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

Chapter 4: Algorithm Overview 41BoundaryContourCurvatureEstimationDensityEstimationEntropyComputationShapeInformationFigure 4.2: Block diagram of our CVM as the informational approach to shapedescription.We use curvature because it is an information preserving feature, invariant to rotationand possesses an intuitively pleasing correspondence to the perceptive property ofsimplicity. Curvature completely parameterizes the boundary contour for efficientshape description of 2D curves and boundary contours. We counter the inverserelation to symmetry by using information theory. Symmetry does not contribute tomore shape information (entropy) but rather reduces it.4.1.2 Curvature-Based Automotive Component DescriptionOur CVM measure of shape on geometric curves is the entropy of curvature along theboundary contour. Curvature along the boundary provides us with sufficient detail inthe 2D case but with 3D models and surfaces, it is not enough. We extend our idea ofshape information on 3D meshes to describe surface variation of the smooth surfacepatches that make up the object and store the list of connected patches. We assumethat we can reasonably describe most objects as a unique network of smooth patches.Then, the uniqueness of our description is to measure the variation in curvature acrosseach of these patches.We describe the algorithm in a pictorial fashion with a block diagram in Figure 4.3.Our description which could be used for purposes such as reverse engineering andinspection takes triangle meshes as the input. We take the example of the disc brakeagain. We break down the triangle mesh into surface patches based on the Dorai’s[Dorai, 1997] definition of curvedness. Curvedness identifies sharp edges and abruptsurface changes. We perform a simple region growing segmentation by identifying apoint and collecting the vertices whose face normal deviation is less than a particularangle. This angle is a free parameter. We have used 85 degrees as the maximumthreshold angle before we meet an edge in the growing procedure. We save theconnectivity information of each of these surface patches. Our segmentation is a crude