基于拟共形映射Teichmüller理论的曲面配准研究

项目名称： 基于拟共形映射Teichmüller理论的曲面配准研究

项目编号： No.61303078

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 自动化技术、计算机技术

项目作者： 于晓康

作者单位： 青岛大学

项目金额： 23万元

中文摘要： 带约束大的非刚性和各向异性形变曲面配准是3D曲面配准的难点。Teichmüller拟共形映射是最小化最大角度扭曲的微分同胚映射，该映射既可满足曲面约束条件的精确配准，又能描绘非刚性各向异性的曲面变形得到曲面间1-1映射，有望成为解决曲面配准问题的有效方法。本课题将研究基于Teichmüller映射带约束任意拓扑曲面的配准问题及应用。内容包括：通过Teichmüller理论分析带约束各向异性形变曲面的特有变形性质对该类配准问题进行统一建模；研究任意拓扑曲面间Teichmüller拟共形映射的计算方法；将通过Teichmüller映射配准任意黎曼曲面到特定的二维平面区域从而计算任意曲面的全局等温坐标；与黎曼几何相结合解决非完整曲面配准问题；将基于Teichmüller映射的曲面配准方法应用于人脸曲面匹配、表情提取及分析、大脑医学形态学诊断等具体领域，给出更高效准确的方法。

中文关键词： Teichmüller映射；曲面配准；人脸追踪；四边形化；

英文摘要： Constrained surface registration with large non-rigid deformation and anisotropic deformation is the one of the most challenging and important. Teichmüller quasi-conformal mapping is a diffeomorphism minimizing the maximum angle distortion. This kind of mapping, which can not only satisfy the constrains between surfaces, but also describe the anisotropic non-rigid surface deformation, is an effective method to solve the surface registration problem. We plan to research on the Teichmüller mapping between surfaces with constrained conditions and the applications of surface registration based on Teichmüller theory. Our researches include the following aspects. We will analyze the properties of non-rigid and anisotropic deformations on the surface with constrained conditions by Teichmüller theory and model the surface registration problems. Then by researching on the properties of the metrics on the original surface and target surface, we will develop the algorithm to search the Teichmüller mapping between general surfaces. By combining with the method in Riemannian geometry, we will develop the algorithm to tackle the incomplete surface registration problem. Research on using the method of surface registration based on Teichmüller mapping to the application fields, which include face matching, expression extraction

英文关键词： Teichmüller mapping；Surface registration；Facial tracking；Quadrangulation；