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Image segmentation can be defined as the detection of closed contours surrounding objects of interest. Given a family of closed curves obtained by some means, a difficulty is to extract the relevant ones. A classical approach is to define an energy minimization framework, where interesting contours correspond to local minima of this energy. Active contours, graph cuts or minimum ratio cuts are instances of such approaches. In this article, we propose a novel efficient ratio-cut estimator which is both context-based and can be interpreted as an active contour. As a first example of the effectiveness of our formulation, we consider the tree of shapes, which provides a family of level lines organized in a tree hierarchy through an inclusion relationship. Thanks to the tree structure, the estimator can be computed incrementally in an efficient fashion. Experimental results on synthetic and real images demonstrate the robustness and usefulness of our method.

Context-based energy estimator: Application to object segmentation on the tree of shapes