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Jonathan Victor, Jason Mintz, Mary Conte; Implementing a maximum-entropy parameterization of texture space. Journal of Vision 2010;10(7):1361. doi: https://doi.org/10.1167/10.7.1361.
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© ARVO (1962-2015); The Authors (2016-present)
Visual textures are an important tool for studying many aspects of perception, including local feature extraction, segmentation, and perception of surface properties. Visual textures are defined by their statistics. Image statistics include the luminance histogram, the power spectrum, and higher-order analogs, and thus, constitute a very large number of parameters. This richness enables construction of visual stimuli that can be used to discriminate among candidate models. However, it also presents a challenge, because image statistics are not only high-dimensional, but also, have complex algebraic interrelationships. To approach this problem, we use maximum-entropy extension. The basic idea is that a texture can be defined by specifying only a small number of image statistics explicitly. The unspecified statistics are then determined implicitly, by creating textures that are as random as possible, but still satisfy the constraints of the explicitly-specified statistics (Zhu et al., 1998). We implement this idea for binary homogeneous textures, focusing on local image statistics. 10 parameters are required to determine the probabilities of the 16 possible 2x2 blocks. Via maximum-entropy extension, these parameters comprehensively describe all homogeneous binary textures with purely local structure, along with the long-range structure that the local organization necessarily implies. We develop algorithms to generate texture examples in all 45 coordinate planes of the space. In most planes, an iterative “glider” rule suffices, but in some, a novel Metropolis (1953) algorithm is required. We show how the Metropolis algorithm can be used to project naturalistic textures into the texture space, thus extracting their local structure. Perceptually, each plane of this space is characterized by salient and distinctive visual structure. We present isodiscrimination contours in several of these planes. While ideal-observer contours are circular, human isodiscrimination contours are strongly elliptical, and may be tilted with respect to the coordinate axes.
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