A non-iterative linear solution of space resection from a single photograph

Abstract

Abstract: The space resection problem is known to be non-linear, and the usual method of solution is iteration of a linearized system of equations derived from the non-linear set. Such solutions, though practical, face some difficult questions like rate of convergence, number of iterations required to reach a stated precision and the chance of the solution converging to an incorrect set of values, etc. In this paper the author describes a non-iterative and purely linear solution of the space resection problem. The elements of exterior orientation are obtained as projective constants, but the usual six elements ω, φ, η, X8 Y8, Z8, can be easily derived therefrom. The problem of computing all three terrain coordinates from the projectivity constants and image data of two overlapping photograms has also been solved.