Self-calibration from Two Perspective Views under Various Conditions: Closed-form Solutions and Degenerate Configurations

The epipolar geometry between two uncalibrated views is completely encapsulated in the fundamental matrix. This paper presents analytic procedures for self-calibrating a perspective camera by decomposing the fundamental matrix into (partially) unknown intrinsic parameters and the camera motion under three conditions: (i) A camera with unknown and varying focal length undergoes general motion, (ii) A camera with unknown but constant focal length undergoes general motion, and (iii) A camera with unknown but constant focal length and principal point undergoes fixation, that is, the optical axis is confined in a plane. For each of these cases, we derive the closed-form solution for the unknown intrinsic parameters and characterize degenerate configurations in which the solution is indeterminate. The derivation is made commonly based on a powerful tool: a special form of the fundamental matrix with horizontally aligned epipoles, which makes the analysis quite simple in virtue of its conciseness.