## 4 Experiments
### Experiments on GPDNet Dataset  
In this experiment, we measured the performance of CMD-Net on the seven categories of the GPDNet dataset, _airplane_, _bench_, _car_, _chair_, _pillow_, _rifle_, and _sofa_, comparing our method with the state of the art. The instances in this dataset were canonicalized, and CMD-Net took in those from the canonical mapping part of the network though, since it had already learned the identity matrix. For a fair comparison, we used the evaluation codes provided in [7]. When the instances were corrupted by the low-level noise (\(\sigma=0.01\)), our method presented relatively competitive results (see Table 1a). GPDNet outperformed on four categories, _airplane_, _bench_, _car_, and _chair_. In the _chair_ category, CMD-Net reported slightly less than GPDNet: 29.50 was of GPDNet and our result was 30.05. APSS showed the best performance in the _pillow_ and _sofa_ categories. Our method performed best on _rifle_, the category that involved instances with high curvature. As the noise level increased, the merits of our method became distinctive. When the instances were corrupted by the mid-level noise (\(\sigma=0.015\)), CMD-Net performed on a par with GPDNet, reporting best results (see Table 1b). GPDNet reached the lowest C2C scores on _airplane_, _car_, _pillow_, and _sofa_ categories. For _airplane_ and _pillow_, our method closely kept track of GPDNet: 28.47-by-30.30 and 23.32-by-26.56. The success of CMD-Net was particularly demonstrated in the categories that involved high-curvature instances,bench_, _chair_, and _rifle_. Moving Least Squares (MLS)-based surface fitting [46, 47], point set resampling [48], sparsity-based [49], and graph-based [50, 51] methods showed degraded performance as the level of noise increased since they employ surface reconstruction or normal estimation. Learning-based PCN [6] deteriorated as it suffered from shrinkage and outliers due to direct displacement prediction. Our method estimated the points lying within the convex hull of the objects' shape through intrinsic structure point representations instead of estimating the displacement of the noisy points. This shows the resilience of our method across shrinkage and outliers. In case target instances are subjected to high-level noise (\(\sigma=0.02\)), CMDNet performs on a par with GPDNet showing the best values (see Table 1c). In general, CMD-Net had a similar pattern as the other methods, when the noise level increased from \(\sigma=0.01\) to \(\sigma=0.02\), the generated C2C scores also increased (see Table 1). For instance, for the _airplane_ category, the scores our method produced were 24.08 for \(\sigma=0.01\), 30.30 for \(\sigma=0.015\), and 43.24 for \(\sigma=0.02\). However, the ratio of the raise of our method was relatively lower. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline  & & & & & & & \\ \hline \hline
**Method** & **Airplane** & **Bench** & **Car** & **Chair** & **Pillow** & **Rife** & **Sofa** \\ \hline Noisy & 50.320 & 48.71 & 64.340 & 60.78 & 69.79 & 38.97 & 69.630 \\ DCCNN [50] & 44.82 & 38.700 & 60.47 & 59.69 & 64.28 & 26.99 & 65.05 \\ APSS [47] & 28.22 & 26.97 & 47.73 & 37.31 & **15.64** & 36.01 & **22.27** \\ RIMLS [46] & 39.73 & 32.76 & 55.56 & 45.650 & 21.23 & 49.37 & 28.04 \\ AWLOP [48] & 31.27 & 34.08 & 54.21 & 47.91 & 46.36 & 27.79 & 53.08 \\ MRPCA [49] & 28.19 & 32.93 & 44.33 & 38.41 & 23.95 & 23.49 & 32.14 \\ GLR [51] & 19.56 & 20.43 & 42.22 & 34.98 & 17.59 & 15.84 & 30.88 \\ PCN [6] & 26.36 & 27.64 & 75.34 & 55.10 & 21.07 & 15.09 & 43.36 \\ GPDNet [7] & **17.22** & **19.33** & **38.09** & **29.50** & 17.110 & 14.450 & 25.870 \\ \hline Ours & 24.08 & 23.16 & 54.63 & 30.05 & 18.12 & **13.12** & 41.17 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Denoising performance of our method (CMD-Net) on the GPDNet dataset is compared using the Chamfer Measure evaluation metric. The numbers in this table are C2C scores (see the metric in Section 4.1). Figure 5 presents several qualitative results.