The goal of this paper is to learn dense 3D shape correspondence for
topology-varying 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 part embedding vector for each
3D point, which is assumed to be similar to its densely corresponded point in
another 3D shape of the same object category. Furthermore, we implement dense
correspondence through an inverse function mapping from the part embedding to a
corresponded 3D point. Both functions are jointly learned with several
effective 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.

本文旨在以无监督的方式学习拓扑变异物体的密集三维形状对应关系，引入了一种新的隐式函数，该函数为每个三维点生成一个部分嵌入向量，实现对点的密集对应，通过面向部分的逆函数将部分嵌入向量映射到对应的三维点上，结合几个有效的损失函数进行联合学习。在推断期间，用户选择源形状上的任意点时，算法可以自动生成相应点的置信度分数和语义点，有效提升人造物体的形状分割及无监督三维语义对应。