本项目主要研究图的Laplace谱理论及其在计算机视觉中若干问题的应用。理论成果包括：（1）刻画图的极端谱性质, 建立了图的特征值和图的结构参数的联系, 如染色数、腰长、点/边连通度、控制数等；（2）首次提出图的Laplace谱跨度的新概念, 对若干类圈空间维数较小的图类刻画了具有极端谱跨度的图；（3）首次开展混合图的Laplace特征向量结构性质的研究, 此外也获得了树的一般Laplace特征向量的结构性质。应用成果为：提出基于图的Laplace谱的匹配、分类或聚类方法，并结合其它方法（如薄板样条法、概率松弛法法、形状上下文法等），充分利用图的结构信息（如最小生成树、图的中心），获得了若干有效的算法。.项目组成员共发表论文52篇, 其中被SCI收录20篇, EI收录21篇, ISTP收录6篇, 出版译著1部. 论文中的一些新方法和新概念已被同行专家引用或跟踪研究。参加9次国际国内学术会议, 并与台湾淡江大学Tam Bit-Shun教授进行合作研究。研究成果《谱图理论及应用》通过安徽省科学技术厅鉴定。培养了15名硕士生, 正在指导4名博士生和16名硕士生。

This program mainly study the Laplacian spectral theory of graphs and its applications in computer vision. The theoretical achievements contain: (1) characterizing the extreme spectral properties of graphs, and establishing the connection between the eigenvalues and the structural parameters of graphs, such as chromatic number, girth, vertex/edge connectivity and domination number; (2) firstly introducing the new concept of Laplacian spectral spread, and characterizing the graphs with extreme spectral spread among several classes of graphs with small ities of cycle space; (3) firstly discussing the structural property of the Laplacian eigenvectors of mixed graphs, and in addition obtaining the structural property of general eigenvectors of trees. For the application achievements, we introduce some methods of matching, classification or clustering based on Laplacian spectra of graphs, which are combined with other methods (thin plate spline, probabilistic relaxation, shape context etc.) and the graph structure information (minimum spanning tree, graph center), and then obtain some efficient algorithms..We published 52 papers, of which 20 papers are indexed by SCI database, 21 papers are indexed by EI datebase and 6 papers are indexed by ISTP database. We published a translation book. Some new methods and concepts are cited or followed in research by our peers. We participated in 9 international or domestic conferences or workshops, and collaborated with Professor Tam Bit-Shun of Tamkang University. The achievement "Spectral Graph Theory and Applications" was appraised by Anhui Science and Technology Department. We trained 15 master students, and are supervising 4 Ph.D. students and 16 master students.

本项目主要研究图的Laplace谱理论及其在计算机视觉中若干问题的应用。理论成果包括：（1）刻画图的极端谱性质, 建立了图的特征值和图的结构参数的联系, 如染色数、腰长、点/边连通度、控制数等；（2）首次提出图的Laplace谱跨度的新概念, 对若干类圈空间维数较小的图类刻画了具有极端谱跨度的图；（3）首次开展混合图的Laplace特征向量结构性质的研究, 此外也获得了树的一般Laplace特征向量的结构性质。应用成果为：提出基于图的Laplace谱的匹配、分类或聚类方法，并结合其它方法（如薄板样条法、概率松弛法法、形状上下文法等），充分利用图的结构信息（如最小生成树、图的中心），获得了若干有效的算法。项目组成员共发表论文52篇, 其中被SCI收录20篇, EI收录21篇, ISTP收录6篇, 出版译著1部. 论文中的一些新方法和新概念已被同行专家引用或跟踪研究。参加9次国际国内学术会议, 并与台湾淡江大学Tam Bit-Shun教授进行合作研究。研究成果《谱图理论及应用》通过安徽省科学技术厅鉴定。培养了15名硕士生, 正在指导4名博士生和16名硕士生。