Data Representation using the Weyl Transform

TL;DR

This paper introduces the Weyl transform as a novel data representation method that captures multiscale features and symmetries, demonstrated on textured image classification tasks.

Contribution

It presents the Weyl transform as a new framework linking autocorrelations and Walsh-Hadamard transforms, enabling compact and discriminative data representations.

Findings

Effective in textured image classification

Captures multiscale autocorrelations and periodicities

Provides symmetry-invariant features

Abstract

The Weyl transform is introduced as a rich framework for data representation. Transform coefficients are connected to the Walsh-Hadamard transform of multiscale autocorrelations, and different forms of dyadic periodicity in a signal are shown to appear as different features in its Weyl coefficients. The Weyl transform has a high degree of symmetry with respect to a large group of multiscale transformations, which allows compact yet discriminative representations to be obtained by pooling coefficients. The effectiveness of the Weyl transform is demonstrated through the example of textured image classification.