## 4 Experiments
### Experiments on CMD-Net Dataset  
We performed this class of experiments on the CMD-Net dataset to demonstrate the performance of our method on rotated unseen instances. Unlike the experiments in Section 4.3, we measured the performance of our method using our evaluation codes. Since this is the first time we introduce the CMD-Net dataset, we present intra-class analyses. Table 2 depicts the denoising performance of our method for \(\sigma=0.01\), \(\sigma=0.015\), and \(\sigma=0.02\), and _noisy_ rows show the C2C scores of the input noise-corrupted test instances. According to the table, our method reached the lowest score on _airplane_, and the score of the _car_ category was the highest for the low-level noise (\(\sigma=0.01\)). In case the test instances was corrupted by mid-level noise (\(\sigma=0.015\)), the value of the _chair_ category was the minimum, and _pillow_ was the maximum. At the high-level noise (\(\sigma=0.02\)), _rife-car_ pair had 0.64-by-0.96 as the minimum-maximum pair of the scores. Despite giving an idea about the performance of CMD-Net, we find this analysis insufficient, since the C2C scores of the test instances involved in each category were different. Therefore, our next error analysis presents the scores of CMD-Net normalized by _noisy_ rows of Table 2.  
The left-most image of Figure 6 is of the normalized C2C scores for the low-level noise. As depicted in the image, our method performed best on the _airplane_ category. Although _chair_ was the third successful category for the low-level noise, CMD-Net performed best on this category when the objects were corrupted by the mid-level noise (see the middle image in Figure 6). The right-most image expresses the normalized score for \(\sigma=0.02\). As apparent, the scores of the _pillow_ category were the minimum, and the method showed degraded performance on the _car_ category. Figure 5: Sample results from experiments on GPD-Net dataset: instances in the first row are of ground truth canonical point clouds, the second row shows inputs to be denoised in the **testing stage** (\(\sigma=0.02\)), the third row shows the outputs of our method. The normalized errors are presented in Figure 7, the left image of which presents the cumulative errors, while the right one indicates the weights of noise levels on the cumulative errors. On the left, we see that when the normalized errors of all noise-levels are summed up, our method performed best on the _chair_ category, and _airplane_, _sofa_, and _pillow_ subsequently follow. The categories of _bench_ and _rife_ were relatively degraded, and the CMD-Net lowest record was on the _car_ category. Given the right image, it is apparent that the error scores of the low-level noise had the highest weight, demonstrating that our method showed better performance as the noise-level increased. We lastly observe the influence of a different registration approach altering the self-supervised canonical mapping part of CMD-Net. We changed the Canonical Mapping part of our network with PointNetLK (PNLK) [52] and named it PNLKD-Net. We show the results in Table 3 in the categories in which our method most underperformed: _car_, _bench_, _rife_. When we alter the canonical mapping part of our network with PNLK, our method outputs increased performance ensuring more accurate canonicalization results. CMD-Net,