无监督孪生函数映射网络的模型对应关系计算

Shape correspondence calculation using the unsupervised siamese functional maps network

针对构建非刚性形变三维模型间对应关系时特征描述符信息涵盖不全面、映射矩阵优化不理想的问题,提出了利用无监督孪生深度函数映射网络计算对应关系的新方法。首先,将源模型和目标模型输入到无监督孪生深度函数映射网络中学习原始三维几何特征,并将学习到的特征分别投影至各自拉普拉斯-贝尔特拉米特征基上获得相应的谱特征描述符;然后,将谱特征描述符输入至正则化函数映射层计算出鲁棒性更强的函数映射对应关系,进而获得最优的函数映射矩阵;再次,利用无监督学习方法计算倒角距离来构建无监督损失函数,以此度量模型间相似性,评估对应关系的计算结果;最后,基于迭代频谱上采样的ZoomOut算法将函数映射矩阵恢复成点到点对应关系。定性和定量的实验结果表明,在SURREAL数据集和TOSCA数据集上构建的模型间对应关系分布均匀一致,测地误差均有所减小。本算法不仅降低了算法的时间复杂度,而且在一定程度上提高了对应关系的计算准确率。此外,无监督孪生深度函数映射网络在不同数据集上泛化能力和可扩展性大大增强。

Aiming at the problems of incomplete feature descriptors information and unsatisfactory mapping matrix optimization when constructing the shape correspondence between non-rigid deformation 3D shapes,a novel approach is presented using the Unsupervised Siamese Deep Functional Maps Network(USDFMN)to calculate the shape correspondence.First,the source and target shapes are input to the USDFMN to learn the original 3D geometric traits,which are respectively projected to the Laplacian-Beltrami bases to get the corresponding spectral feature descriptors.Second,the spectral feature descriptors are input in the functional mapping layer to calculate the more robust correspondence where an optimal functional matrix is obtained.Third,an unsupervised learning model is employed to calculate the chamfer distance metric for designing the unsupervised loss function,which estimates the similarity between shapes and evaluates the final calculated correspondence.Finally,the function mapping matrices are restored to point-to-point correspondences using the ZoomOut algorithm.Qualitative and quantitative experimental results show that the proposed algorithm for the shape correspondence of the SURREAL and TOSCA datasets contributes to a uniform visualization in correspondence distributions and a reduction in the geodesic errors.It can not only reduce the time complexity but also improve the accuracy of the shape correspondence calculation to a certain extent.Moreover,the ability of the USDFMN to be generalized,as well as its scalability,is greatly enhanced on different datasets.