To the Graduate Council: I am submitting herewith a thesis written by ...

Chapter 5: Analysis and Results 595 ANALYSIS AND RESULTSWe begin this section with important implementation decisions on each of the buildingblocks for the proposed CVM algorithm. We discuss our algorithm and justify ourchoice of methods before we present analysis results on intensity images, range imagesand 3D mesh models.5.1 Implementation Decisions on the Building BlocksWe have acquired the data and are ready for shape analysis with the CVM. We usetriangle mesh datasets as our input. Since our algorithm is a curvature-based algorithm,our first task is to compute curvature at the vertices on the mesh. In Section 5.1.1 wediscuss various curvature estimation methods with analysis results on the effectivenessof these measures for surface description. We use curvedness, which is a function ofprincipal curvatures, to perform segmentation. We then perform “region growing” toidentify the regions and create a mapping of the vertex and the region to which itbelongs. We use curvature at each of these vertices in a particular region to compute theCVM. In short, our CVM algorithm is a three pass algorithm; the first pass is for theestimation of curvature and curvedness, the second one to map vertices to smoothpatches (segmentation) and the third one to compute the surface variation measure thatwe represent in a region adjacency graph.5.1.1 Analysis of Curvature Estimation MethodsWe recall the mathematical definition of triangle meshes as a set of vertices and a listof triangles connecting these vertices. We would like to define more specific termsbefore we discuss the implementation of curvature estimation methods. A vertex v i isconsidered as an immediate neighbor of vertex v if edge vv i belongs to the mesh. Wen−v and the set of the triangles containingdenote the set of neighboring vertices by [ ]1n−1the vertex v by [ ]i i=0T i i=0 where 1vTi = Triangle( viv v( i+ 1)modn ), 0 ≤ i ≤ n −(5.1)