Symmetry and the salience of textures

TL;DR

This paper explores how symmetry influences human perception of textures by reducing complex texture statistics to simpler orbit invariants, enabling better understanding and generalization of texture discrimination across various image types.

Contribution

It introduces a novel representation of texture statistics using orbit invariants, simplifying the analysis and generalization of Minkowski functionals for diverse textures.

Findings

Orbit invariants effectively summarize texture symmetry.

Minkowski functionals can be expressed as linear combinations of orbit invariants.

Generalized functionals apply to textures with multiple grey levels and lattice types.

Abstract

In this paper we investigate the role of symmetry in visual stimuli designed to probe human sensitivity to image statistics. Our starting point is a recently published parameter space, a point in which defines a family of binary texture images displaying a prescribed content of \nth{1}- to \nth{4}-order correlations among pixels in 2x2 patches. We show that this parameter space can be represented by fewer variables, namely the \emph{orbit invariants} obtained by exploiting texture symmetry. Next we show how a class of locally countable texture statistics, the Minkowski functionals -- recently shown to be a proxy for human performance in texture discrimination tasks - can be written as a linear combination of the dihedral orbit invariants. Furthermore, by recasting these functionals as a combination of dihedral invariants, a generalization of these functionals can be obtained for textures of any number of grey-levels, patch sizes, or lattice types -- greatly reducing the number of dimensions/parameters needed to characterize the generated images. Orbit invariants may therefore provide a clue on the discrimination of these richer textures, as the ordinary Minkowski functionals do for binary textures.