Tolerance for Misalignment in Contour Interpolation: Retinal or Relational?

James D. Hilger & Philip J. Kellman

Abstract:

Contour interpolation has been shown to be largely scale-invariant in some respects, as in the effect of support ratio on contour strength (Banton & Levi, 1992; Shipley & Kellman, 1992b). Kellman and Shipley (1991) hypothesized that the mathematical criteria of contour relatability included a small tolerance for misaligned parallel edges. Empirical estimates have suggested that collinear edges can be misaligned up to about 15 arc min and still support interpolation. We investigated whether a retinal metric or a scale-invariant notion, such as ratio of misalignment to edge separation, could account for the data. Tolerance for misalignment was tested in a two interval, forced choice, path detection paradigm (Field, Hayes, & Hess, 1993). Targets were paths of 4 spatially separated contour segments (illusory contour inducers) that were collinear or misaligned to varying degrees. Paths were presented in noise consisting of identical contour segments, randomly oriented. The target inducers were collinear or misaligned relative to the axis of global alignment. Within each level of retinal misalignment, inducers were also positioned to create 5 different relative angles between interpolating elements. Angular mis- alignment had no independent effect on performance. Instead, a retinal tolerance of 10–15 min was confirmed. There was a reliable interaction between relative and retinal misalignment; at particular retinal misalignments beyond 10–15 arc min, larger relative angles markedly low- ered performance. The geometry of the displays dictated that this increase in relative angle increased the distance, or gap size, between the target elements. Further experiments tested whether this is a more general grouping constraint not limited to interpolation processes. The data indicate that tolerance for misalignment is largely determined by a retinal metric. Angular misalignment appears to modulate residual interpolation effects beyond 10–15 arc min, a re- sult that may be explainable in terms of increased position or orientation uncertainty for more separated contours.

Surface Interpolation and 3D Relatability

Carlo Fantoni, James D. Hilger, Walter Gerbino, & Philip J. Kellman

Abstract:

Models of visual interpolation emphasize contour relationships. Although the role of surface-level processes has been demonstrated (Yin, Kellman & Shipley, 1998; Fantoni, Bertamini & Gerbino, 2004; for a recent review see Kellman, 2003), specific surface properties and geometric constraints that govern surface interpolation are not well understood. In this study we hypothesize that, even in the absence of contour information, visual interpolation can occur as a product of surface-based processes grounded on orientation information derived from image cues such as scale and shear disparities. To investigate 3D surface interpolation we asked observers to classify pairs of planar surfaces specified by random dot disparities, visible through circular apertures on a fronto-parallel occluder. Surface slant was manipulated by varying scale and shear disparities. On each trial, slanted textures belonged to either parallel or intersecting planar surfaces with the same absolute slant. Observers made a speeded parallel/intersecting classification of texture pairs of different slants. Surfaces were presented in 20 conditions resulting from the combination of three factors: 3D relatability of the surface pair (relatable vs. non-relatable); tilt of the aperture pair (aligned vs. tilted), absolute surface orientation (20, 35, 46, 54, 60 deg). As in contour interpolation (Kellman et al., in press) observers performed better on the parallel/intersecting classification task when surfaces were 3D-relatable. The orientation of the aperture pair did not play a clear role. The effect of absolute slant was stronger on non-relatable than relatable surfaces. Results support the notion that visual interpolation includes surface-based processes, independent of contour information and specified by the 3D orientation of visible patches. Scale and shear disparities of isolated textures provide sufficient information for surface interpolation.