An extended Mumford-Shah model for shape partitioning

This paper proposes a 3D mesh segmentation method based on the Mumford-Shah model, which is composed by two terms: data fidelity and regularisation term. The minimisation of these ones is performed with the primal dual algorithm, by alternating a gradient descend in the primal variable and a gradient ascend in the dual variable. The estimation of the partition numbers is a potential step in the segmentation process. Various computation techniques were proposed in the literature but never coincide with the human perception for all models. In this paper we propose a new method for automatic computation of the optimal partitions number by analysing the behaviour of the second order difference of eigenvalues obtained from the dual Laplacian spectrum. By applying these partitions numbers in mesh segmentation, we obtained better values of the Rand Index metric compared with the state of the art.