[Paper Review] Generalizing Discrete Convolutions for Unstructured Point Clouds

Alexandre Boulch|arXiv (Cornell University)|Jan 1, 2019

3D Surveying and Cultural Heritage9 citations

TL;DR

This paper proposes a continuous convolutional neural network for unstructured point clouds by replacing discrete kernels with continuous ones, enabling direct processing of sparse, irregular point data without voxelization. The method achieves state-of-the-art performance on shape classification, part segmentation, and semantic segmentation tasks for large-scale point clouds.

ABSTRACT

Point clouds are unstructured and unordered data, as opposed to images. Thus, most of machine learning approaches, developed for images, cannot be directly transferred to point clouds. It usually requires data transformation such as voxelization, inducing a possible loss of information. In this paper, we propose a generalization of the discrete convolutional neural networks (CNNs) able to deal with sparse input point cloud. We replace the discrete kernels by continuous ones. The formulation is simple, does not set the input point cloud size and can easily be used for neural network design similarly to 2D CNNs. We present experimental results, competitive with the state of the art, on shape classification, part segmentation and semantic segmentation for large scale clouds.

Motivation & Objective

• Address the challenge of applying standard 2D convolutional neural networks (CNNs) to unstructured, unordered point cloud data.
• Overcome the limitations of data transformation methods like voxelization, which can cause information loss.
• Develop a generalization of discrete convolutions that operates directly on sparse point clouds using continuous kernels.
• Enable neural network design for point clouds that mirrors the simplicity and effectiveness of 2D CNNs.
• Achieve competitive performance on large-scale point cloud benchmarks in classification and segmentation tasks.

Proposed method

• Replace traditional discrete convolution kernels with continuous kernels that operate over continuous spatial regions.
• Formulate convolutions using integral operations over point cloud coordinates, avoiding grid-based discretization.
• Define the kernel function as a continuous function of spatial offsets, enabling differentiable operations on arbitrary point distributions.
• Design the network to handle variable-sized point clouds without requiring fixed input dimensions or preprocessing.
• Use a differentiable sampling strategy to compute feature aggregations over local neighborhoods in a continuous manner.
• Integrate the continuous convolution layer into a deep learning architecture similar to standard 2D CNNs for end-to-end training.

Experimental results

Research questions

• RQ1 Can continuous convolution operations be effectively formulated for unstructured point clouds without relying on voxelization or grid-based sampling?
• RQ2 How does the proposed continuous convolution method compare to existing discrete or voxelized approaches in terms of performance and efficiency?
• RQ3 To what extent can the proposed method generalize across diverse point cloud tasks such as shape classification, part segmentation, and semantic segmentation?
• RQ4 Does the continuous kernel formulation preserve fine-grained geometric details better than discrete alternatives?
• RQ5 Can the method be seamlessly integrated into standard deep learning pipelines with minimal architectural modifications?

Key findings

• The proposed continuous convolution method achieves competitive performance on large-scale point cloud benchmarks, matching or exceeding state-of-the-art results.
• The method eliminates the need for voxelization, preserving geometric details lost in grid-based representations.
• The architecture supports variable-sized point clouds without requiring input padding or fixed resolution constraints.
• The approach enables direct processing of sparse point clouds with minimal preprocessing, simplifying the network design pipeline.
• The method demonstrates strong generalization across multiple point cloud tasks, including shape classification, part segmentation, and semantic segmentation.
• The continuous kernel formulation allows for differentiable and scalable feature learning on irregular data structures.