DIRECT COMPUTATION OF SHAPE CUES USING SCALE-ADAPTED SPATIAL DERIVATIVE OPERATORS

This paper addresses the problem of computing cues to the three-dimens ional structure of surfaces in the world directly from the local struc ture of the brightness pattern of either a single monocular image or a binocular image pair. It is shown that starting from Gaussian derivat ives of order up to two at a range of scales in scale-space, local est imates of (i) surface orientation from monocular texture foreshortenin g, (ii) surface orientation from monocular texture gradients, and (iii ) surface orientation from the binocular disparity gradient can be com puted without iteration or search, and by using essentially the same b asic mechanism. The methodology is based on a multi-scale descriptor o f image structure called the windowed second moment matrix, which is c omputed with adaptive selection of both scale levels and spatial posit ions. Notably, this descriptor comprises two scale parameters; a local scale parameter describing the amount of smoothing used in derivative computations, and an integration scale parameter determining over how large a region in space the statistics of regional descriptors is acc umulated. Experimental results for both synthetic and natural images a re presented, and the relation with models of biological vision is bri efly discussed.