Generalizing the Convolution Operator to extend CNNs to Irregular Domains

TL;DR

This paper introduces a new method to extend CNNs to irregular domains using graph-based operators, achieving similar performance on regular grids and improved results on distorted data.

Contribution

The paper proposes a novel approach that generalizes CNNs to irregular domains through weight sharing and graph-based operators, addressing limitations of previous methods.

Findings

Models resemble CNNs on regular domains

Outperform multilayer perceptrons on distorted data

Better handling of irregular input structures

Abstract

Convolutional Neural Networks (CNNs) have become the state-of-the-art in supervised learning vision tasks. Their convolutional filters are of paramount importance for they allow to learn patterns while disregarding their locations in input images. When facing highly irregular domains, generalized convolutional operators based on an underlying graph structure have been proposed. However, these operators do not exactly match standard ones on grid graphs, and introduce unwanted additional invariance (e.g. with regards to rotations). We propose a novel approach to generalize CNNs to irregular domains using weight sharing and graph-based operators. Using experiments, we show that these models resemble CNNs on regular domains and offer better performance than multilayer perceptrons on distorded ones.