Straight-forward keras implementations for 90-degree roto-reflections equivariant CNNs. See a working example.
Install: pip install git+https://github.com/nom/GrouPy#egg=GrouPy -e git+https://github.com/basveeling/keras-gcnn.git#egg=keras_gcnn
Requires python 3, up to date keras and a tensorflow backend. Please report any problems in the issues.
Conventional fully-convolutional NNs are 'equivariant' to translation: as the input shifts in the spatial plane, the output shifts accordingly. This can be extended to include other forms of transformations such as 90 degree rotations and reflection. This is formalized by [2].
If you use these implementations in your work, we appreciate a citation to our paper:
[1] B. S. Veeling, J. Linmans, J. Winkens, T. Cohen, M. Welling. "Rotation Equivariant CNNs for Digital Pathology". arXiv:1806.03962
Biblatex entry:
@ARTICLE{Veeling2018-qh,
title = "Rotation Equivariant {CNNs} for Digital Pathology",
author = "Veeling, Bastiaan S and Linmans, Jasper and Winkens, Jim and
Cohen, Taco and Welling, Max",
month = jun,
year = 2018,
archivePrefix = "arXiv",
primaryClass = "cs.CV",
eprint = "1806.03962"
}
We provide a Group-equivariant version of DenseNet [3] as proposed in [1].
h_input='Z2'
and h_output='C4'
or 'D4'
.h_input=h_output='D4'
(or 'C4'
).