Markov Random Fields for Improving 3D Mesh Analysis and Segmentation

Abstract

Mesh analysis and clustering have became important issues in order to improve the efficiency of common processing operations like compression, watermarking or simplification. In this context we present a new method for clustering / labeling a 3D mesh given any field of scalar values associated with its vertices (curvature, density, roughness etc.). Our algorithm is based on Markov Random Fields, graphical probabilistic models. This Bayesian framework allows (1) to integrate both the attributes and the geometry in the clustering, and (2) to obtain an optimal global solution using only local interactions, due to the Markov property of the random field. We have defined new observation and prior models for 3D meshes, adapted from image processing which achieve very good results in terms of spatial coherency of the labeling. All model parameters are estimated, resulting in a fully automatic process (the only required parameter is the number of clusters) which works in reasonable time (several seconds).