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J. T. Chen, F. Domini, C. Caudek; Perception of tilt: The role of the optic flow gradients. Journal of Vision 2001;1(3):328. doi: https://doi.org/10.1167/1.3.328.
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The orthographic projection of a moving planar surface produces a linear optic flow that can be described by the horizontal and vertical velocity gradients. Theoretical studies have established that the tilt of the projected surface can be recovered from the information provided by the first-order optic flow by calculating the arctangent of the ratio between the vertical and horizontal gradient (e.g. Domini and Caudek, 1999). This mathematical analysis stands on the hypothesis that the optic flow is measured instantaneously. To investigate whether this hypothesis is psychologically plausible we manipulated the horizontal and vertical gradients of a constant linear optic flow produced by dynamic random-dot displays. The observer's task was to judge the tilt of the perceived 3D surface. The results indicate that the judged tilt magnitudes systematically deviated from those predicted by the gradient ratio. These findings are to be expected if the visual system is able to measure of the gradients only on the basis of discrete samples of the optic flow. It can be mathematically shown, in fact, that the ratio between the gradients does not correspond to the tilt of the projected surface if instantaneous measures of the flow cannot be obtained.
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