HexaConv

By Emiel Hoogeboom, Jorn W. T. Peters, Taco Cohen, Max Welling. 2018

62 citations recorded by the source corpus.

The effectiveness of Convolutional Neural Networks stems in large part from their ability to exploit the translation invariance that is inherent in many learning problems. Recently, it was shown that CNNs can exploit other invariances, such as rotation invariance, by using group convolutions instead of planar convolutions. However, for reasons of performance and ease of implementation, it has been necessary to limit the group convolution to transformations that can be applied to the filters without interpolation. Thus, for images with square pixels, only integer translations, rotations by multiples of 90 degrees, and reflections are admissible. Whereas the square tiling provides a 4-fold rotational symmetry, a hexagonal tiling of the plane has a 6-fold rotational symmetry. In this paper we show how one can efficiently implement planar convolution and group convolution over hexagonal lattices, by re-using existing highly optimized convolution routines. We find that, due to the reduced anisotropy of hexagonal filters, planar HexaConv provides better accuracy than planar convolution with square filters, given a fixed parameter budget. Furthermore, we find that the increased degree of symmetry of the hexagonal grid increases the effectiveness of group convolutions, by allowing for more parameter sharing. We show that our method significantly outperforms conventional CNNs on the AID aerial scene classification dataset, even outperforming ImageNet pre-trained models.

Subfields: Aerospace Engineering, Computer Vision and Pattern Recognition

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Citations in the corpus

General E(2)-Equivariant Steerable CNNs (2019, methodology): “As a result, we are able to implement a wide range of equivariant models, covering regular GCNNs [6, 7, 8, 9, 10, 11], classical Steerable CNNs [1], Harmonic Networks [12], gated Harmonic Networks [2], Vector Field Networks [13], Scattering Transforms [14, 15, 16, 17, 18] and entirely new…”
B-Spline CNNs on Lie Groups (2019, background): “It can be roughly divided into work on discrete G-CNNs (Cohen & Welling, 2016; Dieleman et al., 2016; Winkels & Cohen, 2018; Worrall & Brostow, 2018; Hoogeboom et al., 2018), regular continuous G-CNNs (Oyallon & Mallat, 2015; Bekkers et al., 2015a; 2018b; Weiler et al., 2018a; Zhou et al., 2017;…”
Dense Steerable Filter CNNs for Exploiting Rotational Symmetry in Histology Images (2020, methodology): “To counter the limitation of working wih square grids in the G -CNN, Hoogeboom et al. [29] used hexagonal ﬁlters.”