Indexed Operations for Non-rectangular Lattices Applied to Convolutional Neural Networks

Abstract

The present paper introduces convolution and pooling operators for indexed images. These operators can be used on images that do not provide Cartesian grids of pixels, as long as a list of neighbor's indices can be provided for each pixel. They are foreseen being useful for convolutional neural networks (CNN) applied to special sensors, especially in science, without requiring image pre-processing. The present work explains the method and its implementation in the Pytorch framework and shows an application of the indexed kernels to the classification task of images with hexagonal lattices using CNN. The obtained results show that the method gives the same performances as the standard convolution kernels. Indexed convolution thus makes deep neural network frameworks more general and capable of addressing unconventional image lattices. The current implementation, as well as code to reproduce the experiments described in this paper are made available as open-source resources on the repository www.github.com/IndexedConv.