A Metric Approach to Vector-Valued Image Segmentation PabloArbel´aez (arbelaez@ceremade.dauphine.fr) and Laurent D. Cohen (cohen@ceremade.dauphine.fr) CEREMADE, UMR CNRS 7534 Universit´ e Paris Dauphine, Place du mar´ echal de Lattre de Tassigny, 75775 Paris cedex 16, France Abstract. We address the issue of low-level segmentation of vector-valued images, focusing on the case of color natural images. The proposed approach relies on the formulation of the problem in the metric framework, as a Voronoi tessellation of the image domain. In this context, a segmentation is determined by a distance transform and a set of sites. Our method consists in dividing the segmentation task in two successive sub-tasks : pre-segmentation and hierarchical representation. We design specific distances for both sub-problems by considering low-level image attributes and, particularly, color and lightness information. Then, the interpretation of the metric formalism in terms of boundaries allows the definition of a soft contour map that has the property of producing a set of closed curves for any threshold. Finally, we evaluate the quality of our results with respect to ground-truth segmentation data. To appear in International Journal of Computer Vision, Special issue on Variational and Level Set methods Keywords: image segmentation, distance transforms, path variation, ultrametrics, vector- valued image, color, boundary detection.