  Histology images are inherently symmetric under rotation, where each
orientation is equally as likely to appear. However, this rotational symmetry
is not widely utilised as prior knowledge in modern Convolutional Neural
Networks (CNNs), resulting in data hungry models that learn independent
features at each orientation. Allowing CNNs to be rotation-equivariant removes
the necessity to learn this set of transformations from the data and instead
frees up model capacity, allowing more discriminative features to be learned.
This reduction in the number of required parameters also reduces the risk of
overfitting. In this paper, we propose Dense Steerable Filter CNNs (DSF-CNNs)
that use group convolutions with multiple rotated copies of each filter in a
densely connected framework. Each filter is defined as a linear combination of
steerable basis filters, enabling exact rotation and decreasing the number of
trainable parameters compared to standard filters. We also provide the first
in-depth comparison of different rotation-equivariant CNNs for histology image
analysis and demonstrate the advantage of encoding rotational symmetry into
modern architectures. We show that DSF-CNNs achieve state-of-the-art
performance, with significantly fewer parameters, when applied to three
different tasks in the area of computational pathology: breast tumour
classification, colon gland segmentation and multi-tissue nuclear segmentation.
