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Laurie M. Wilcox, Phil A. Duke; Spatial scaling of 3D surface interpolation. Journal of Vision 2001;1(3):177. doi: https://doi.org/10.1167/1.3.177.
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Patterns of sparse texture elements that vary smoothly in depth appear to lie on a three-dimensional surface when depth is interpolated across the intervening blank spaces. Estimates of the upper limit of 3D surface interpolation range from 3 min to 0.3 deg (Westheimer 1986, Yang and Blake 1995). However, physiological studies have shown that there is a broad range of receptive field sizes in the visual cortex. Simple cells in area V1 range in width from 0.05 to 0.5 deg (Parker and Hawkin, 1988) and in cortical areas such as V2, V3 and V4 receptive fields are substantially larger. The existence of different sized receptive fields at a given retinal location indicates that processing occurs at different scales. Thus, one might expect that surface interpolation is supported over a range of stimulus scales, and the upper limit is scale dependent. We tested this proposition by assessing 3D interpolation at a large range of scales using a bisection task that has proven to be a reliable index of 3D interpolation. Surface interpolation was assessed for stimuli with widths ranging from 15 to 58 deg. Once irrelevant task variables are taken into account, 3D surface interpolation is scale invariant up to an average nearest neighbour element spacing of 3 deg (SD 2 deg). These experiments provide strong evidence for scale invariance of 3D surface interpolation, and for an upper limit that is scale dependent. These data also show that previous estimates underestimate the capacity of the human visual system to interpolate surfaces in depth.
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