  The ability to handle large scale variations is crucial for many real world
visual tasks. A straightforward approach for handling scale in a deep network
is to process an image at several scales simultaneously in a set of scale
channels. Scale invariance can then, in principle, be achieved by using weight
sharing between the scale channels together with max or average pooling over
the outputs from the scale channels. The ability of such scale channel networks
to generalise to scales not present in the training set over significant scale
ranges has, however, not previously been explored. We, therefore, present a
theoretical analysis of invariance and covariance properties of scale channel
networks and perform an experimental evaluation of the ability of different
types of scale channel networks to generalise to previously unseen scales. We
identify limitations of previous approaches and propose a new type of foveated
scale channel architecture, where the scale channels process increasingly
larger parts of the image with decreasing resolution. Our proposed FovMax and
FovAvg networks perform almost identically over a scale range of 8, also when
training on single scale training data, and do also give improvements in the
small sample regime.
