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The ability to handle large scale variations is crucial for many real worldvisual tasks. A straightforward approach for handling scale in a deep networkis to process an image at several scales simultaneously in a set of scalechannels. Scale invariance can then, in principle, be achieved by using weightsharing between the scale channels together with max or average pooling overthe outputs from the scale channels. The ability of such scale channel networksto generalise to scales not present in the training set over significant scaleranges has, however, not previously been explored.  In this paper, we present a systematic study of this methodology byimplementing different types of scale channel networks and evaluating theirability to generalise to previously unseen scales. We develop a formalism foranalysing the covariance and invariance properties of scale channel networks,and explore how different design choices, unique to scaling transformations,affect the overall performance of scale channel networks. We first show thattwo previously proposed scale channel network designs do not generalise well toscales not present in the training set. We explain theoretically anddemonstrate experimentally why generalisation fails in these cases.  We then propose a new type of foveated scale channel architecture}, where thescale channels process increasingly larger parts of the image with decreasingresolution. This new type of scale channel network is shown to generaliseextremely well, provided sufficient image resolution and the absence ofboundary effects. Our proposed FovMax and FovAvg networks perform almostidentically over a scale range of 8, also when training on single scaletraining data, and do also give improved performance when learning fromdatasets with large scale variations in the small sample regime.

Scale-invariant scale-channel networks: Deep networks that generalise to previously unseen scales