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Francois Xavier Sezikeye, Rick Gurnsey; Modelling texture discrimination asymmetries using quadratic forms of random variables. Journal of Vision 2005;5(8):475. doi: 10.1167/5.8.475.
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© ARVO (1962-2015); The Authors (2016-present)
Purpose: Rubenstein and Sagi (1990, JOSA) argued that local variability within textures makes an important contribution to texture discrimination asymmetries and modelled their results using Signal Detection Theory (SDT). We asked whether differences in orientation variability alone would produce discrimination asymmetries, and modelled our results using distributions of quadratic forms of random variables.
Method: The stimulus comprised four quadrants of 8x8 lines (256 items per display). Each quadrant contained lines drawn from one or two distributions. Both distributions had a mean of 0 deg. (vertical). One distribution (fixed) had a standard deviation of 2 deg. and the other (variable) had a standard deviation varying from two to six deg. in seven equal logarithmic steps. In one condition the target quadrant comprised 32 lines drawn from the fixed distribution and 32 drawn from the variable distribution. The lines in the remaining three quadrants were drawn from the fixed distribution. In the second condition the reverse was true (one fixed quadrant in three variable quandrants). Three participants performed a 4AFC in which they were to indicate the different quadrant.
Accuracy was measured as a function of the variability difference between target and background textures in the two conditions.
Results: Threshold was defined as the standard deviation that elicited 72% correct responses. All subjects showed a lower threshold for the quadrant with two distributions, i.e. a higher variability signal in a low variability background was more salient than a low variability signal in a high variability background. An SDT model constructed from distributions of quadratic forms was found to be in qualitative agreement with the empirical data.
Conclusion: Differences in orientation variability alone are sufficient to produces a texture discrimination asymmetry. Quadratic forms in random variables provide a useful representational tool for modelling decision processes.
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