This work investigates the ability of the human visual system to discriminate self-similar Gaussian random textures. The power spectra of such textures are similar to themselves when rescaled by some factor $h > 1$. As such, these textures provide a natural domain for testing the hypothesis that texture perception is based on a set of spatial-frequency channels characterized by filters of similar shape.
Some general properties of self-similar random textures are developed. In particular, the relations between their covariance functions and power spectra are established, and are used to show that many self-similar random textures are stochastic fractals. These relations also lead to a simple texture-generation algorithm that allows independent and orthogonal variation of several properties of interest.
Several sets of psychophysical experiments are carried out to determine the statistical properties governing the discrimination of self-similar line textures. Results show that both the similarity parameter $H$ and the scaling ratio $h$ influence discriminability. These two quantities, however, are insufficient to completely characterize perceived texture.
The ability of the visual system to discriminate between various classes of self-similar random texture is analyzed using a simple multichannel model of texture perception. The empirical results are found to be compatible with the hypothesis that texture perception is mediated by the set of spatial-frequency channels putatively involved in form vision.
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