Stereo Slant Estimation of Planar Surfaces: Standard Cross-Correlation vs. Planar-Correlation

Abstract

Estimating the three dimensional structure of surfaces is an essential visual task. We studied how the visual system uses binocular information to estimate the slant of planar surfaces. Specifically, we compared how well two candidate computational models explain the data from a psychophysical experiment, where participants were asked to decide whether a textured test plane is more or less slanted than a textured reference plane. Surfaces were viewed from 100 cm and reference plane slants ranged 0 to 50 deg. The stimuli were designed so that performance depends primarily on stereo information. In general, slant discrimination thresholds were found to decrease with baseline slant and to increase with the contrast of white noise added to the test plane. Fronto-parallel bias also increased with noise contrast. Although individuals varied in overall performance, the variation was mostly explained by a single efficiency (scaling) parameter. Our first candidate model was the standard cross-correlation model for disparity estimation, which has been successful in explaining various psychophysical results and can be implemented in a biologically plausible fashion. In this model, estimation of surface slant involves estimating disparities at various surface locations and then estimating the gradient of those disparities across the surface. However, standard cross-correlation implicitly assumes that the surface is locally fronto-parallel, which is not true for slanted surfaces. Our second candidate model, the planar cross-correlation model, does not suffer from this assumption and is motivated by the computations needed for ideal estimation of slant for planar surfaces. The planar cross-correlation model simultaneously estimates slant and depth in an image region by incorporating information about the expected differences in the left and right eye images as a function of distance and slant. We find that the standard cross-correlation model better explains discrimination thresholds, but neither model predicts the fronto-parallel bias.

Meeting abstract presented at VSS 2018