A General Formalization Of Stereo Vision

Lawrence B. Wolff

doi:10.1117/12.942770

19 February 1988 A General Formalization Of Stereo Vision

Lawrence B. Wolff

Proceedings Volume 0848, Intelligent Robots and Computer Vision VI; (1988) https://doi.org/10.1117/12.942770
Event: Advances in Intelligent Robotics Systems, 1987, Cambridge, CA, United States

Abstract

Developed herein is a formal theory for stereo vision which unifies existing stereo methods and predicts a large variety of stereo methods not yet explored. The notion of "stereo" is redefined using terms which are both general and precise giving stereo vision a broader and more rigorous foundation. The variations in imaging geometry between successive images used in parallax stereo and conventional photometric stereo techniques are extended to stereo techniques which involve variations of arbitrary sets of physical imaging parameters. Physical measurement of visual object features is defined in terms of solution loci in feature space arising from constraint equations that model the physical laws that relate the object feature to specific image features. Ambiguity in physical measurement results from a solution locus which is a subset of feature space larger than a single measurement point. Stereo methods attempt to optimally reduce ambiguity of physical measurement by intersecting solution loci obtained from successive images. A number of examples of generalized stereo techniques are presented. This new conception of stereo vision offers a new perspective on many areas of computer vision including areas that have not been previously associated with stereo vision (e.g. color imagery). As the central focus of generalized stereo vision methods is on measurement ambiguity mathematical developments are presented that characterize the "size" of measurement ambiguity as well as the conditions under which disambiguation of a solution locus takes place. The dimension of measurement ambiguity at a solution point is defined using the structure of a differentiable manifold and an upper bound is established using the Implicit Function theorem. Inspired by the Erlanger program of F. Klein generalized stereo methods are equivalently described by the algebraic interaction of the symmetry group of automorphisms (i.e. bijections) of feature space into itself leaving a measurement solution locus invariant, with the set of automorphisms of feature space induced by arbitrary variations of a set of physical parameters. A purely group theoretic characterization of the conditions under which measurement disambiguation takes place is given.

Citation Download Citation

Lawrence B. Wolff "A General Formalization Of Stereo Vision", Proc. SPIE 0848, Intelligent Robots and Computer Vision VI, (19 February 1988); https://doi.org/10.1117/12.942770

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