Direct Solution to the Minimal Generalized Pose

Pose estimation is a relevant problem for imaging systems whose applications range from augmented reality to robotics. In this paper we propose a novel solution for the minimal pose problem, within the framework of generalized camera models and using a planar homography. Within this framework and considering only the geometric elements of the generalized camera models, an imaging system can be modeled by a set of mappings associating image pixels to 3-D straight lines. This mapping is defined in a 3-D world coordinate system. Pose estimation performs the computation of the rigid transformation between the original 3-D world coordinate system and the one in which the camera was calibrated. Using synthetic data, we compare the proposed minimal-based method with the state-of-the-art methods in terms of numerical errors, number of solutions and processing time. From the experiments, we conclude that the proposed method performs better, especially because there is a smaller variation in numerical errors, while results are similar in terms of number of solutions and computation time. To further evaluate the proposed approach we tested our method with real data. One of the relevant contributions of this paper is theoretical. When compared to the state-of-the-art approaches, we propose a completely new parametrization of the problem that can be solved in four simple steps. In addition, our approach does not require any predefined transformation of the dataset, which yields a simpler solution for the problem.