Human discrimination of surface slant in fractal and related textured images

Slant-discrimination thresholds were measured for textures with the property that their power spectra, when log transformed, are inversely proportional to log spatial frequency: P(f) alpha f-beta. As the exponent beta changes from high values to low values, the slope of the power spectrum of the image decreases. As the parameter passes through values in the fractal range the resulting texture changes from having the appearance of a cloud-like surface through to a granite-like surface. Exponents below the fractal range produce textures that converge towards the appearance of a random grey-level noise pattern. Since fractal patterns are self-similar at a range of scales, one might think it would be difficult to recover changes in depth in fractal images; however, slant-discrimination thresholds did not differ substantially as a function of the slope of the power spectrum. Reducing the size of the viewing aperture increased thresholds significantly, suggesting that slant discrimination benefits from a global analysis. The effect of texture regularity on perceived slant was investigated using bandpassed fractal textures. As the bandwidth of a bandpass filter is reduced, the bandpassed texture was perceived to be increasingly more slanted than its fractal counterpart.