Symmetry and the salience of textures

Marconi Barbosa; Ted Maddess

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arXiv · 1909.01689

Symmetry and the salience of textures

Marconi Barbosa·Ted Maddess

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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.

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Marconi Barbosa, Ted Maddess. 2019-09-04. Symmetry and the salience of textures. https://arxiv.org/abs/1909.01689

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