General Orientation Problem of Photographs with Planar Objects

Abstract

The orientation problem of photographs taken of planar objects can be treated as a special case for that of a three-dimensional object space. Based on this concept, this paper derived an orientation theory for a two-dimensional object space where the geometry of a picture can, in general, be determined by eight independent central projective parameters. First, the relationship between an object plane and its picture was explored in different ways. Then, the characteristics of the orientation problem were clarified for a stereopair of photographs and for multiple pictures overlapped. The orientation calculation was formulated algebraically with the DLT approach. The orientation methods proposed here are quite general and applicable to the rectification of non-metric photographs with planar objects. In particular, using distances as object space controls, we can form a model congruent to the object by means of a single photograph having non-linear distortions. Also, elements describing the non-linear errors can be provided from the potential of a stereopair of photographs. Furthermore, by employing three pictures overlapped, a united model similar to the object can be constructed without object space information, when we can assume that the interior orientation is unchanged in the three photographs.