To the Graduate Council: I am submitting herewith a dissertation ...

global properties. Hebert and Ikeuchi [35] created a Spherical Attribute Image (SAI) bymapping all the surface points to a sphere. A regular mesh is first created by deformingan initial geodesic dome onto the object surface.Each node on the geodesic domestores the corresponding surface point’s curvature value. The surfaces are matched byaligning the curvature map on the geodesic domes. SAI only works for objects withspherical topology.Dorai and Jain [25] proposed the Curvedness Orientation ShapeMap On Sphere (COSMOS) by combining the local and global geometric information.An object is characterized by a set of maximally sized surface patches of constant shapeindex and their orientation-dependent mapping onto the unit sphere. Constant ShapeMaximal Patch (CSMP) is defined as a group of points with the same shape index. Theaverage normal of each CSMP is used to generate the Gauss map. The surface area andthe connectivity list of CSMPs are recorded. All these descriptors are used for objectrecognition.Generally, the representations using global geometry are less flexible indealing with arbitrary topology and occlusion. A detailed survey of free-form objectrepresentation can be found in [15].In this research, a new surface representation scheme called 3D point fingerprint [84]and its application to surface registration are proposed. The proposed point fingerprintis a set of 2D contours that are the projections of geodesic circles onto the tangentplane. Point fingerprint is so named because it looks like human fingerprints and canbe used as a discriminating feature for the surface point. It can carry more informationthan the existing schemes using only one contour or 2D histogram. The computation20