基于度量几何的三维关节变形模型的形状匹配研究

项目名称： 基于度量几何的三维关节变形模型的形状匹配研究

项目编号： No.61272229

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 自动化技术、计算机技术

项目作者： 刘玉身

作者单位： 清华大学

项目金额： 82万元

中文摘要： 三维形状匹配是指根据几何模型的形状特征，按一定的度量准则来衡量两个或多个模型间局部或整体的相似性。三维形状匹配是一个重要研究问题，在计算机图形学、计算机辅助设计、计算机视觉、模式识别和生物信息学等多个领域具有广泛的应用。传统的匹配方法大多仅针对刚性的三维实体处理，而缺少对非刚性形状匹配的深入研究。本课题基于度量几何的理论和方法，提出非刚性模型中三维关节变形模型的形状匹配框架和方法。本项目将系统地分析关节变形模型的变形原理和特性，研究基于度量几何的形状内蕴度量定义、表示和计算方法，提出新的形状匹配算法，从而为关节变形模型的形状比较、识别、检索和重用提供必要的技术保障。研究内容包括：基于Cauchy-Crofton 公式和最小中位数平方(LMS)优化的积分不变量的并行计算，基于谱分析技术的内部谱距离计算，基于正则形式和Gromov-Hausdorff距离的形状匹配算法。

中文关键词： 三维模型匹配；三维关节变形模型；度量几何；三维模型语义检索；三维模型语义标注

英文摘要： Given two or more 3D shapes, the goal of shape matching is to determine the global or partial similarities among these shapes by considering their geometrical features. 3D shape matching is a fundamental problem in various applications, such as computer graphics, computer aided design, computer vision, and pattern recognition. However, most conventional methods of shape matching are only effective for matching 3D rigid models, but they cannot handle the non-rigid models well. This proposal presents a new framework and methodology of shape matching for 3D articulated models, which is one representative class of non-rigid models, based on the theories and methods of metric geometry. It consists of three steps as follows. First, we will systematically analyze the shape deformation principle and characteristics of articulated models. We then propose the new intrinsic metric, representation and calculation algorithms for 3D articulated shapes based on metric geometry. Finally, a novel shape matching framework and methodology will be presented, and the new techniques will provide the necessary technical support for 3D articulated shape comparison, recognition, retrieval and reusing. The research topics include: the parallel computation of integral invariants based on the Cauchy-Crofton formula and LMS(least median of

英文关键词： 3D shape matching；3D articulated models；metric geometry；semantic retrieval of 3D models；semantic annotation of 3D models