离散曲面匹配问题研究

With the widely usage of discrete surface in the field of 3D computer animation and game designing, discrete surface matching problem have received a lot of attention and research from academics home and abroad. But the traditional algorithms still cannot achieve a good understanding of the semantic structures for discrete surface, and it is also difficult to apply them to process large-scale discrete surface for their heavy computation burden. This project applies kernel methods, which are a class of important methods in pattern recognition, to discrete surface matching problem, and carry out the researches on discrete surface matching algorithms based on kernel methods. The goal of the project is to make the new discrete surface matching algorithms can not only have the advantages of pose-invariance and low computation cost but also identify the semantic structures of mesh models much better by utilizing the advantage of kernel methods. To achieve this goal, the methods of converting mesh data to vectors are firstly considered for discrete surface matching problem, then suitable high dimensional spaces and corresponding kernel functions are looked for, and suitable discrete surface matching methods are tried to find out in high dimensional spaces lastly. The research of this project will improve the effectiveness and efficiency of current discrete surface matching algorithms further, and thereby enhance the efficiency in the production of 3D computer animations and games. It is meaningful in theory and practice.

随着离散曲面在计算机三维动画制作和游戏设计等领域的广泛应用，离散曲面的匹配问题引起了国内外学者的大量关注和研究。但传统的匹配算法仍不能很好的实现对离散曲面语义结构的理解，同时所需的计算量也较大，难以应用在大规模离散网格曲面的处理上。本项目结合模式识别中的重要方法——核方法，开展离散曲面匹配算法研究。其目标是通过利用核方法的优势，使得离散曲面匹配新算法能够具有姿势不变和计算效率高等优点，同时能够较传统算法更好的识别离散曲面的语义结构特征。为实现上述目标，需要首先针对离散曲面匹配问题，研究确定将离散曲面数据转化为向量的方法，并寻找问题适用的高维特征空间和核函数，继而寻找高维特征空间中适用的离散曲面匹配方法。本项目的研究将进一步提高离散曲面匹配算法的效果和效率，从而提升计算机三维动画和游戏设计制作的效率，具有一定的理论意义与应用价值。

随着离散曲面在计算机三维动画制作和游戏设计等领域的广泛应用，离散曲面的匹配问题，作为三维模型分类、检索等问题的本质问题，引起了国内外学者的大量关注和研究。本项目组以离散曲面匹配算法为研究目标展开了深入而广泛的研究工作，提出了2种新的离散曲面匹配算法。这些算法不但具有姿势不变、放缩不变、以及刚体变换不变等优点，而且实现简单、计算效率高、鲁棒性强，与现有算法相比，能够更好的衡量离散曲面间的相似度。基于这2种新的离散曲面匹配算法，项目组撰写了2篇论文，1篇已由国外EI期刊发表，另1篇已被国内EI期刊录用。同时，相关算法已经被编写成软件系统，并获得软件著作权授权1项。在项目的研究期间内，项目组圆满完成了项目的预期目标，今后将一方面积极与企业合作，争取将研究成果应用于计算机三维动画制作和游戏设计等相关产业，提高企业的生产效率，另一方面将继续深入开展相关研究，争取发现更多性质优越的离散曲面特征提取方法和相似度衡量方法，并发表相关论文。