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.

翻译：本文的目的是以不受监督的方式为表层变异的通用对象学习密度 3D 形状对应。 常规隐含功能估计3D 点的占用情况, 给定了一个形状潜伏代码 。 相反, 我们的新隐含功能产生一种概率嵌入, 以在嵌入空间中代表每个 3D 点。 假设相应的点在嵌入空间中相似, 我们通过嵌入矢量部分的反函数映射执行密度对应3D 点。 两种功能都是与若干有效且具有不确定性的丢失函数共同学习的, 以实现我们的假设, 以及生成形状潜伏代码的编码 。 在推断中, 如果用户选择源形状上的任意点, 我们的算法可以自动产生信任度分数, 显示目标形状上是否有对应点, 如果有的话, 以及对应的语系点 。 这种机制必然有利于具有不同形状的人造物体。 我们的方法的有效性通过不超的 3D 语义对应和形状分割来显示。