## 2 Related Work
### 3D Structure Learning  
There are important studies in the literature addressing 3D structure learning in an unsupervised fashion. FoldingNet [21] presents a folding decoder that constructs the 3D surface of a point cloud by deforming a 2D canonical manifold. The sequential folding operations preserve the point correspondence. PPF-FoldNet [22] leverages the well-known point pair features (PPFs) to generate discriminatively encoded code words, which are then fed into the decoder to reconstruct PPFs by folding. AtlasNet [12] deforms  
Figure 1: CMD-Net is a self-supervised method that addresses category-level 3D shape denoising through canonicalization: (**top left**) synthetic objects; (**top right**) cluttered real data; and (**bottom**) denoised samples in the canonical space shown at different viewpoints. primitive structures to generate structured point clouds; however, the primitives depend on hand-chosen parametric shapes. TopNet [13] circumvents this dependency designing a tree-structured decoder network. Being similar to FoldingNet, the study in [23] deforms primitive shapes, but it also has a supervised setting in which point correspondences across training samples are utilized. 3D-PointCapsNet [24] encodes shape information in latent capsules. The Tree-GAN method [25] generates 3D point clouds introducing tree-structured graph convolution network (TreeGCN). TreeGCN increases the representational power of the features through ancestor information, which is also utilized for generating objects' parts. The study in [26] explores geometrically and semantically consistent category-specific 3D keypoints exploiting the symmetric linear basis representation. It exploits the symmetric linear basis representation for modeling the 3D shapes of objects of a given category. KeypointDeformer [27] represents different instances of a given category with semantically consistent 3D keypoints. When the instance changes, it controls the deviation in shape through its deformation model that propagates the keypoint displacement to the rest of the shape. The autoencoder architecture of Skeleton Merger [28] leverages the skeletal representation; the encoder generates keypoint proposals, and the decoder reconstructs point clouds from their skeletons. The generator of SP-GAN [29] makes use of a uniform sphere as a global prior and a random latent code as a local prior for each point involved in the sphere to finally generate part-aware shapes. LAKe-Net [30] localizes aligned keypoints for the topology-aware point cloud completion task. There recently has been a surge of interest in self-supervised point cloud understanding. Some important works learn 3D structures of the point clouds via 3D keypoints [31; 32; 33; 34; 35]. The framework in KeypointNet [31] is applicable for any downstream task as long as the loss function is differentiable with respect to the location of the keypoints. KeypointNet formulates 3D pose estimation as the downstream task for which 3D keypoints are jointly optimized as a set of latent variables. USIP [32] detects stable (repeatable and accurate) keypoints from 3D point clouds using the feature proposal network (FPN) whose training is employed through transformation matrices automatically created for each training pair. As employed in [32; 33], the authors use rotation information in an auxiliary task and produce semantic features 3D keypoint prediction. D3 Feat [34] proposes a joint keypoint and descriptor learning framework for point cloud alignment. It designs a density-invariant keypoint selection scheme to increase repeatability and uses a keypoint-guided loss to increase consistency. The studies in [36; 37] present a self-supervised upsampling autoencoder. [PERSON] et al. [37] use a pretrained upsampling autoencoder network for initializing any downstream task (e.g., classification, segmentation) that will benefit from the network's capabilities on learning high-level semantics and low-level geometry. [PERSON] et al.