关于SPMVIF方法的几何分析

GEOMETRY ANALYSIS ON SPMVIF METHOD

基于粒子运动模拟的边缘检测法(SPMVIF方法)是N.Eua-Anant等人提出的一个新颖而有效的图像边缘检测方法.本文首先概要介绍SPMVIF方法的原理和应用,然后对其展开理论分析并获得一些重要的结果:1)总结出构建图像边缘概念的一对充分必要条件,即综合考虑边缘切向和法向的灰度变化信息;2)利用古典微分几何的知识建立了新的SPMVIF方法的几何分析框架,重点解释运动控制参数的物理意义及其选取规则;3)提出了一个与边缘临界性相关的零-法曲率原理,它可以看作是经典的零交叉点原理的推广;4)在这个几何框架下研究得出等高线和边缘曲线之间可以通过零交叉点原理产生联系,具体结论归结为文中的两个命题.

Simulation of Particle Motion in a Vector Image Field (SPMVIF) method, proposed by N. Eua-Anant et al, is a novel and established approach to image boundary detection. This paper firstly introduces the principle of SPMVIF and its applications to image processing, followed by an elaborate theory analysis of SPMVIF method. Our geometry analysis leads to four important results: 1) A new concept regarding image boundary is established by means of the dual constraint conditions which describe the nature of image boundary; 2) A new geometry analysis framework for SPMVIF method is constructed enlightened by classical differential geometry theory. Our new framework describes the physical background of the motion parameters as well as their choice rules; 3) A zero - normal - curvature principle is proposed which is closely related to boundary critical property. It can be regarded as the generalization of the classical zero-cross point principle; 4) Under the novel geometry framework, we prove two propositions concerning the contour line and boundary curve. These results show that the relationship between contour line and boundary curve can be depicted by the zero-cross point principle.