Generalizing Convolution to Point Clouds

Published: 27 Jun 2024, Last Modified: 20 Aug 2024Differentiable Almost EverythingEveryoneRevisionsBibTeXCC BY 4.0
Keywords: Point Cloud, Convolution
TL;DR: Convolution is relaxed in a way to allow the processing of (possibly irregular) point clouds.
Abstract: Convolution, a fundamental operation in deep learning for structured grid data like images, cannot be directly applied to point clouds due to their irregular and unordered nature. Many approaches in literature that perform convolution on point clouds achieve this by designing a convolutional operator from scratch, often with little resemblance to the one used on images. We present two point cloud convolutions that naturally follow from the convolution in its standard definition popular with images. We do so by relaxing the indexing of the kernel weights with a "soft" dictionary that resembles the attention mechanism of the transformers. Finally, experimental results demonstrate the effectiveness of the proposed relaxations on two benchmark point cloud classification tasks.
Submission Number: 9
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