Abstract
It is well known that textures with sufficiently distinct power spectra are perceptually distinct, and that some higher-order spatial correlations also support texture discrimination and segmentation. However, a concise parameterization of the correlation structure relevant to perception is as yet elusive. We attempt to bring together a range of psychophysical and analytical results to suggest a minimal structure for the perceptual space of textures.
The motivation for the present approach is that the visual system is likely to represent image statistics in a manner that is efficient, but perhaps not comprehensive. We hypothesize that any texture is perceptually equivalent to a texture for which all statistics of all orders can be reconstructed from a small subset of image statistics. A natural formalization of this reconstruction is maximum entropy extension (Zhu et al., 1998).
Filtered Gaussian noises can always be set in this framework, consistent with the notion that second-order statistics typically support texture discrimination. For textures defined by high-order correlations extended along one dimension, discriminability appears to be based on induced differences in the luminance histogram of multicheck blocks, or induced long-range second-order statistics. In two dimensions, the simplest scenario is that of binary textures in 2x2 blocks. Only a small subset of assignments of block probabilities allows for maximum entropy extension. Two of these correspond to previously-recognized families of binary isodipole textures, but other components of this subset correspond to as-yet unrecognized isodipole textures that are highly discriminable. These observations suggest that perceptual texture space is usefully parameterized by maximum-entropy extension of pixel histogram and second-order statistics at many scales, and fourth-order statistics restricted to two-dimensional nearest-neighbor cliques. Predictions and shortcomings of this view will be discussed.