A modified method for image triangulation using inclined angles

The ongoing technical improvements in photogrammetry, Geomatics, computer vision (CV), and robotics offer new possibilities for many applications requiring efficient acquisition of three-dimensional data. Image orientation is one of these important techniques in many applications like mapping, precise measurements, 3D modeling and navigation.

Image orientation comprises three main techniques of resection, intersection (triangulation) and relative orientation, which are conventionally solved by collinearity equations or by using projection and fundamental matrices. However, different problems still exist in the state – of –the –art of image orientation because of the nonlinearity and the sensitivity to proper initialization and spatial distribution of the points. In this research, a modified method is presented to solve the triangulation problem using inclined angles derived from the measured image coordinates and based on spherical trigonometry rules and vector geometry. The developed procedure shows promising results compared to collinearity approach and to converge to the global minimum even when starting from far approximations. This is based on the strong geometric constraint offered by the inclined angles that are enclosed between the object points and the camera stations.

Numerical evaluations with perspective and panoramic images are presented and compared with the conventional solution of collinearity equations. The results show the efficiency of the developed model and the convergence of the solution to global minimum even with improper starting values.