Surface segmentation, a process which divides a surface into parts, is the basis for many surface manipulation applications which include model metamorphosis, model simplifica- tion, model retrieval, model alignment and texture mapping. This dissertation discusses novel methods for geometric surface analysis and segmentation and applications for these methods. Novel work within this dissertation includes a new 3D mesh segmentation algo- rithm which is referred to as the ridge-walking algorithm. The main benefit of this algo- rithm is that it can dynamically change the criteria it uses to identify surface parts which allows the algorithm to be adjusted to suit different types of surfaces and different segmen- tation goals. The dynamic segmentation behavior allows users to extract three different types of surface regions: (1) regions delineated by convex ridges, (2) regions delineated by concave valleys, and (3) regions delineated by both concave and convex curves. The ridge walking algorithm is quantitatively evaluated by comparing it with competing algo- rithms and human-generated segmentations. The evaluation is accompanied with a detailed geometrical analysis of a select subset of segmentation results to facilitate a better under- standing of the strengths and weaknesses of this algorithm.
The ridge walking algorithm is applied to three domain-specific segmentation prob- lems. The first application uses this algorithm to partition bone fragment surfaces into three semantic parts: (1) the fracture surface, (2) the periosteal surface and (3) the articular surface. Segmentation of bone fragments is an important computational step necessary in developing quantitative methods for bone fracture analysis and for creating computational tools for virtual fracture reconstruction. The second application modifies the 3D ridge walking algorithm so that it can be applied to 2D images. In this case, the 2D image is modeled as a Monge patch and principal curvatures of the intensity surface are computed iv for each image pixel. These principal curvatures are then used by ridge walking algorithm
to segment the image into meaningful parts. The third application uses the ridge walking algorithm to facilitate analysis of virtual 3D terrain models. Specifically, the algorithm is integrated as a part of a larger software system designed to enable users to browse, visualize and analyze 3D geometric data generated by NASA’s Mars Exploratory Rovers Spirit and Opportunity. In this context, the ridge walking algorithm is used to identify surface features such as rocks in the terrain models
