  We present Neural Correspondence Prior (NCP), a new paradigm for computing
correspondences between 3D shapes. Our approach is fully unsupervised and can
lead to high-quality correspondences even in challenging cases such as sparse
point clouds or non-isometric meshes, where current methods fail. Our first key
observation is that, in line with neural priors observed in other domains,
recent network architectures on 3D data, even without training, tend to produce
pointwise features that induce plausible maps between rigid or non-rigid
shapes. Secondly, we show that given a noisy map as input, training a feature
extraction network with the input map as supervision tends to remove artifacts
from the input and can act as a powerful correspondence denoising mechanism,
both between individual pairs and within a collection. With these observations
in hand, we propose a two-stage unsupervised paradigm for shape matching by (i)
performing unsupervised training by adapting an existing approach to obtain an
initial set of noisy matches, and (ii) using these matches to train a network
in a supervised manner. We demonstrate that this approach significantly
improves the accuracy of the maps, especially when trained within a collection.
We show that NCP is data-efficient, fast, and achieves state-of-the-art results
on many tasks. Our code can be found online: https://github.com/pvnieo/NCP.
