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Jonathan D. Victor, Ana Ashurova, Charles Chubb, Mary M. Conte; Isodiscrimination contours in a three-parameter texture space. Journal of Vision 2006;6(6):205. doi: https://doi.org/10.1167/6.6.205.
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We recently (VSS 2005) described a framework for study of visual textures that incorporates histogram statistics and spatial correlations, based on maximum-entropy extension (Zhu et al., 1998) of statistics defined on small blocks. When applied to statistics on 2×2 blocks, this approach yields a three-dimensional space of binary textures, in which mean luminance (“gamma”), third-order spatial correlations (“theta”), and fourth-order spatial correlations (“alpha”) can be independently manipulated, and second-order correlations are absent. For the ideal observer, isodiscrimination contours at the origin are spherical.
Subjects (N=2) segregated textures with specified correlation structure from a random (coinflip) texture in a 4-AFC paradigm. Twelve directions were studied in both the gamma-theta and theta-alpha planes. Weibull functions (exponent 2) fit the data well along each ray. Sensitivities along the gamma, theta, and alpha coordinates are approximately in ratio 1:0.2:0.25. In the gamma-theta plane, isodiscrimination contours were tilted, with their long axis directed into the quadrants in which gamma and theta have opposite sign. In the theta-alpha plane, isodiscrimination contours were elongated into the quadrant in which both coordinates were negative.
Unlike the simple behavior in the gamma-alpha plane in which isodiscrimination contours were oriented along the cardinal axes (VSS 2003), isodiscrimination contours reveal interactions in the other cardinal planes. The tilt in the gamma-theta plane is consistent with combination of first- and third- order statistics by the “blackshot” mechanism (Chubb et al. 2005), but the distortion in the theta-alpha plane is not readily explained on this basis.
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