Implicit field supervision for robust non-rigid shape matching

Establishing a correspondence between two non-rigidly deforming shapes is one of the most fundamental problems in visual computing. Existing methods often show weak resilience when presented with challenges innate to real-world data such as noise, outliers, self-occlusion etc. On the other hand, auto-decoders have demonstrated strong expressive power in learning geometrically meaningful latent embeddings. However, their use in shape analysis and especially in non-rigid shape correspondence has been limited. In this paper, we introduce an approach based on auto-decoder framework, that learns a continuous shape-wise deformation field over a fixed template. By supervising the deformation field for points on-surface and regularising for points off-surface through a novel Signed Distance Regularisation (SDR), we learn an alignment between the template and shape volumes. Unlike classical correspondence techniques, our method is remarkably robust in the presence of strong artefacts and can be generalised to arbitrary shape categories. Trained on clean water-tight meshes, without any data-augmentation, we demonstrate compelling performance on compromised data and real-world scans.