Riesz networks: scale invariant neural networks in a single forward pass

TL;DR

The paper introduces Riesz networks, a novel neural network architecture that inherently achieves scale invariance through the Riesz transform, enabling it to generalize to unseen scales in a single forward pass, demonstrated on crack segmentation and MNIST data.

Contribution

The Riesz network is the first neural network to incorporate the Riesz transform for natural scale invariance, eliminating the need for data augmentation.

Findings

Successfully generalizes to unseen scales in crack segmentation.

Achieves scale invariance in a single forward pass.

Performs well on the MNIST Large Scale dataset.

Abstract

Scale invariance of an algorithm refers to its ability to treat objects equally independently of their size. For neural networks, scale invariance is typically achieved by data augmentation. However, when presented with a scale far outside the range covered by the training set, neural networks may fail to generalize. Here, we introduce the Riesz network, a novel scale invariant neural network. Instead of standard 2d or 3d convolutions for combining spatial information, the Riesz network is based on the Riesz transform which is a scale equivariant operation. As a consequence, this network naturally generalizes to unseen or even arbitrary scales in a single forward pass. As an application example, we consider detecting and segmenting cracks in tomographic images of concrete. In this context, 'scale' refers to the crack thickness which may vary strongly even within the same sample. To prove its scale invariance, the Riesz network is trained on one fixed crack width. We then validate its performance in segmenting simulated and real tomographic images featuring a wide range of crack widths. An additional experiment is carried out on the MNIST Large Scale data set.