  Incorporating either rotation equivariance or scale equivariance into CNNs
has proved to be effective in improving models' generalization performance.
However, jointly integrating rotation and scale equivariance into CNNs has not
been widely explored. Digital histology imaging of biopsy tissue can be
captured at arbitrary orientation and magnification and stored at different
resolutions, resulting in cells appearing in different scales. When
conventional CNNs are applied to histopathology image analysis, the
generalization performance of models is limited because 1) a part of the
parameters of filters are trained to fit rotation transformation, thus
decreasing the capability of learning other discriminative features; 2)
fixed-size filters trained on images at a given scale fail to generalize to
those at different scales. To deal with these issues, we propose the
Rotation-Scale Equivariant Steerable Filter (RSESF), which incorporates
steerable filters and scale-space theory. The RSESF contains copies of filters
that are linear combinations of Gaussian filters, whose direction is controlled
by directional derivatives and whose scale parameters are trainable but
constrained to span disjoint scales in successive layers of the network.
Extensive experiments on two gland segmentation datasets demonstrate that our
method outperforms other approaches, with much fewer trainable parameters and
fewer GPU resources required. The source code is available at:
https://github.com/ynulonger/RSESF.
