On the Epipolar Geometry of the Crossed-Slits Projection

  • Authors:
  • Doron Feldman;Tomás Pajdla;Daphna Weinshall

  • Affiliations:
  • -;-;-

  • Venue:
  • ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
  • Year:
  • 2003

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Abstract

The Crossed-Slits (X-Slits) camera is defined by two non-intersectingslits, which replace the pinhole in the commonperspective camera. Each point in space is projected to theimage plane by a ray which passes through the point and thetwo slits. The X-Slits projection model includes the pushb-roomcamera as a special case. In addition, it describesa certain class of panoramic images, which are generatedfrom sequences obtained by translating pinhole cameras.In this paper we develop the epipolar geometry of the X-Slitsprojection model. We show an object which is similarto the fundamental matrix; our matrix, however, describesa quadratic relation between corresponding image points(using the Veronese mapping). Similarly the equivalent ofepipolar lines are conics in the image plane. Unlike the pin-holecase, epipolar surfaces do not usually exist in the sensethat matching epipolar lines lie on a single surface; we analyzethe cases when epipolar surfaces exist, and characterizetheir properties. Finally, we demonstrate the matchingof points in pairs of X-Slits panoramic images.