# Rotation Invariant Graph Neural Network for 3D Point Clouds
## 8 Conclusions  
We used a new rotation normalization algorithm based on oriented bounding boxes to achieve rotation invariant for classification and semantic segmentation. We created an annotation tool for part segmentation on real camera data by using bounding-box rotation normalization. Classification and part segmentation networks were successfully trained on real camera data and deployed on an embedded device. Tests on synthetic datasets have shown that the networks are invariant to random rotations. By augmenting the training set with noisy data, the network performance was improved for Gaussian noise. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Nr. Points** & **Preproc (ms)** & **Inference (ms)** & **Total (ms)** \\ \hline \multirow{3}{*}{Pointnet} & 512 & - & 6.28 & 6.28 \\  & 1024 & - & 6.88 & 6.88 \\  & 2048 & - & 8.46 & 8.46 \\ \hline \multirow{3}{*}{RGCNN} & 512 & - & 4.91 & 4.91 \\  & 1024 & - & 12.09 & 12.09 \\  & 2048 & - & 57.39 & 57.39 \\ \hline \multirow{3}{*}{RGCNN BB} & 512 & 0.3 & 4.91 & 5.21 \\  & 1024 & 0.5 & 12.09 & 12.59 \\  & 2048 & 0.76 & 57.39 & 58.15 \\ \hline \multirow{3}{*}{RGCNN PCA} & 512 & 0.41 & 4.91 & 5.32 \\  & 1024 & 0.4 & 12.09 & 12.49 \\  & 2048 & 0.47 & 57.39 & 57.86 \\ \hline \multirow{3}{*}{RGCNN Gram (GPU)} & 512 & 0.85 & 6.07 & 6.92 \\  & 1024 & 2.16 & 23.75 & 25.91 \\  & 2048 & 10.71 & 143.22 & 153.93 \\ \hline \multirow{3}{*}{BB multi view} & 512 & 0.3 & 12.45 & 12.75 \\  & 1024 & 0.5 & 30.8 & 31.3 \\  & 2048 & 0.76 & 103.49 & 104.25 \\ \hline \multirow{3}{*}{PCA multi view} & 512 & 0.41 & 12.45 & 12.86 \\  & 1024 & 0.4 & 30.8 & 31.2 \\ \cline{1-1}  & 2048 & 0.47 & 103.49 & 103.96 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: All classification tests have been conducted on a Nvidia AGX Xavier 32 GB embedded platform. The inference of the models was conducted on the GPU, while the preprocessing step used the CPU, with the exception of the Gram method, for which we used the GPU. As can be seen, the unmodified RGCNN network is the fastest for small point clouds, while Pointnet maintains almost constant speed for a higher number of points. Furthermore, for 512 points in the point cloud, the bounding-box preprocessing method is slightly faster than the eigenvector matrix method, but becomes slower than the eigenvector matrix method when we increase the number of points. Gram matrix is considerably slower than the other two methods in the preprocessing stage. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Network** & **Model Size (MB)** & **Number of Parameters** \\ \hline Pointnet & 14 & 3.478.796 \\ \hline DGCNN & **7** & **1.809.576** \\ \hline RGCNN & 16 & 4148680 \\ \hline RGCNN Gram & 18 & 4539592 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Model size and number of parameters for Pointnet, DGCNN, RGCNN, and RGCNN with Gram matrix for the classification task. We consider the case where the input point cloud has 512 points. DGCNN has the smallest number of parameters. The Gram matrix RGCNN has a higher number of parameters and a larger model size than normal RGCNN because Gram preprocessing increases the size of the first convolution weight matrix from \(N\times 3\) to \(N\times N\). The network offers new estimations about the occupied volume and orientation of the point cloud which other rotation invariant methods do not provide. This is relevant for a number of tasks, including segmentation and classification pipelines. We aim to extend the network capability to multi-object classification and multi-object part segmentation for embedded devices. With a run-time efficient and robust method against noise, the results of the proposed algorithm are comparable with the ones from the main literature. Conceptualization, A.P. and L.T. ; funding acquisition, L.T. ; investigation, A.P. ; resources, A.P. and V.D. ; software, A.P. and V.D. ; supervision, L.T. ; validation, A.P. ; visualization, A.P. and V.D. ; writing--original draft, A.P. and V.D. ; writing review and editing, L.T.