Geometric decomposition of 3D surface meshes using Morse theory and region growing

This paper presents a new algorithm for decomposition (segmentation) of surfaces using curvature labeling, Morse theory, and region growing technologies. The geometric properties are estimated on triangular meshes and all mesh elements (vertices and triangles) are labeled with different surface types. The surface decomposition method proposed consists of two steps: initial segmentation and refinement. The initial segmentation is performed by grouping the topologically adjacent mesh elements with the same surface type using the region growing technique. A Morse function is then defined based on the smoothed curvatures using bilateral filtering to extract the critical points of a triangular surface mesh. The final segmentation is obtained by a combination of the steepest ascent/descent strategy and region growing technique. The experimental results on many 3D models, particularly molecular surfaces, have demonstrated the effectiveness and robustness of the proposed segmentation method.