Using a MAP-MRF Model to Improve 3D Mesh Segmentation Algorithms

This paper proposes a novel method for improving the performance of a 3D-mesh segmentation algorithm. Our method takes a 3D-mesh object and a segmentation algorithm as input. Our approach uses a Markov Random Field (MRF) to estimate, for each mesh vertex, the likelihood that the vertex lies on a segmentation boundary. This is accomplished by repeating a process where we perturb the 3D mesh data and re-segmenting the surface using the provided algorithm and then analyzing the variation in the provided segmentation boundaries. Our MRF uses these segmentations as data to estimate the likelihood that each vertex is a member of a segmentation boundary. A prior is incorporated into the MRF that encourages solutions to satisfy smoothness conditions. The likelihood and prior are combined to generate a a-posteriori distribution for the mesh vertices that lie on a segmentation boundary. The improved segmentation is then taken as the collection of vertices which Maximize the A-Posteriori distribution, referred to as a MAP-MRF estimation. Results are provided for 2 different input algorithms and 3 different input surfaces and quantitative measures of the segmentation improvement are provided. The method can be applied to many segmentation algorithms to improve results which may otherwise suffer from over-segmentation or under-segmentation.