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

### Mikael Jacquemont, Luca Antiga, Thomas Vuillaume, Giorgia Silvestri, Alexandre Benoit, Patrick Lambert, Gilles Maurin

#### 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.

Download#### Paper Citation

#### in Harvard Style

Jacquemont M., Antiga L., Vuillaume T., Silvestri G., Benoit A., Lambert P. and Maurin G. (2019). **Indexed Operations for Non-rectangular Lattices Applied to Convolutional Neural Networks**.In *Proceedings of the 14th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 5: VISAPP,* ISBN 978-989-758-354-4, pages 362-371. DOI: 10.5220/0007364303620371

#### in Bibtex Style

@conference{visapp19,

author={Mikael Jacquemont and Luca Antiga and Thomas Vuillaume and Giorgia Silvestri and Alexandre Benoit and Patrick Lambert and Gilles Maurin},

title={Indexed Operations for Non-rectangular Lattices Applied to Convolutional Neural Networks},

booktitle={Proceedings of the 14th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 5: VISAPP,},

year={2019},

pages={362-371},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0007364303620371},

isbn={978-989-758-354-4},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 14th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 5: VISAPP,

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

SN - 978-989-758-354-4

AU - Jacquemont M.

AU - Antiga L.

AU - Vuillaume T.

AU - Silvestri G.

AU - Benoit A.

AU - Lambert P.

AU - Maurin G.

PY - 2019

SP - 362

EP - 371

DO - 10.5220/0007364303620371