A general expression of the fundamental matrix for both perspective and affine cameras

  • Authors:
  • Zhengyou Zhang;Gang Xu

  • Affiliations:
  • ATR Human Information Processing Res. Lab., Soraku-gun, Kyoto, Japan;Department of Computer Science, Ritsumeikan University, Kusatsu, Shiga, Japan

  • Venue:
  • IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
  • Year:
  • 1997

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Abstract

This paper addresses the recovery of structure and motion from two uncalibrated images of a scene under full perspective or under affine projection. Epipolar geometry, projective reconstruction, and affine reconstruction are elaborated in a way such that everyone having knowledge of linear algebra can understand the discussion without difficulty. A general expression of the fundamental matrix is derived which is valid for any projection model without lens distortion (including full perspective and affine camera). A new technique for affine reconstruction from two affine images is developed, which consists in first estimating the affine epipolar geometry and then performing a triangulation for each point match with respect to an implicit common affine basis. This technique is very efficient.