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Mikhail Katkov, Hila Harris, Dov Sagi; 1,2,3, many: Perceptual order is computed by patches containing 3x3 "repetitions" of Motifs. Journal of Vision 2017;17(10):171. doi: 10.1167/17.10.171.
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© ARVO (1962-2015); The Authors (2016-present)
It is believed that symmetry plays an important role in human visual perception, as is manifested by the Gestalt laws. Mathematically, symmetry is defined as a transformation mapping an image to itself. An important class of such transformations is the Wallpaper Group that consists of repetitive patterns (Motifs). Strict symmetry rarely appears in nature. In statistical physics the deviation from symmetry is characterized by the Order Parameter, ranging from zero (random) to one (symmetry). Operationally, it is usually defined as the first order statistic over a local symmetry measure. Here we are interested in estimating the size of the local symmetry measure in the human visual system, defined in terms of the number of Motif repetitions. We used a 4AFC spatial odd-ball discrimination task: three quadrants of stimulus contained randomly generated textures, whereas the fourth quadrant contained a texture with varying degree of order. Order was controlled by the thermodynamic temperature in a Boltzmann distribution with potentials having different symmetries. Images were generated by a Chromatic Gibbs Sampler. Motif size was NxM Gaussian blobs (N=7-9, M=7-9 depending on the symmetry of the potential). Results from 4 observers show that psychometric functions (discrimination performance vs. temperature) were not different between images trimmed to size of 3x3 motifs and larger images, whereas discrimination of images of one motif size was practically at chance level for all temperatures. Images of 2x2 motifs were in between (at high temperatures these patches do not have obvious repetitions). Importantly, scaling the trimmed images leads to the same performance. We conclude from these results that if order is computed in the brain it is performed by patches containing 3x3 motifs. Moreover, the amount of the information in the patches, and not the physical size, is important for order perception.
Meeting abstract presented at VSS 2017
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