A new two-stage mesh surface segmentation method

Partitioning a mesh surface into several semantic components is a fundamental task in geometry processing. This paper presents a new stable and effective segmentation method, which contains two stages. The first stage is a spectral clustering procedure, while the second stage is a variational refining procedure. For spectral clustering, we construct a new Laplacian matrix which reflects more semantic information than classical Laplacian matrices. By this new Laplacian, we introduce a simple and fast spectral clustering method, which gives quite satisfying segmentation results for most surfaces and provides a good initialization for the second stage. In the second stage, we propose a variational refining procedure by a new discretization of the classical non-convex Mumford–Shah model. The variational problem is solved by efficient iterative algorithms based on alternating minimization and alternating direction method of multipliers (ADMM). The first stage provides a good initialization for the second stage, while the second stage refines the result of the first stage well. Experiments demonstrated that our method is very stable and effective compared to existing approaches. It outperforms competitive segmentation methods when evaluated on the Princeton Segmentation Benchmark.