The Approximation Power Of Resampling In Surface Matching

3-D geometric matching and similarity research aim at achieving recognition, similaritymeasurement and matching of 3-D geometric objects,by means of object analysis, transforma-tion and feature extraction. As a major part of this research, 3-D surface matching is of greatimportance in a variety of areas such as reverse engineering, virtual reality, computer vision,medical image registration and molecules structure design of drug.With the increasing importance of 3-D surface modeling in computer vision and computergraphics, 3-D surface analysis and matching have been more researched as core problems. Fortwo given 3-D models, it is required to find a transformation(rigid transformation or scalingtransformation) such that the distance of the two models minimized. Based on this transforma-tion, one can implement more comparison and analysis for their shapes.Assuming a point cloud with noise sampled over a smooth surface is provided, this thesisaddresses the point-wise error function of differential properties. The main contribution of thethesis is the error bounds of normal and principal curvature estimation in R~3.There are four chapters in this thesis and are organized as follows:This paper begins by discussing value of the thesis and some results in surface matching inchapter 1. Chapter 2 and 3 then review a wide variety of existing algorithms in surface matchingand feature extraction. Chapter 4 demonstrates the approximation power of resampling in dif-ferential quantities estimation, this is the main work of this thesis. Finally, we summarize thework of the thesis and discuss some future research directions of the work.