A Convex Approach to K-means Clustering and Image Segmentation

Laurent Condat (1)

1 GIPSA-AGPIG - GIPSA - Architecture, Géométrie, Perception, Images, Gestes

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.

Mots clés: k-means clustering; image segmentation; Mumford-Shah problem

Domaines: Traitement du signal et de l'image [eess.SP]; Machine Learning [stat.ML]

Laurent Condat. A Convex Approach to K-means Clustering and Image Segmentation. [Research Report] Gipsa-Lab. 2017. ⟨hal-01504799v1⟩