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Craig Abbey, Miguel Eckstein; Efficiency in the discrimination of 1/f textures. Journal of Vision 2007;7(9):961. doi: 10.1167/7.9.961.
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© 2017 Association for Research in Vision and Ophthalmology.
Human observer performance in visual texture discrimination tasks has become an important tool for understanding how the visual system encodes natural images (See, for example, Hansen and Hess, JOV, 2006). Much of the work in this area has built on a seminal set of experiments by Knill and colleagues (Knill, Field, and Kersten, JOSA-A, 1990) that used stationary and isotropic Gaussian textures with constant RMS contrast and power-law noise-power spectra (P(f) ≈1/fb). Exponents in the range of 2 to 4 are considered to be fractals. They find increased sensitivity for power-law exponents in the range of 2.8 to 3.6, and conclude that this may represent tuning of the visual system to these textures. While sensitivity is an important measure of visual function, it can also be revealing to consider efficiency, which is sensitivity normalized by the sensitivity of the ideal observer. To investigate the efficiency of texture discrimination for power-law processes, we have derived the Bayesian ideal observer, the optimal discriminator for a forced-choice discrimination task under reasonable prior probabilities and decision costs. The ideal observer decision variable is equivalent to a weighted integration of the stimulus power-spectrum, and performance of the ideal observer can be evaluated through Monte-Carlo simulations. The ideal observer sensitivity to Gaussian power-law textures increases substantially going from an exponent of 1 to 4. As a result, the efficiency of texture discrimination is approximately an order of magnitude higher at exponents near 1 compared to the exponents reported by Knill et al. Thus, from an efficiency perspective, the visual system is tuned to much lower exponents, well out of the fractal range.
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