Volume Completion Between Contour Fragments at Discrete Depths.

Peter Ulric Tse

doi:10.1177/2041669517747001

Abstract

Building on the modal and amodal completion work of Kanizsa, Carman and Welch showed that binocular stereo viewing of two disparate images can give rise to a percept of 3D curved, nonclosed illusory contours and surfaces. Here, it is shown that binocular presentation can also give rise to the percept of closed curved surfaces or volumes that appear to vary smoothly across discrete depths in binocularly fused images, although in fact only two binocular disparities are discretely defined between corresponding contour elements of the inducing elements. Surfaces are filled in from one depth layer’s visible contours to another layer’s visible contours within virtual contours that are interpolated on the basis of good contour continuation between the visible portions of contour. These single depth contour segments are taken not to arise from surface edges, as in Kanizsa’s or Carman and Welch’s examples, but from segments of “rim” where the line of sight just grazes a surface that continues behind and beyond the rim smoothly. When there are two or more surface-propagating contour segments, the propagated surfaces can continue away from the inferred rim, merge, and then close behind the self-occluding visible surface into an everywhere differentiable closed surface or volume. Illusory surfaces can possess a depth and perceived surface curvature that is consistent with all visible contour segments, despite the absence of local disparity cues at interpolated 3D surface locations far from any visible contour. These demonstrations cannot be easily explained by existing models of visual processing. They place constraints on the surface and volume generation processes that construct our 3D world under normal viewing conditions.

Highlights

In the late 1990s, several researchers began providing evidence (Albert & Tse, 2000; Tse, 1998; Tse & Albert, 1998; Tse 1999a, 1999b, 2002; Van Lier, 1999; Van Lier & Wagemans, 1999) that amodal and modal completion take place at a 3D object or volumetric level of representation, rather than at the level of image contours or the level of visible surfaces
Because illusory surfaces are taken to continue before, behind, and beyond the visible or illusory contour arising from the rim of the modally completing surface, they can close into a volume that encloses space
The interpolated surface solution is influenced by nonlocal cues: When there are two or more surface-propagating contour segments, they can merge and possess a depth and perceived surface curvature that is consistent with all visible contour segments, despite the absence of local disparity cues in regions far from any inducing contours

Summary

Introduction

In the late 1990s, several researchers began providing evidence (Albert & Tse, 2000; Tse, 1998; Tse & Albert, 1998; Tse 1999a, 1999b, 2002; Van Lier, 1999; Van Lier & Wagemans, 1999) that amodal and modal completion take place at a 3D object or volumetric level of representation, rather than at the level of image contours or the level of visible surfaces. Curved 3D surfaces are interpolated by the visual system to vary smoothly across depths in binocularly fused images, even when only two (or more) discrete binocular disparities are defined between corresponding elements of the inducing image contours. These illusory surfaces are generated in the 3D space inferred to lie between the two (or more) disparity-defined depths, and only arise in uniform regions where there are no disparity cues that could define depth upon binocular fusion. Because surfaces are assumed to close smoothly, there are cases where the interpolated curved closed surfaces appear to lie closer or farther than the nearest or farthest depth respectively implied by binocular disparity cues at visible contours

Historical Background

Dynamic Modally Completing Volumes

Discussion