Title: An extended Mumford-Shah model for shape partitioning

Authors: Habiba Nabi; Ali Douik

Addresses: National Engineering School of Monastir, University of Monastir, Street Ibn Eljazzar, Monastir 5000, Tunisia ' National Engineering School of Sousse, University of Sousse, Sousse Technology Park, Sahloul, Sousse 4054, Tunisia

Abstract: 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.

Keywords: mesh segmentation; Mumford-Shah model; dual graph; Laplacian matrix; primal dual method; hierarchical segmentation; shape partitioning; data fidelity; regularisation; Rand index.

DOI: 10.1504/IJSISE.2016.078263

International Journal of Signal and Imaging Systems Engineering, 2016 Vol.9 No.4/5, pp.226 - 232

Received: 23 May 2015
Accepted: 06 Mar 2016
Published online: 10 Aug 2016 *

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