Generalizing the Convolution Operator to extend CNNs to Irregular Domains
This addresses the limitation of CNNs in handling irregular data structures, which is incremental as it builds on existing graph-based methods.
The paper tackles the problem of extending CNNs to irregular domains by generalizing the convolution operator, showing that the proposed models resemble CNNs on regular domains and outperform multilayer perceptrons on distorted ones.
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.