Local-consistent Transformation Learning for Rotation-invariant Point Cloud Analysis

TL;DR

Equipped with LCRF and RPR, the LocoTrans is capable of learning local-consistent transformation and preserving local geometry, which benefits rotation invariance learning.

Abstract

Rotation invariance is an important requirement for point shape analysis. To achieve this, current state-of-the-art methods attempt to construct the local rotation-invariant representation through learning or defining the local reference frame (LRF). Although efficient, these LRF-based methods suffer from perturbation of local geometric relations, resulting in suboptimal local rotation invariance. To alleviate this issue, we propose a Local-consistent Transformation (LocoTrans) learning strategy. Specifically, we first construct the local-consistent reference frame (LCRF) by considering the symmetry of the two axes in LRF. In comparison with previous LRFs, our LCRF is able to preserve local geometric relationships better through performing local-consistent transformation. However, as the consistency only exists in local regions, the relative pose information is still lost in the intermediate layers of the network. We mitigate such a relative pose issue by developing a relative pose recovery (RPR) module. RPR aims to restore the relative pose between adjacent transformed patches. Equipped with LCRF and RPR, our LocoTrans is capable of learning local-consistent transformation and preserving local geometry, which benefits rotation invariance learning. Competitive performance under arbitrary rotations on both shape classification and part segmentation tasks and ablations can demonstrate the effectiveness of our method. Code will be available publicly at https://github.com/wdttt/LocoTrans.

Figures (7)

• Figure 2: Overall framework of our LocoTrans. Our network consists of the invariant branch and the equivariant branch. To reduce the local geometric perturbation caused by local region transformation, we construct LCRF using the features from the equivariant branch to perform the local-consistent transformation. However, such a perturbation is difficult to completely eliminate. The RPR module is presented to alleviate this issue, restoring the relative pose between local patches. At the output level, we merge the features from two branches to aggregate information.
• Figure 3: Comparison between the ways of generating LRF with equivariant features. (a) Gram-Schmidt process. (b) Our LCRF. The two red dashed arrows in (b) are orthogonal. We present the visualized results of $u_{r,1}$ and $u_{r,2}$ in LRF generated by Gram-Schmidt process.
• Figure 4: Visualization of part segmentation results on ShapeNetPart dataset under z/SO(3) setting. From top to bottom, we present the segmentation results for four categories: airplane, chair, car, and pistol. The leftmost column is the ground truth and the right four columns are the predictions of our network under arbitrary rotations.
• Figure 5: Visualization of $u_r^1$ (Red) and $u_r^2$ (Green) in LRF. (a) LRF generated with the Gram-Schmidt process. (b) LCRF. While the Gram-Schmidt process fails to maintain local consistency in $u_r^2$, Our LCRF learns local-consistent orientation in both axes.
• Figure 6: Illustration of LCRF.