Enhancing Local Geometry Learning for 3D Point Cloud via Decoupling Convolution

TL;DR

This paper introduces a Laplacian Unit (LU) that explicitly decouples local and global components in convolution to improve local geometry learning in 3D point cloud understanding, achieving superior performance.

Contribution

The paper proposes a novel Laplacian Unit that enhances local geometry learning by decoupling convolution components, with theoretical insights based on curvature flow.

Findings

Networks with LUs outperform baselines on point cloud tasks.

LU effectively enhances local surface geometry learning.

The approach offers interpretability through curvature analysis.

Abstract

Modeling the local surface geometry is challenging in 3D point cloud understanding due to the lack of connectivity information. Most prior works model local geometry using various convolution operations. We observe that the convolution can be equivalently decomposed as a weighted combination of a local and a global component. With this observation, we explicitly decouple these two components so that the local one can be enhanced and facilitate the learning of local surface geometry. Specifically, we propose Laplacian Unit (LU), a simple yet effective architectural unit that can enhance the learning of local geometry. Extensive experiments demonstrate that networks equipped with LUs achieve competitive or superior performance on typical point cloud understanding tasks. Moreover, through establishing connections between the mean curvature flow, a further investigation of LU based on curvatures is made to interpret the adaptive smoothing and sharpening effect of LU. The code will be available.