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A robust and informative local shape descriptor plays an important role inmesh registration. In this regard, spectral descriptors that are based on thespectrum of the Laplace-Beltrami operator have been a popular subject ofresearch for the last decade due to their advantageous properties, such asisometry invariance. Despite such, however, spectral descriptors often fail togive a correct similarity measure for non-isometric cases where the metricdistortion between the models is large. Hence, they are not reliable forcorrespondence matching problems when the models are not isometric. In thispaper, it is proposed a method to improve the similarity metric of spectraldescriptors for correspondence matching problems. We embed a spectral shapedescriptor into a different metric space where the Euclidean distance betweenthe elements directly indicates the geometric dissimilarity. We design andtrain a Siamese neural network to find such an embedding, where the embeddeddescriptors are promoted to rearrange based on the geometric similarity. Wedemonstrate our approach can significantly enhance the performance of theconventional spectral descriptors by the simple augmentation achieved via theSiamese neural network in comparison to other state-of-the-art methods.

Embedded Spectral Descriptors: Learning the point-wise correspondence metric via Siamese neural networks