Ridge Walking for 3D Surface Segmentation

This paper describes a new 3D surface segmentation algorithm that separates a closed surfaces into regions by computing surface contours that traverse ridges of highcurvature surface regions. We refer to the approach as ridge-walking since these contours tend to follow convex ridge-like structures and concave valley-like substructures present within the geometry of the model. Segmentation is achieved by solving for closed ridge contours on the surface, each of which serves to divide the surface into two disjoint regions. A collection of such curves then provides a segmentation of the surface into surface patches which is the segmentation result. The proposed approach also introduces a new parametrization for 3D models in term of the mesh vertices and edges that is a significant departure from standard methods that parametrize the surface based on mesh polygons. Solving directly for the boundary allows for direct control of the segmentation solution in ways that cannot be easily controlled with polygon-based parametrization. This can include control of the boundary length, shape, and, most importantly, the overall salience of the region boundary as defined by an optimization function such as the minima rule, which seeks to place boundaries along concave surface regions. We detail the segmentation algorithm, the surface parametrization use to develop the parametrization and provide analysis of several segmentation results for standard test surfaces from the literature in this area. Segmentation is an important surface analysis step needed when processing both synthetic (CADgenerated) and real-world (via 3D scanning) models which are commonplace in many contexts today. Applications of segmentation include surface compression, object recognition, texture mapping, surface re-parametrization, animation, collision detection and reverse engineering. (a) (b) Figure 1: We propose a new method to parametrize surfaces based on their ridges and apply this parametrization for the purposes of 3D model segmentation which takes a 3D model as input (a) and provides a decomposition of the model surface into meaningful parts shown in (b) as surface patches having distinct colors.