PointCNN: Convolution On $\mathcal{X}$-Transformed Points, Li, Bu, Sun, Wu, Di, Chen; 2018 - Summary
author: liyanc
score: 6 / 10

Point cloud representation learning suffers from poor topology-preservation and permutation variances. In order to take advantage of the current CNN works, the authors propose a learned $\chi$-transformation for both weighting and permuting the features, which is named as $\chi$-Conv.

$\chi$-Conv operator

Implementation details are illustrated in following figures. TU3 3_J_7PN0@{S4FW9)6VM M _N5L8{8)I1Z@VFS}0QQW1 RU Y89N6GY~FY5( S %D4J6

Permutation invariance and orientation invariance

Since the neighboring points are projected into a local frame and the reweighting matrix is learned on input, the combined $\chi$-transformation handles the orientation variance by reorienting the patch. Additionally, the permutation is explicitly rearanged by the $\chi$-transformation, it’s supposed to be permutation invariant as well.

Putting together

Raw points are grouped by their centers and processed layerwisely. If it’s a classification task, the network is constructed in a contrastive manner. On the other hand, a segmentation network would be constructed in a first constrastive and then expanding manner (hourglass). The following figure shows the architecture. {CO}6LTKE8Y (6UMDKHM%TS

The segmentation task runs on ShapeNet parts, S3DIS, ScanNet, with the results shown below, which is leading the SOTA. VA3K2C)B K$SHR%EXYWT165