## 5 Conclusions  
In this paper, we have introduced the Canonical Mapping and Denoising Network (CMD-Net) for _category-level 3D shape denoising through canonicalization_. Unlike the standard learning-based denoising methods that predict displacement of noise-corrupted points from the underlying surface, CMD-Net formulates denoising as a 3D semantic shape correspondence estimation task. Exploring ordered intrinsic structure points is particularly important to eliminate corruption from unseen instances of given categories, thus bringing increased resilience across shrinkage and outliers.  
From the data point of view, the strengths of our method are four-fold: (i) our self-supervised design. Pseudo labels are automatically populated, and thus with no resort to data labels, our training is employed. (ii) Canonical Mapping. Being capable of canonicalizing noise-corrupted clouds under arbitrary rotations, we circumvent the dependency on pre-aligned data. (iii) CMD-Net can operate on both synthetic and real data. (iv) The CMD-Net dataset is another plus of the presented research. It comprises rotated and noise-corrupted instances of given categories. These strengths enable us to increase the generalization capability of our method.  
Regarding the challenges, CMD-Net has multiple merits: (i) clutter. The depth image of an hypothesis generated by any 2D (or 3D) object detector potentially contains background clutter that affects the representation of the object of interest. Our self-supervised method, learning the convex hull of the shapes, copes with this challenge and suppresses the points  
Figure 9: Sample results from experiments on real data. Our method can deal with clutter and missing pixels (points) challenges. In each triplet, left is the rotated input cloud, middle is the canonicalization, and the right-most is the denoised and the canonicalized.  
existing beyond the object's hull. (ii) Missing pixels (points). The designs of both the canonical mapping part and the denoising part of CMD-Net are based on PointNet++. Learning the representations of objects in a hierarchical fashion, CMD-Net handles missing points. (iii) Intra-class variation. CMD-Net leverages intrinsic structure points to learn the structures of the instances given in a category of interest. This correspondingly enables our method to handle intra-class variations.  
Despite the advantages of CMD-Net, there are limitations: (i) Number of structure points and GPU memory. CMD-Net denoises the interested objects exploring their intrinsic structures. In accordance with our network design and interested problem, the generation of a high number of structure points gives rise to an increase in the memory usage exceeding the limits of resources. In such cases, we generate a limited number of structure points and then employ upsampling. (ii) Canonicalization. Currently, CMD-Net operates in a relatively narrower search space for canonicalizing any arbitrarily rotated objects.  
In the future, we are planning to improve the performance of CMD-Net, particularly on arbitrarily rotated objects. Investigating the effect of our method on the instances that have severe topological discrepancies will be a potential research direction. One of our aims will be to extend the search space of CMD-Net for canonical mapping. We are planning to define novel loss functions to improve the performance of our method for canonicalization purposes.  
This research received no external funding.  
Not applicable.  
One project page for this research is under construction. The project web-page will be announced in the following web-page: [[https://avesis.medeniyet.edu.tr/caner.sahin/en](https://avesis.medeniyet.edu.tr/caner.sahin/en)]([https://avesis.medeniyet.edu.tr/caner.sahin/en](https://avesis.medeniyet.edu.tr/caner.sahin/en)).  
The author would like to thank the anonymous reviewers and journal editors for their constructive comments and suggestions, which improve the quality of the paper.  
The author declares no conflict of interest.