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Least-Squares Algorithm for Computing 3-D Surface Orientation

Authors: [tex2html_wrap4138]D.G.Jones, J.Malik (University of California, Berkeley)

Investigator username: djones

Category: perception

Subcategory: computer vision

Binocular differences in orientation and foreshortening are systematically related to surface slant and tilt and could potentially be exploited by biological and machine vision systems.

We have derived constraint equations relating orientation and spatial frequency disparities to the local surface normal. We have determined 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 have developed 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. Quantitative experimental results using stereo pairs of test surfaces with known orientation have been used to demonstrate the success of this approach.