Direct retrieval of exterior orientation parameters using a 2D projective transformation

Direct solutions are very attractive because they obviate the need for initial approximations associated with non‐linear solutions. The direct linear transformation (DLT) establishes itself as a method of choice for direct solutions in photogrammetry and other fields. The use of the DLT with coplanar object space points leads to a rank deficient model. This rank deficient model leaves the DLT defined up to a 2D projective transformation, which makes the direct retrieval of the exterior orientation parameters (EOPs) a non‐trivial task. This paper presents a novel direct algorithm to retrieve the EOPs from the 2D projective transformation. It is based on a direct relationship between the 2D projective transformation and the collinearity model using homogenous coordinates. This representation offers a direct matrix correspondence between the 2D projective transformation parameters and the collinearity model parameters. This correspondence lends itself to a direct matrix factorisation to retrieve the EOPs. An important step in the proposed algorithm is a normalisation process that provides the actual link between the 2D projective transformation and the collinearity model. This paper explains the theoretical basis of the proposed algorithm as well as the necessary steps for its practical implementation. In addition, numerical examples are provided to demonstrate its validity.