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

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Abstract

This paper addresses the recovery of structure and motion from uncalibrated images of a scene under full perspective or under affine projection. Particular emphasis is placed on the configuration of two views, while the extension to N views is given in Appendix. A unified expression of the fundamental matrix is derived which is valid for any projection model without lens distortion (including full perspective and affine camera). Affine reconstruction is considered as a special projective reconstruction. The theory is elaborated in a way such that everyone having knowledge of linear algebra can understand the discussion without difficulty. A new technique for affine reconstruction 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.

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