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Jacqueline M. Fulvio, Manish Singh, Laurence T. Maloney; The human visual spline: Interpolation contours between relatable inducers follow quintic polynomials. Journal of Vision 2006;6(6):100. doi: https://doi.org/10.1167/6.6.100.
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Previously, we investigated extrapolation (“good continuation”) of contours that disappear behind occluders by obtaining measurements of perceived position and orientation of the visually-extrapolated contours at multiple distances from the point of occlusion (Singh & Fulvio, PNAS2005). Here we extend the investigation to contour interpolation.
Methods: Observers viewed interpolation displays consisting of two linear inducers and an occluding rectangle. On each trial, a vertical slit appeared at one of six locations within the occluder revealing a line probe. Observers iteratively adjusted the height and orientation of the probe until it appeared to smoothly interpolate between the inducers. We varied turning angle between the inducers, and vertical offset between their points of occlusion. Vertical offsets were selected such that the two inducers were either (i) symmetric and relatable (Kellman & Shipley, CogPsych1991), (ii) non-symmetric and relatable, (iii) non-symmetric and non-relatable.
Results: SDs of height and orientation settings increased with both turning angle and vertical offset, indicating reduced precision in the representation of interpolated contours. Mutual consistency between height and orientation settings (the extent to which the two settings are consistent with a single smooth curve) also declined with increasing inducer offset and turning angle. The positional settings for the relatable inducers (symmetric & non-symmetric) were remarkably well fit by quintic interpolants, and yielded high consistency with the orientation settings. Surprisingly, parabolic fits were insufficient for the symmetric inducer conditions, unlike Warren, Maloney, & Landy (VR2004). For non-relatable inducers, however, fits of quintic polynomials exhibited small but consistent deviations for all subjects.
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