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Lavanya Sharan, Edward Adelson, Isamu Motoyoshi, Shin'ya Nishida; Histogram skewness is useful and easily computed in neural hardware. Journal of Vision 2007;7(9):966. doi: 10.1167/7.9.966.
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There has been much interest in natural image statistics, notably the power spectrum of images and the kurtotic nature of histograms produced by subband filters. That is to say, the second moment (variance) and the fourth moment (kurtosis) of subband histograms have been widely studied, but the third moment (skewness) has been largely ignored. We have previously demonstrated that skewness is diagnostic of reflectance properties of surfaces such as albedo and gloss. In addition, skewness is correlated with perceptual judgments of albedo and gloss, suggesting that skewness or a related mechanism (e.g. blackshot, Chubb et al 2004) is utilized in surface perception. How might the human visual system compute skewness? We suggest a framework based on Heeger's contrast normalization model (Heeger 1993) with the following stages— i) linear filtering with on and off center-surround filters ii) half-wave rectification and an accelerating non-linearity iii) divisive normalization with pooling over both on-center and off-center streams iv) subtraction of the normalized on-center and off-center streams followed by spatial pooling. The resulting signal provides a measure of local skewness, similar to Pearson's skewness. By maintaining separate on and off-center streams, the model can keep track of contrast sign, an essential step in skewness calculations. There have been reports of cells in V1 and V2 that are selective for sign, and respond to either bright or dark dots and lines but not both. The accelerating non-linearity in ii) is required because it emphasizes the tails of the histogram. We find that squaring or cubing non-linearities work; in fact the precise choice of the exponent is not crucial. Thus, skewness or a similar measure of the asymmetry of a distribution can be computed with neural mechanisms and hardware.
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