Journal Article

Scale-Covariant and Scale-Invariant Gaussian Derivative Networks

Lindeberg, Tony

2022

Overview

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, or other permutation-invariant pooling over scales, a resulting network architecture for image classification also becomes provably scale invariant. We investigate the performance of such networks on the MNIST Large Scale dataset, which contains rescaled images from the original MNIST dataset 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 spanned by the training data.

• Publisher: Springer US,Springer Nature B.V
• Subject: Applications of Mathematics / Channels / Computer architecture / Computer Science / Datalogi / Datasets / Deep learning / Gaussian derivative / Image classification / Image Processing and Computer Vision / Invariants / Machine learning / Mathematical Methods in Physics / Permutations / Scale covariance / Scale generalisation / Scale invariance / Scale selection / Scale space / Signal,Image and Speech Processing / Training