Learning Implicit Functions for Dense 3D Shape Correspondence of Generic Objects

TL;DR

This paper introduces an unsupervised method for dense 3D shape correspondence that uses a probabilistic embedding approach, enabling automatic correspondence and confidence scoring between topology-varying objects.

Contribution

It proposes a novel implicit function that produces probabilistic embeddings for 3D points, facilitating dense correspondence without supervision and handling shape variability.

Findings

Effective unsupervised 3D semantic correspondence achieved

Automatic confidence scoring for correspondences demonstrated

Shape segmentation performance improved

Abstract

The objective of this paper is to learn dense 3D shape correspondence for topology-varying generic objects in an unsupervised manner. Conventional implicit functions estimate the occupancy of a 3D point given a shape latent code. Instead, our novel implicit function produces a probabilistic embedding to represent each 3D point in a part embedding space. Assuming the corresponding points are similar in the embedding space, we implement dense correspondence through an inverse function mapping from the part embedding vector to a corresponded 3D point. Both functions are jointly learned with several effective and uncertainty-aware loss functions to realize our assumption, together with the encoder generating the shape latent code. During inference, if a user selects an arbitrary point on the source shape, our algorithm can automatically generate a confidence score indicating whether there is a correspondence on the target shape, as well as the corresponding semantic point if there is one. Such a mechanism inherently benefits man-made objects with different part constitutions. The effectiveness of our approach is demonstrated through unsupervised 3D semantic correspondence and shape segmentation.