Point clouds are a popular representation for 3D shapes. However, they encode a particular sampling without accounting for shape priors or non-local information. We advocate for the use of a hierarchical Gaussian mixture model (hGMM), which is a compact, adaptive and lightweight representation that probabilistically defines the underlying 3D surface. We present PointGMM, a neural network that learns to generate hGMMs which are characteristic of the shape class, and also coincide with the input point cloud. PointGMM is trained over a collection of shapes to learn a class-specific prior. The hierarchical representation has two main advantages: (i) coarse-to-fine learning, which avoids converging to poor local-minima; and (ii) (an unsupervised) consistent partitioning of the input shape. We show that as a generative model, PointGMM learns a meaningful latent space which enables generating consistent interpolations between existing shapes, as well as synthesizing novel shapes. We also present a novel framework for rigid registration using PointGMM, that learns to disentangle orientation from structure of an input shape.

中文翻译：

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PointGMM：点云的神经 GMM 网络

点云是 3D 形状的流行表示。然而，它们对特定采样进行编码，而不考虑形状先验或非局部信息。我们提倡使用分层高斯混合模型 (hGMM)，这是一种紧凑、自适应和轻量级的表示，可以概率性地定义底层 3D 表面。我们提出了 PointGMM，这是一种神经网络，它学习生成具有形状类特征的 hGMM，并且与输入点云一致。PointGMM 在一系列形状上进行训练，以学习特定于类的先验。分层表示有两个主要优点：（i）从粗到细学习，避免收敛到较差的局部最小值；(ii)（无监督的）输入形状的一致分区。我们表明，作为一个生成模型，PointGMM 学习一个有意义的潜在空间，它能够在现有形状之间生成一致的插值，以及合成新的形状。我们还提出了一个使用 PointGMM 进行刚性配准的新框架，该框架学习从输入形状的结构中解开方向。