The ability to handle large scale variations is crucial for many real world visual tasks. A straightforward approach to handling scale in a deep neural network is to process multiple rescaled image copies in a set of scale channels (subnetworks). 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 give improvements in the small sample regime.

Spatial transformer networks (STNs) were designed to enable convolutional neural networks (CNNs) to learn invariance to image transformations. STNs were originally proposed to transform CNN feature maps as well as input images. This enables the use of more complex features when predicting transformation parameters. However, since STNs perform a purely spatial transformation, they do not, in the general case, have the ability to align the feature maps of a transformed image with those of its original. STNs are therefore unable to support invariance when transforming CNN feature maps. We present a simple proof for this and study the practical implications, showing that this inability is coupled with decreased classification accuracy. We therefore investigate alternative STN architectures that make use of complex features. We find that while deeper localization networks are difficult to train, localization networks that share parameters with the classification network remain stable as they grow deeper, which allows for higher classification accuracy on difficult datasets. Finally, we explore the interaction between localization network complexity and iterative image alignment.