The photogrammetric spatial resection using quaternions

Photogrammetry basically uses the colinearity equation in which the rotations according to the Cartesian axis are given with the Euler angles. However, there may be angle combinations that leave the rotation matrix unstable and thus, the solution may not converge or even be undefined. This problem, called gimbal lock, is very common in robotics, computer vision and aeronautics, when its necessary to define the position and orientation of a chamber in tridimensional space and has been solved with the substitution of Euler angles by quaternions. This study aims to use this solution to solve critical photogrammetry orientation problems, in cases of spatial resection. Programs with iterative and direct methods with the substitution of Euler angles by quaternaries were implemented in order to compare against the colinearity method using data of a real situation of measurements obtained with terrestrial photogrammetry. The different implementations and tests made showed the advantages and disadvantages of both methods and that the quaternions are more robust, get better results and allow spatial resection calculation of photographs in positions of rotation ambiguities and critical situations of gimbal lock.

Keywords:
Gimbal Lock; Quaternions; Rotations; Photogrammetry