A Convex Approach to K-means Clustering and Image Segmentation

Laurent Condat 1
1 GIPSA-AGPIG - AGPIG
GIPSA-DIS - Département Images et Signal
Abstract : A new convex formulation of data clustering and image segmentation is proposed, with fixed number K of regions and possible penalization of the region perimeters. So, this problem is a spatially regularized version of the K-means problem, a.k.a. piecewise constant Mumford–Shah problem. The proposed approach relies on a discretization of the search space; that is, a finite number of candidates must be specified, from which the K centroids are determined. After reformulation as an assignment problem, a convex relaxation is proposed, which involves a kind of l 1,infinity norm ball. A splitting of it is proposed, so as to avoid the costly projection onto this set. Some examples illustrate the efficiency of the approach.
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Communication dans un congrès
11th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR), Oct 2017, Venice, Italy. 2017
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Dernière modification le : vendredi 8 décembre 2017 - 09:28:20

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Laurent Condat. A Convex Approach to K-means Clustering and Image Segmentation. 11th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR), Oct 2017, Venice, Italy. 2017. 〈hal-01504799v3〉

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