Generalised Epipolar Constraints

  • Authors:
  • Kalle Åström;Roberto Cipolla;Peter Giblin

  • Affiliations:
  • Department of Mathematics, Lund University, Lund, Sweden;Department of Engineering, University of Cambridge, Cambridge, UK;Department of Pure Mathematics, University of Liverpool, Liverpool, UK

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

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Abstract

In this paper we will discuss structure and motion problemsfor curved surfaces. These will be studied using the silhouettes or apparent contours in the images. The problem ofdetermining camera motion from the apparent contours of curvedthree-dimensional surfaces, is studied. It will be shown how specialpoints, called epipolar tangency points or frontier points, can beused to solve this problem. A generalised epipolar constraint isintroduced, which applies to points, curves, as well as to apparentcontours of surfaces. The theory is developed for both continuous anddiscrete motion, known and unknown orientation, calibrated anduncalibrated, perspective, weak perspective and orthographic cameras.Results of an iterative scheme to recover the epipolar line structurefrom real image sequences using only the outlines of curved surfaces,is presented. A statistical evaluation is performed to estimate thestability of the solution. It is also shown how the motion of thecamera from a sequence of images can be obtained from the relativemotion between image pairs.