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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 first-passage 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.Abstract: 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.
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图 1 逐对形状匹配方法可能导致错误结果的示例
Fig. 1 An example of misunderstanding of objects caused by pairwise shape matching methods
图 3 由2个类别样本对应的7个状态构成状态空间的示例
Fig. 3 An example of state space consisting of 7 states which corresponds to the samples from 2 categories
图 4 Tari-1000数据集中部分类别形状样本示例
Fig. 4 Examples of shapes from different categories in Tari-1000 database
图 5 MPEG-7数据集中部分类别形状样本示例
Fig. 5 Examples of shapes from different categories in MPEG-7 database
表 1 Kimia-216数据集在不同方法下检索结果比较
Table 1 Comparison of retrieval rates for different algorithms tested on Kimia-216 database
方法 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 全部 SC 216 216 215 210 210 209 208 204 200 191 175 2 254 IDSC 216 216 215 211 211 210 211 207 203 198 185 2 283 SC + LP 216 216 214 212 211 211 215 209 209 206 197 2 316 IDSC + LP 216 216 214 211 213 213 212 210 207 208 203 2 323 SC + MD 215 215 215 213 212 212 214 211 211 209 208 2 335 IDSC + MD 215 215 215 211 212 213 212 212 207 209 209 2 330 SC + MFPT 216 216 216 212 212 212 212 212 212 211 212 2 343 IDSC + MFPT 216 216 216 212 212 212 212 212 212 212 212 2 344 SC + GMFPT 216 216 216 216 216 216 216 216 216 216 216 2 376 IDSC + GMFPT 216 216 216 216 216 216 216 216 216 216 216 2 376 
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表 2 Tari-1000数据集在不同方法下的结果比较
Table 2 Comparison of results for different algorithms tested on Tari-1000 database
方法 检索精度 (%) SC 88.01 IDSC 90.43 SC + LP 94.22 IDSC + LP 96.44 SC + MD 94.98 IDSC + MD 98.49 SC + MFPT 97.02 IDSC + MFPT 99.11 SC + GMFPT 97.15 IDSC + GMFPT 99.27
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表 3 MPEG-7数据集在不同方法下的结果比较
Table 3 Comparison of results for different algorithms tested on MPEG-7 database
方法 检索精度 (Bullseye) (%) IDSC + LP[5] 91.61 SC + GM + Meta Descriptor[10] 92.51 IDSC + LCDP[6] 93.32 IDSC + Mutual Graph[22] 93.40 SC + MFPT[13] 94.04 ASC + LCDP[8] 95.96 ASC + TPG Diffusion[11] 96.47 SC + IDSC + Co-transduction[23] 97.72 IDSC + SSC+LCDP[9] 98.85 AIR + TPG Diffusion[11] 99.99 AIR + Generic Diffusion Framework[12] 100.00 AIR + GMFPT 100.00
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