A Unified Theory of Uncalibrated Stereo for Both Perspective and Affine Cameras

  • Authors:
  • Zhengyou Zhang;Gang Xu

  • Affiliations:
  • Microsoft Research, One Microsoft Way, Redmond, WA 98052-6399. E-mail: zhang@microsoft.com;Computer Science Department, CV Lab, Ritsumeikan University, Kusatsu, Shiga 525, Japan. E-mail: xu@cs.ritsumei.ac.jp

  • Venue:
  • Journal of Mathematical Imaging and Vision
  • Year:
  • 1998

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Abstract

This paper addresses the recovery of structure and motion fromuncalibrated images of a scene under full perspective or under affineprojection. Particular emphasis is placed on the configuration of twoviews, while the extension to $N$ views is given in Appendix. Aunified expression of the fundamental matrix is derived which is validfor any projection model without lens distortion (including fullperspective and affine camera). Affine reconstruction is considered asa special projective reconstruction. The theory is elaborated in a waysuch that everyone having knowledge of linear algebra can understandthe discussion without difficulty. A new technique for affinereconstruction is developed, which consists in first estimating theaffine epipolar geometry and then performing a triangulation for eachpoint match with respect to an implicit common affine basis.