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Xin Meng, Qasim Zaidi; Perceived velocity gradients and the rigidity of 3-D shape percepts. Journal of Vision 2006;6(6):372. doi: 10.1167/6.6.372.
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If one cycle of an upright, vertical, sinusoidal corrugation, centered at the zero-crossing, is rotated smoothly around the horizontal axis between +/− 30 degrees, the main component of the optic-flow is a horizontal velocity gradient with maxima in opposite directions at peaks and troughs, and minima at zero crossings. A feature correspondence algorithm (Koenderink & van Doorn, 1991) can recover the veridical 3-D shape with a rigidity or smooth deformation assumption. However, with central fixation, observers perceive a grossly non-rigid surface of two convexities rotating in opposite directions (confirmed by separate measures of perceived 3-D curvature and direction-of-rotation for each half-cycle of corrugation). This percept is consistent with a Helmholzian algorithm that assigns relative depth inversely proportional to relative velocity (Sperling & Landy, 1989). The non-rigid percept occurs whether the surface texture conveys veridical 3-D shape or not (Zaidi & Li, 2002) and even if the rotation begins after a static upright view.
On prolonged viewing of the rotation, however, sometimes the percept changes to that of a rigidly rotating corrugation in either the veridical or the opposite phase. Is this due to changes in perceived optic-flow as fixation wanders? When fixation location was varied, observers reported the nearer half-cycle as having the greater curvature. It is possible that sensitivity to velocity waveforms falls rapidly with retinal eccentricity (Sachtler & Zaidi, 1995), and that in the absence of strong velocity gradients, 3-D shape capture takes place. Fixation variation alone, however, is not sufficient to reliably create rigid percepts.
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