## 1 Introduction  
Point clouds provide a compact representation of 3D shape. However, the imperfections on acquisition processes corrupt clouds by noise, thus diminishing point clouds' 3D shape representation power. Deep architectures directly consuming raw point clouds [1, 2], removing the requirement of 3D data preprocessing, pave the way for the learning-based point cloud denoising methods [3]. Forefront studies [4, 5, 6, 7] estimate the displacement of noisy points from the noise-free cloud and restore the underlying surface through reconstruction. However, incorrect displacement estimations cause performance degradation, therefore suffering from shrinkage and outliers. [PERSON] et al. [8] present a differentiable manifold reconstruction approach to learn the underlying manifold of a noisy point cloud. They aim to capture _intrinsic_ structures in point clouds, and they test their method on a ShapeNet dataset. However, they do not leverage the semantic consistency of the _categories_ to learn intrinsic structures consistently. Learning structures of 3D shapes are important for the tasks where different shape instances in a given category are co-analyzed, e.g., co-segmentation [9], shape abstraction [10], and shape correspondence estimation [11]. Such tasks present a structural understanding of the entire set. To this end, they necessarily leverage semantic consistency among shape instances. Recent deep learning methods learn to generate point clouds with structure information in an unsupervised way [12, 13]. Intrinsic structural representation points [11] are yet other unsupervised technique satisfying the consistency requirement through ordered sets of structure points. In this study, we leverage semantic consistency among the shape instances of a given category and formulate the denoising problem as a 3D semantic shape correspondence estimation task [11]. The aforementioned learning-based denoising methods generally require pre-aligned datasets. Contemporary studies for 3D scene understanding examine categorical objects in different poses. One distinct class of such studies is the category-level 6D object pose estimators [14; 15; 16; 17]. This class of pose estimators, employing category-level reasoning, align different instances of a given category in a shared pose-normalized canonical shape space and prompt interest in canonicalization learning, particularly in designing self-supervised approaches [18; 19; 20]. Condor [20] uses rotation information as a supervisory signal and is able to canonicalize point clouds. Our work circumvents the requirement on pre-aligned data, canonicalizing arbitrarily rotated clouds through a novel transformer. In this paper, we present a self-supervised method, Canonical Mapping and Denoising Network (CMD-Net), and address category-level point cloud denoising through canonicalization. Inspired by [11], we formulate denoising as a 3D semantic shape correspondence estimation task where we find out semantically consistent and ordered 3D intrinsic structure points. To this end, we leverage semantic consistency among the shape structures co-analyzing the variety of shape instances of a given category in the pose-normalized canonical space. Utilizing the convex hull of the explored structure points, the corruption on objects' surfaces is eliminated. Our method is also capable of canonicalizing noise-corrupted clouds under arbitrary rotations, therefore circumventing the requirement on pre-aligned data. The learning of the complete model is employed in a self-supervised fashion: the network automatically creates rotation matrices as supervisory signals through axis-aligned representation. By multiplying those with the unlabelled foreground clouds of the canonical 3D CAD models, rotated data are populated, and they are corrupted by noise. Using the data, the complete model learns to canonicalize the noise-corrupted input cloud through a novel transformer that serves as a proxy in the downstream denoising task.