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A. Li, Q. Zaidi; Phase spectra are irrelevant in 3D shape from natural textures. Journal of Vision 2001;1(3):149. https://doi.org/10.1167/1.3.149.
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We show that the capacity of a texture pattern to convey veridical 3-dimensional shape is a function of its amplitude spectrum regardless of its phase spectrum. 56 natural textures were used from the Brodatz (1966) collection. For each texture, a synthetic pattern was created with an identical amplitude spectrum but randomized phase spectrum. Each pattern was overlaid on a flat surface that was corrugated sinusoidally in depth as a function of horizontal position with an amplitude of 2, and projected in perspective on a CRT monitor. Observers were asked to identify simulated concave and convex surfaces in a 3AFC task (concave, convex, neither). 38-50% of the Brodatz patterns correctly conveyed concavities and convexities. The concordance between the shapes perceived from the Brodatz patterns and their phase-randomized versions was 80-88%, suggesting that the information for conveying shape is encapsulated in the amplitude spectrum, and that phase relations between the texture's Fourier components are irrelevant. Li and Zaidi (Vis Res, 2001) showed formally that for this surface, only components oriented within 3 deg of the axis of maximum curvature contain sufficient information to distinguish between concavities and convexities. We used this result to devise an objective measure for predicting whether a pattern will convey veridical 3D shape. For each texture pattern, the energy contained within each spatial frequency band in a 6° wedge around the axis of maximum curvature was multiplied by the ratio of the energy contained in this wedge to the energy contained in the encompassing 18° wedge, weighted by the human CSF, and then summed across spatial frequency. This measure, based solely on the critical component in the amplitude spectrum, correctly classified 84–97% of the patterns according to their capacity to convey veridical shape.
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