Rotation Perturbation Robustness in Point Cloud Analysis: A Perspective of Manifold Distillation

TL;DR

The point cloud is remodeled from the perspective of manifold as well as a manifold distillation method to achieve the robustness of rotation perturbation without any coordinate transformation, which shows excellent performance in resisting noise and outliers.

Abstract

Point cloud is often regarded as a discrete sampling of Riemannian manifold and plays a pivotal role in the 3D image interpretation. Particularly, rotation perturbation, an unexpected small change in rotation caused by various factors (like equipment offset, system instability, measurement errors and so on), can easily lead to the inferior results in point cloud learning tasks. However, classical point cloud learning methods are sensitive to rotation perturbation, and the existing networks with rotation robustness also have much room for improvements in terms of performance and noise tolerance. Given these, this paper remodels the point cloud from the perspective of manifold as well as designs a manifold distillation method to achieve the robustness of rotation perturbation without any coordinate transformation. In brief, during the training phase, we introduce a teacher network to learn the rotation robustness information and transfer this information to the student network through online distillation. In the inference phase, the student network directly utilizes the original 3D coordinate information to achieve the robustness of rotation perturbation. Experiments carried out on four different datasets verify the effectiveness of our method. Averagely, on the Modelnet40 and ScanobjectNN classification datasets with random rotation perturbations, our classification accuracy has respectively improved by 4.92% and 4.41%, compared to popular rotation-robust networks; on the ShapeNet and S3DIS segmentation datasets, compared to the rotation-robust networks, the improvements of mIoU are 7.36% and 4.82%, respectively. Besides, from the experimental results, the proposed algorithm also shows excellent performance in resisting noise and outliers.

Figures (8)

• Figure 1: Different segmentation results of PointNet++. (a) Original segmentation results; (b) The segmentation results when the axis is rotated 30°.
• Figure 2: The procedure of manifold mapping. $\alpha$ is a point on the manifold $\mathcal{M}$, open set ${U_\alpha }$ is the neighborhood of $\alpha$, and ${P_\alpha }$ is the discrete sampling of ${U_\alpha }$. A coordinate mapping ${\varphi _\alpha }$ maps $P_{\alpha}$ to $X_{\alpha}$, which is located in local Euclidean space $R^n$, while the image of $\alpha$ is $x_{\alpha}$. $\bar{f}$, a mapping from $R^n$ to $R^{n'}$, maps $X_{\alpha}$ to $x_{\beta}$, which is the image by applying mapping ${\varphi _\beta }$ on $\beta$ of the manifold $\mathcal{M'}$. This process equals to the manifold mapping $f$ from $\mathcal{M}$ to $\mathcal{M'}$.
• Figure 3: Overall framework of our network.
• Figure 4: The architectures of MM model and alignment model.
• Figure 5: The t-SNE results of different networks at 0° and 30°, where 0°/30° refer to the corresponding degrees of rotation on coordinate axis. Different colors represent different categories. (a) PointNet; (b) PointNet++; (c) PointCNN; (d) DGCNN; (e) SPRIN; (f) Li $et\ al$; (g) Riconv++; (h) Ours.