  On Fitting Mixture Models , 1999, EMMCVPR.

[7]  Daniel Crevier,et al.  A Probabilistic Method for Extracting Chains of Collinear Segments , 1999, Comput. Vis. Image Underst..

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

[9]  Jiri Matas,et al.  Junction detection using probabilistic relaxation , 1993, Image Vis. Comput..

[10]  Lance R. Williams,et al.  Stochastic Completion Fields: A Neural Model of Illusory Contour Shape and Salience , 1995, Neural Computation.

[11]  John S. Bridle,et al.  Training Stochastic Model Recognition Algorithms as Networks can Lead to Maximum Mutual Information Estimation of Parameters , 1989, NIPS.

[12]  Will Dickson.  Feature grouping in a hierarchical probabilistic network , 1990, BMVC.

[13]  Nikos A. Vlassis,et al.  A kurtosis-based dynamic approach to Gaussian mixture modeling , 1999, IEEE Trans. Syst. Man Cybern. Part A.

[14]  Shimon Ullman,et al.  Structural Saliency: The Detection Of Globally Salient Structures using A Locally Connected Network , 1988, [1988 Proceedings] Second International Conference on Computer Vision.

[15]  Rüdiger von der Heydt,et al.  A computational model of neural contour processing: Figure-ground segregation and illusory contours , 1993, 1993 (4th) International Conference on Computer Vision.

[16]  Gérard G. Medioni,et al.  Inferring global perceptual contours from local features , 1993, Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[17]  Steven W. Zucker,et al.  Trace Inference, Curvature Consistency, and Curve Detection , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

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

[19]  David J. Field,et al.  Contour integration by the human visual system: Evidence for a local “association field” , 1993, Vision Research.

[20]  G. Kitagawa,et al.  Akaike Information Criterion Statistics , 1988 .

[21]  Seth Hutchinson,et al.  A Probabilistic Approach to Perceptual Grouping , 1996, Comput. Vis. Image Underst..

[22]  Edwin R. Hancock,et al.  Iterative Curve Organisation with the EM Algorithm , 1996, SBIA.

[23]  Lance R. Williams,et al.  Local Parallel Computation of Stochastic Completion Fields , 1996, Neural Computation.

[24]  Peng-Yeng Yin.  Algorithms for straight line fitting using k-means , 1998, Pattern Recognit. Lett..

[25]  G. Kitagawa,et al.  Akaike Information Criterion Statistics , 1988 .

[26]  Edwin R. Hancock,et al.  Grouping Line-segments using Eigenclustering , 2000, BMVC.

[27]  Kim L. Boyer,et al.  Quantitative Measures of Change Based on Feature Organization: Eigenvalues and Eigenvectors , 1998, Comput. Vis. Image Underst..