Riesz feature representation: scale equivariant scattering network for classification tasks

TL;DR

This paper introduces a Riesz transform-based feature representation for image classification that is scale equivariant, eliminating the need for scale sampling, reducing feature count, and improving robustness to unseen scales.

Contribution

It proposes a mathematically grounded, scale-equivariant feature representation based on the Riesz transform, avoiding scale sampling and reducing feature complexity.

Findings

Performs comparably to scattering networks in texture classification.

Achieves stable accuracy on digit classification with scales four times larger than training.

Demonstrates superior generalization to unseen scales due to scale equivariance.

Abstract

Scattering networks yield powerful and robust hierarchical image descriptors which do not require lengthy training and which work well with very few training data. However, they rely on sampling the scale dimension. Hence, they become sensitive to scale variations and are unable to generalize to unseen scales. In this work, we define an alternative feature representation based on the Riesz transform. We detail and analyze the mathematical foundations behind this representation. In particular, it inherits scale equivariance from the Riesz transform and completely avoids sampling of the scale dimension. Additionally, the number of features in the representation is reduced by a factor four compared to scattering networks. Nevertheless, our representation performs comparably well for texture classification with an interesting addition: scale equivariance. Our method yields superior performance when dealing with scales outside of those covered by the training dataset. The usefulness of the equivariance property is demonstrated on the digit classification task, where accuracy remains stable even for scales four times larger than the one chosen for training. As a second example, we consider classification of textures.