Determining Three-Dimensional Shape from Orientation and Spatial

When a surface slanted away from the fronto-parallel plane is viewed binocularly, surface markings and texture are imaged with slightly different orientations and degrees of foreshortening. These orientation and spatial frequency disparities are systematically related to surface slant and tilt and could potentially be exploited by biological and machine vision systems. There is evidence suggesting that human stereopsis has a mechanism that specifically makes use of orientation and spatial frequency disparities, in addition to the usual cue of horizontal positional disparity. In this paper we derive constraint equations relating orientation and spatial frequency disparities to the local surface normal. We derive necessary and sufficient conditions for recovering surface normals: (I) Two measurements of orientation disparity, or (ii) One measurement of orientation disparity and associated spatial frequency disparity. These conditions are readily met in local regions of real images, for example in texture patches and in the neighborhood of brightness edges and lines that are curved or form corners and junctions. We develop a least squares algorithm that provides more reliable computation of 3-D surface normals when more than the minimum number of orientation and spatial frequency disparities are available. Experimental results are presented to demonstrate the success of this approach.