Fast mesh segmentation by using the LexicoGraph Cut algorithm

Since segmentation of surface data is of growing interest, many image segmentation algorithms have already been applied to surfaces. Mesh segmentation can not only be based on color and texture but also on shape properties like curvature. Graph Cuts based methods are very popular and also applicable to mesh data having irregular vertex neighborhoods. However, Graph Cuts suffer from problems such as shortcuts, generation of small regions and sensitivity to variations of the boundary indicator function. Moreover, they are often hard to implement and computationally expensive. Here we show that a quite old approach for image segmentation, a fast and extremely simple greedy algorithm, which we call LexicoGraph Cut, avoids the problems mentioned above. In this paper we use this algorithm to segment triangulated surface meshes and we introduce new boundary indicator functions, which combine color and curvature properties. We show that using these boundary indicator functions the LexicoGraph Cut algorithm produces a globally optimal result regarding a lexicographic optimization criterion.