Section: New Results

Multi-Region Segmentation on Manifolds

We have addressed the problem of segmenting data defined on a manifold into a set of regions with uniform properties. This issue is fundamental in a number computer vision and graphics applications. Here we have considered this issue in order to introduce segmentation constraints on the reflectance properties in 3D shape reconstruction problems.

We propose a numerical method when the manifold is represented by a triangular mesh. Based on recent image segmentation models, our method minimizes a convex energy and then enjoys significant favorable properties: it is robust to initialization and avoid the problem of the existence of local minima present in many variational models. Our contributions are threefold: firstly we adapt the convex image labeling model to manifolds; in particular the total variation formulation. Secondly we show how to implement the proposed method on triangular meshes, and finally we show how to use and combine the method in other computer vision problems, such as 3D reconstruction. For more details, see our ICCV'09 paper [29] .