The photogrammetric inner constraints

Abstract

A derivation of the complete inner constraints, which are required for obtaining "free network" solutions in close-range photogrammetry, is presented. The inner constraints are derived analytically for the bundle method, by exploiting the fact that the rows of their coefficient matrix from a basis for the null subspace of the design matrix used in the linearized observation equations. The derivation is independent of any particular choice of rotational parameters and examples are given for three types of rotation angles used in photogrammetry, as well as for the Rodriguez elements. A convenient algorithm based on the use of the S-transformation is presented, for the computation of free solutions with either inner or partial inner constraints. This approach is finally compared with alternative approaches to free network solutions.