The Application Of Partial Differential Equations In The Shape Classification

As the terminal link of pattern recognition, shape classification is a really hot topic which are paid great attention by the researchers. Based on the advanced achievements in this field, this thesis discusses mainly the systems of partial differential equations and their applications in image and graphics processing by means of some techniques and methods from image processing etc. This thesis firstly explains the developments, current situations and applications of the system of partial differential equations. In this paper, two novel descriptors for 2D models were presented . Based on the idea of random walks, we can calculate, for every internal point in the silhouette, a value reflecting the mean time required for a random walk beginning at the point to hit the boundaries. This function can be formalized as a Poisson equation. We then use the solution of the Poisson equation to extract various properties of a shape. The proposed algorithm takes the advantages of U-system or V-system and the Poisson's geometric descriptor by Lena Gorelick. To classify shapes, the new normalized Poisson-U system moment descriptor and Poisson-V system moment descriptor are introduced, which is invariant in the rotation, translation and scale transform. The experimental results show the accuracy and efficiency of new descriptors in classification of 2D shapes.This thesis is divided into several sections as follows:1. The summarization of the shape classification: Shape classification as a very important topic is an intellectual frontier in the field of computer vision. Many methods of the shape classification have been proposed, such as based on relative distaneds of feature points, moment invariant, Fourier-based descriptors etc. The thesis tries to offer relevant information for their characteristics and application.2. Based on Poisson equation-U System Moment Descriptor and V System Moment Descriptor: The shape descriptors based on the contour may be not suitable to describe those shapes which contains many different regions. This thesis take the advantages of U-system or V-system, based on poisson equation. The features are introduced in details.3.The application of moment descriptors: The new descriptors have many special features, so they may achieve good recognition of 2D shapes and occupy a dominant position in some fields.