13. Self-calibration of Perspective Cameras

We extend the affine camera self-calibration technique of the preceding chapter to perspective projection. We show that the factorization of the preceding chapter can be applied to perspective cameras if we introduce new unknowns called projective depths. They are determined so that the observation matrix can be factorized, for which two approaches exist. One, called the primary method, iteratively determines the projective depths with the result that the observation matrix has column rank 4, and the other, called the dual method, iteratively determines them with the result that it has row rank 4. However, the reconstructed 3D shape is a projective transformation of the true shape, called projective reconstruction. The correct shape is obtained by applying an appropriate Euclidean upgrading. The entire self-calibration procedure requires a large number of iterations over a large number of unknowns, therefore the computational efficiency is the main concern. We discuss the complexity and efficiency of the involved computation.