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2021

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

Cheng, Sihao, Ménard, Brice

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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.

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