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

TL;DR

This paper introduces a neural network-based method to improve spectral shape descriptors for non-isometric shape correspondence, enhancing their reliability and accuracy in complex geometric scenarios.

Contribution

It proposes embedding spectral descriptors into a learned metric space using Siamese neural networks, which better captures geometric dissimilarities for shape matching.

Findings

Significantly improves spectral descriptor performance in non-isometric cases

Outperforms state-of-the-art methods in shape correspondence tasks

Demonstrates robustness across various shape models

Abstract

A robust and informative local shape descriptor plays an important role in mesh registration. In this regard, spectral descriptors that are based on the spectrum of the Laplace-Beltrami operator have been a popular subject of research for the last decade due to their advantageous properties, such as isometry invariance. Despite such, however, spectral descriptors often fail to give a correct similarity measure for non-isometric cases where the metric distortion between the models is large. Hence, they are not reliable for correspondence matching problems when the models are not isometric. In this paper, it is proposed a method to improve the similarity metric of spectral descriptors for correspondence matching problems. We embed a spectral shape descriptor into a different metric space where the Euclidean distance between the elements directly indicates the geometric dissimilarity. We design and train a Siamese neural network to find such an embedding, where the embedded descriptors are promoted to rearrange based on the geometric similarity. We demonstrate our approach can significantly enhance the performance of the conventional spectral descriptors by the simple augmentation achieved via the Siamese neural network in comparison to other state-of-the-art methods.