International Journal of Computer Vision

, Volume 69, Issue 1, pp 119–126 | Cite as

A Metric Approach to Vector-Valued Image Segmentation

  • Pablo A. ArbeláezEmail author
  • Laurent D. Cohen
Short Papers


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.


image segmentation distance transforms path variation ultrametrics vector-valued image color boundary detection 


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Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.CEREMADEUMR CNRS 7534 Université Paris DauphineParis cedex 16France

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