How to quantify fields or textures? A guide to the scattering transform

TL;DR

The paper advocates for the scattering transform as an interpretable, training-free statistical tool for analyzing stochastic fields and textures, offering advantages over traditional power spectrum analysis and CNNs.

Contribution

It introduces the scattering transform as a compact, interpretable statistic for scientific data analysis, bridging the gap between power spectra and CNNs without requiring training.

Findings

Provides a visual, interpretable set of summary statistics

Demonstrates effectiveness across various scientific applications

Shows how understanding scattering transform elucidates CNN inner workings

Abstract

Extracting information from stochastic fields or textures is a ubiquitous task in science, from exploratory data analysis to classification and parameter estimation. From physics to biology, it tends to be done either through a power spectrum analysis, which is often too limited, or the use of convolutional neural networks (CNNs), which require large training sets and lack interpretability. In this paper, we advocate for the use of the scattering transform (Mallat 2012), a powerful statistic which borrows mathematical ideas from CNNs but does not require any training, and is interpretable. We show that it provides a relatively compact set of summary statistics with visual interpretation and which carries most of the relevant information in a wide range of scientific applications. We present a non-technical introduction to this estimator and we argue that it can benefit data analysis, comparison to models and parameter inference in many fields of science. Interestingly, understanding the core operations of the scattering transform allows one to decipher many key aspects of the inner workings of CNNs.