Enzymind Labs

2007-02-06 The following outline was motivated by the interesting visual appearance of Thue-Morse sequence tilings (also see T-M gallery), and "request for hypothesis" by PSR. I might further illustrate and design the experiment, but have no current plans to implement what is described.

Periodicity and Redundancy in Human Visual Perception

Both periodic and redundant patterns are central elements in the process of human vision. Deviations from periodicity, or any perfect symmetry, are also highly salient. Across all scales of image features, from fine texture to global composition, images can be characterized by both periodicity and redundancy. In human vision this information is extracted in parallel, not by serial search, and is used to encode the content of images. What are the relative roles of our perception of periodic and redundant information, and how do they interact?

I propose that human vision is finely tuned to locally distinguish the magnitude of both periodicity and redundancy, but that across broad spatial spans we can only distinguish periodicity well; redundancy is not distinguished from a combination of periodicity and randomness.

To assess these relative contributions, subjects will perform two tasks; 1) matching and distinguishing of various textures with a set of textures of controlled periodicity and redundancy properties and 2) attempt to find shapes that are only distinguished by regions of slightly different periodicity and redundancy.

To assess the interaction between image periodicity and redundancy, test pattens will be constructed with different fine scale (high spatial frequency) properties than global (low spatial frequency) properties. The test pattern constructions will be accomplished by using tilings (see below), where the properties of tiles and tiling patterns can be independently varied.

The testing will be performed by presenting images in a web-based interface, with un-timed, forced choice subject response. Subjects may respond to as many or as few test items as they desire.

Periodic patterns have fully redundant features. But a randomly spaced set of identical image objects will only have a strong periodicity at the spatial frequencies of the individual objects, not at lower spatial frequencies. In this case the image will have high redundancy and no periodicity at low spatial frequencies.

Simple tiling patterns provide a method of closely controlling the amount of redundancy and periodicity in 2-D images. Consider a square grid with each square region colored in one of two ways (A or B). Filling each row/column randomly will result in a minimum redundancy and minimum periodicity; all sets of local features of any particular size will occur with equal probability across the image. Alternating the coloring (ABABAB...) will result in a maximum periodicity in the direction of alternation, and maximum redundancy of the square-free group {A, B}.

The two symbol Thue-Morse sequence is a non-periodic cube-free sequence with group members {A, B, AA, BB, AB, BA}. It has the quantitative property of a maximal redundancy and no periodicity for all substrings. 2-D tilings using the Thue-Morse sequence can be constructed that have this property in all directions.

A set of tilings can be generated, by increasingly "breaking" the Thue-Morse ordering of tiles, that are accurately controlled for image periodicity and redundancy while maintaining a constant average image density. This set is a near continuum of patterns between fully periodic / maximally redundant, non-periodic / maximally redundant, and non-periodic / minimally redundant. Furthermore, all members of the set have little or no long range structure, other than the continuity of periodicity and/or redundancy across the image; they are textures.

By comparing subject's percepts of these textures, and tilings that have a global texture, the relative contribution of, sensitivity to, and interaction of periodicity and redundancy can be assessed.

These psychophysical measurements are potentially relevant to aspects of information theory and aesthetic perception.

Human vision is adapted to efficiently encode complex scenes with a near minimum of information. It is certain that high information content texture information is "compressed" (represented by a small set of parameters). The visual system is not equipped to encode the exact spatial details across a texture, only the more salient features and boundaries of textured regions. This form of representation has applications in image compression and machine vision.

It has long been recognized that aesthetically pleasing images have the characteristics of 1) not being too simple or ordered (low information content) and 2) not being too disordered or containing too many disparate elements (high information content, and low redundancy). A characterization of images in terms of periodicity and redundancy at a range of spatial frequencies, may lead to a metric relevant to aesthetic perception. While this experiment does not propose to describe general imagery in terms of periodicity and redundancy, a metric of the effect of these perceptual parameters may be used for future research.

Similar issues can be explored with respect to images generated with Iterated Function Systems, and fractal patterns in general. Fractal systems always display high redundancy (when scaling is considered), and a logarithmically scaled periodicity. They also generally include a rotational scaling. I've deliberately avoided scaling and rotation issues in this proposal.