中文摘要：

形状距离学习是形状匹配框架中引入的后处理步骤,能够有效改善逐对计算得到的形状间距离.利用期望首达时间分析形状间相似度可能导致距离更新不准确,针对这一问题提出了一种基于广义期望首达时间（Generalized mean firstpassage time,GMFPT）的形状距离学习方法.将形状样本集合视作状态空间,广义期望首达时间表示质点由一个状态转移至指定状态集合所需的平均时间步长,本文将其视作更新后的形状间距离.通过引入广义期望首达时间,形状距离学习方法能够有效地分析上下文相关的形状相似度,显式地挖掘样本空间流形中的最短路径,并消除冗余上下文形状信息的影响.将所提出的方法应用到不同形状数据集中进行仿真实验,本文方法比其他方法能够得到更准确的形状检索结果.

英文摘要：

With the help of shape distance learning introduced into shape matching framework as a post-processing procedure, shape distances obtained by pairwise shape similarity analysis can be improved effectively. A novel shape distance learning method based on generalized mean first-passage time（GMFPT） is proposed to solve the problem of inaccurate matching results caused by mean first-passage time. Given a set of shapes as the state space, the generalized mean first-passage time, which is regarded as the updated shape distance, is used to represent the average time step from one state to a certain set of states. With the generalized mean first-passage time introduced into the distance learning algorithms, context-sensitive similarities can be evaluated effectively, and the shortest paths on the distance manifold can be explicitly captured without redundant context. Simulation experiments are carried out on different shape datasets with the proposed method, and the results demonstrate that the retrieval score can be improved significantly.