Embedded Spectral Descriptors: Learning the point-wise correspondence metric via Siamese neural networks
This addresses a bottleneck in 3D shape analysis for applications like computer graphics and medical imaging, offering an incremental improvement over existing spectral descriptors.
The paper tackles the problem of spectral descriptors failing to measure similarity correctly for non-isometric shapes in mesh registration, and proposes embedding them into a metric space using a Siamese neural network to improve correspondence matching, demonstrating significant performance enhancement over state-of-the-art methods.
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.