稀疏性在数字几何处理中的应用研究

项目名称： 稀疏性在数字几何处理中的应用研究

项目编号： No.61303148

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： 张举勇

作者单位： 中国科学技术大学

项目金额： 25万元

中文摘要： 本项目将主要围绕稀疏性在数字几何处理中的应用研究，通过应用数学、计算机科学、数字信号处理等领域的理论与方法，开展数字几何处理相关问题的数学建模和高效数值算法设计的探索研究。这一类问题的研究不仅为数字几何处理领域注入了新的活力，而且对特征检测、曲面分割、局部网格编辑等问题提供了更加有效的解决思路。由于几何信号复杂的拓扑结构和不规则的采样、稀疏模型的非线性与不可微等特性，稀疏性在数字几何处理中的应用研究具有建模难、求解难、结构复杂等特点，有很大的挑战性。本项目将结合稀疏性在图像处理中的研究方法和申请人在图形图像处理中的研究经验，深入挖掘稀疏性在数字几何处理中的应用，探索数字几何处理中可能的新研究方法，力争在理论和方法上取得较大突破，实现拟定的研究目标。在项目实施过程中加强国内外学术交流，为培养具有创新能力的高水平人才，提高我国几何建模与数字几何处理理论研究水平和国际影响力做出贡献。

中文关键词： 数字几何处理；稀疏模型；数值最优化算法；网格恢复；网格重建

英文摘要： This project aims to study the application research on sparsity in digital geometry processing. By applying the theories and methods from applied mathematics、computer science and digital signal processing, relevant problems in digital geometry processing are formulated as sparse models,and solved by efficient numerical solvers. This kind of research not only stimulates the development of digital geometry processing, but also supplies more effective solutions to the problems such as feature detection、surface segmentation、local mesh editting, etc. However, due to the complex topology and irregular sampling of geometry signals as well as nonlinearity of the sparse models, this research has the characteristic that it is hard to be modelled and hard to be solved, besides, it has complex data structures. We can see that it is a challenging topic. In this project, we will combine the methods from the research of sparsity in image processing area and the applicant's research experiences in image and geometry processing to dig the applications of sparsity in geometry processing. To achieve this aim, we have to make a breakthrough at some new ideas and creative techniques. In the process of this project, we will further promote academic intercommunion with international experts, train young talents with innovative abiliti

英文关键词： Digital Geometry Processing；Sparse Model；Numerical Optimization Algorithm；Mesh Restoration；Mesh Reconstruction