Abstract
Estimating three-dimensional (3D) surface orientation (slant and tilt) is an important first step toward estimating 3D shape. Here, we examine how three local image cues from the same location (disparity gradient, luminance gradient, and dominant texture orientation) should be combined to estimate 3D tilt in natural scenes. We collected a database of natural stereoscopic images with precisely co-registered range images that provide the ground-truth distance at each pixel location. We then analyzed the relationship between ground-truth tilt and image cue values. Our analysis is free of assumptions about the joint probability distributions and yields the Bayes optimal estimates of tilt, given the cue values. Rich results emerge: (a) typical tilt estimates are only moderately accurate and strongly influenced by the cardinal bias in the prior probability distribution; (b) when cue values are similar, or when slant is greater than 40°, estimates are substantially more accurate; (c) when luminance and texture cues agree, they often veto the disparity cue, and when they disagree, they have little effect; and (d) simplifying assumptions common in the cue combination literature is often justified for estimating tilt in natural scenes. The fact that tilt estimates are typically not very accurate is consistent with subjective impressions from viewing small patches of natural scene. The fact that estimates are substantially more accurate for a subset of image locations is also consistent with subjective impressions and with the hypothesis that perceived surface orientation, at more global scales, is achieved by interpolation or extrapolation from estimates at key locations.