耦合映射的非等距三维模型簇对应关系计算  

Correspondence Calculation for Non-isometric 3D Shape Collection via Coupled Maps

作　　者：杨军[1,2] 薛又中 YANG Jun;XUE Youzhong(School of Electronic and Information Engineering,Lanzhou Jiaotong University,Lanzhou 730070;Faculty of Geomatics,Lanzhou Jiaotong University,Lanzhou 730070)

机构地区：[1]兰州交通大学电子与信息工程学院,兰州730070 [2]兰州交通大学测绘与地理信息学院,兰州730070

出　　处：《模式识别与人工智能》2025年第2期116-131,共16页Pattern Recognition and Artificial Intelligence

基　　金：国家自然科学基金项目(No.42261067);2025年度甘肃省重点人才项目(No.2025RCXM031)资助。

摘　　要：针对现有非等距模型簇对应关系计算方法准确率较低且泛化能力较差的问题,文中提出耦合映射的非等距三维模型簇对应关系计算方法.首先,使用DiffusionNet直接从三维模型中提取初始特征,获取具有鉴别能力的特征描述符.然后,使用描述符分别计算函数映射矩阵与逐点映射矩阵,并对两种矩阵分别施加结构正则化约束与执行Softmax归一化,得到最优耦合映射矩阵.最后,基于虚拟模板的模型簇匹配模块以模型初始特征作为输入,结合耦合映射构建的点分类器,直接预测模型与虚拟模型之间的匹配关系,通过Gumbel-Sinkhorn归一化,得到最终的非等距模型簇对应关系.实验表明,文中方法能有效处理非等距模型簇中的伪影噪声,对应关系计算的测地误差较小,结果较准确,泛化性较优.To address the issues of low accuracy and poor generalization ability in existing non-isometric 3D shape collection correspondence calculation methods,a correspondence calculation method for non-isometric 3D shape collection via coupled maps is proposed.First,DiffusionNet is employed to directly extract initial features from the 3D shape,and thus discriminative feature descriptors are obtained.Then,functional maps matrix and point-to-point maps matrix are computed using these descriptors.Structural regularization constraints and softmax normalization are applied to both matrices,respectively,to obtain an optimal coupled maps matrix.Finally,a shape collection matching module based on a virtual template takes the initial model features as input and employs a point classifier constructed with the coupled maps to directly predict the correspondence between the shapes and the virtual templates.The final correspondence for the non-isometric shape collection is obtained through Gumbel-Sinkhorn normalization.Experimental results demonstrate that the proposed method effectively handles topological noise within non-isometric shapes,achieves low geodesic error in correspondence calculation,provides accurate results,and exhibits strong generalization ability.

关 键 词：对应关系 非等距三维模型簇 深度学习 耦合映射 Gumbel-Sinkhorn归一化 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]