What Tasks can be Performed with an Uncalibrated Stereo Vision System?

  • Authors:

  • J. P. Hespanha;Z. Dodds;G. D. Hager;A. S. Morse

  • Affiliations:

  • Electrical Engineering-System, University of Southern California, Los Angeles, CA 90089-2563. hespanha@usu.edu;Center for Computational Vision and Control, c/o Computer Science Department, P.O. Box 208285, Yale University, New Haven, CT, 06520. zachary.dodds@yale.edu;Center for Computational Vision and Control, c/o Computer Science Department, P.O. Box 208285, Yale University, New Haven, CT, 06520. gregory.hager@yale.edu;Center for Computational Vision and Control, c/o Computer Science Department, P.O. Box 208285, Yale University, New Haven, CT, 06520. as.morse@yale.edu

  • Venue:
  • International Journal of Computer Vision
  • Year:
  • 1999

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Abstract

This article studies the following question: “When is itpossible to decide, on the basis of images of point-features observedby an imprecisely modeled two-camera stereo vision system, whether ornot a prescribed robot positioning task has been preciselyaccomplished?” Results are shown for three camera model classes:injective cameras, weakly calibrated projective cameras, anduncalibrated projective cameras. In particular, given a weaklycalibrated stereo pair, it is shown that a positioning task can beprecisely accomplished if and only if the task specification isinvariant to projective transformations. It is shown that injectiveand uncalibrated projective cameras can accomplish fewer tasks, butare still able to accomplish tasks involving point coincidences.The same formal framework is applied to the problem of determining the set of taskswhich can be precisely accomplished with the well-known position-based control architecture. It isshown that, for any class of camera models, the set of tasks which can be precisely accomplishedusing a position-based control architecture is a subset of the complete set of tasks which can bedecided on the set, but includes all positioning tasks based on point coincidences. Two ways ofextending the idea of position-based control to accomplish more tasks are also presented.