广义凸分解理论及应用

项目名称： 广义凸分解理论及应用

项目编号： No.60873127

项目类型： 面上项目

立项/批准年度： 2009

项目学科： 矿业工程

项目作者： 刘文予

作者单位： 华中科技大学

项目金额： 33万元

中文摘要： 本项目研究广义凸分解理论及应用。从发掘和处理互斥关系的角度出发，简化凸分解问题，建立凸分解问题的解决方案。针对数据集的特性构建Morse函数，提出一种有效融合多个Morse函数的方法，获得一种全新的、适用于任何连续或离散数据集的凸分解理论。定义尺度描述子，研究尺度描述子的性质并挖掘其几何意义，通过将尺度描述子引入凸分解，获得满足视觉特性的多尺度凸分解理论方法。提出先粗略、后精确的分割线两步定位方法，同时将凸分解的求解过程归结为线性规划问题，研究凸分解的快速算法。以多尺度广义凸分解的性质为基础，研究其在计算机视觉、计算机图形学和科学数据可视化等领域，包括多尺度形状骨架提取、三维传感器网络覆盖问题研究、高维数据PCA分析等方面的应用。

中文关键词： 凸分解；广义；多尺度；互斥；视觉

英文摘要： This project focuses on generalized convex decomposition theory and its applications. We started from the perspective of exploring and dealing with mutually exclusive relation, to simplify the problem of convex decomposition and build the solution for the problem. We constructed Morse function based on the character of the dataset, and proposed an effective method to fuse multiple Morse functions, and developed a novel theory of convex decomposition suitable for any continuous or discrete dataset. We defined a descriptor of scale, and studied its properties and explored its geometric meaning. By introducing the scale descriptor into convex decomposition, we got theoretic method of convex decomposition satisfying visual characteristics. We proposed a two-step method by first roughly then precisely positioning the cut line. At the same time, we formulated the process of solving the convex decomposition as linear programming problem to study fast algorithm of convex decomposition. Based on the properties of multi-scale generalized convex decomposition, we studied its applications in fields such as computer vision, computer graphics and visualization of scientific data, etc., including multi-scale shape skeleton extraction, 3D sensor network coverage, and high dimensional data PCA analysis.

英文关键词： convex decomposition; generalized; multi-scale; mutually exclusive; visual