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The objective of this paper is to learn dense 3D shape correspondence fortopology-varying generic objects in an unsupervised manner. Conventionalimplicit functions estimate the occupancy of a 3D point given a shape latentcode. Instead, our novel implicit function produces a probabilistic embeddingto represent each 3D point in a part embedding space. Assuming thecorresponding points are similar in the embedding space, we implement densecorrespondence through an inverse function mapping from the part embeddingvector to a corresponded 3D point. Both functions are jointly learned withseveral effective and uncertainty-aware loss functions to realize ourassumption, together with the encoder generating the shape latent code. Duringinference, if a user selects an arbitrary point on the source shape, ouralgorithm can automatically generate a confidence score indicating whetherthere is a correspondence on the target shape, as well as the correspondingsemantic point if there is one. Such a mechanism inherently benefits man-madeobjects with different part constitutions. The effectiveness of our approach isdemonstrated through unsupervised 3D semantic correspondence and shapesegmentation.

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