Stereo slant discrimination of planar 3D surfaces: Frontoparallel versus planar matching

Abstract

Binocular stereo cues are important for discriminating 3D surface orientation, especially at near distances. We devised a single-interval task where observers discriminated the slant of a densely textured planar test surface relative to a textured planar surround reference surface. Although surfaces were rendered with correct perspective, the stimuli were designed so that the binocular cues dominated performance. Slant discrimination performance was measured as a function of the reference slant and the level of uncorrelated white noise added to the test-plane images in the left and right eyes. We compared human performance with an approximate ideal observer (planar matching [PM]) and two subideal observers. The PM observer uses the image in one eye and back projection to predict a test image in the other eye for all possible slants, tilts, and distances. The estimated slant, tilt, and distance are determined by the prediction that most closely matches the measured image in the other eye. The first subideal observer (local planar matching [LPM]) applies PM over local neighborhoods and then pools estimates across the test plane. The second suboptimal observer (local frontoparallel matching [LFM]) uses only location disparity. We find that the ideal observer (PM) and the first subideal observer (LPM) outperforms the second subideal observer (LFM), demonstrating the additional benefit of pattern disparities. We also find that all three model observers can account for human performance, if two free parameters are included: a fixed small level of internal estimation noise, and a fixed overall efficiency scalar on slant discriminability.

Good continuation in 3D: the neurogeometry of stereo vision

“…Although this section has been based on the geometry of space curves and their projections, we observe that related geometric approaches have been developed for planar patches and surfaces; see, e.g., Li and Zucker, 2008;Oluk et al, 2022 and references therein.…”

When is a disparity not a disparity? Toward an old theory of three-dimensional vision

“…And this includes the ground plane surface. Recent work on the modeling of binocular stereopsis has shown that correlational algorithms based on the matching of local surface patches are more successful than conventional point-based solutions (Banks et al, 2004;Oluk et al, 2022). It is rather ironic that Bela Julesz's attempt to model the processing of binocular disparities 50 years ago was essentially a correlational algorithm (Julesz, 1971).…”

“…In other words, we are still describing the correspondence (or lack of correspondence) between individual points or features in the two optic arrays or the retinal images (e.g., Read et al, 2009 ). A quite different approach is to think about how the optic array created by a surface (rather than points or features) is transformed or mapped from one (binocular) optic array to the other ( Banks et al, 2004 ; Michaels & Carello, 1981 ; Oluk et al, 2022 ). The simplest example of such a transformation is in the viewing of a surface that lies at an eccentric location with respect to the two binocular vantage points: that is, off to one side.…”

Stereoscopic slant contrast revisited

“…The perceived slant of a random-dot stereoscopic surface is altered by the presence of a surrounding slanted surface, a phenomenon termed stereo slant contrast ( Gillam & Pianta, 2005 ; Goutcher & Wilcox, 2021 ; Graham & Rogers, 1982 ; Poom, Olsson, & Börjesson 2007 ; Rogers, Cagenello, & Rogers, 1988 ; van der Kooij & te Pas, 2009a ; van der Kooij & te Pas, 2009b ; van Ee, Banks, & Backus, 1999 ; Wardle & Gillam, 2016 ; reviewed in Howard & Rogers, 2002 ). Here, we use the term “slant” to characterize a planar surface oriented around the horizontal axis (as, for example, in Oluk, Bonnen, Burge, Cormack, & Giesler, 2022 )—in other words, an inclination (although note that others have defined “slant” as a surface oriented around a vertical axis and hence distinct from inclination; e.g., Howard & Rogers, 2002 ). Stereo slant contrast is “bidirectional” in that the perceived slant of the test surface is invariably shifted away from that of the surround surface (see Figure 1 ).…”