  This paper presents a hybrid approach between scale-space theory and deep
learning, where a deep learning architecture is constructed by coupling
parameterized scale-space operations in cascade. By sharing the learnt
parameters between multiple scale channels, and by using the transformation
properties of the scale-space primitives under scaling transformations, the
resulting network becomes provably scale covariant. By in addition performing
max pooling over the multiple scale channels, a resulting network architecture
for image classification also becomes provably scale invariant. We investigate
the performance of such networks on the MNISTLargeScale dataset, which contains
rescaled images from original MNIST over a factor of 4 concerning training data
and over a factor of 16 concerning testing data. It is demonstrated that the
resulting approach allows for scale generalization, enabling good performance
for classifying patterns at scales not present in the training data.
