Pose estimation from one conic correspondence

Abstract

In this thesis we attempt to solve the problem of camera pose estimation from one conic correspondence by exploiting the epipolar geometry. For this we make two important assumptions which simplify the geometry further. The assumptions are, (a) The scene conic is a circle and (b) The translation vector is contained in a known plane. These two assumptions are justified by noting that many artifacts in scenes(especially indoor scenes), contain circles, which are wholly in front of the camera. Additionally, there is a good possibility that the plane which contains the translation vector would be known. Through the epipolar geometry framework, a matrix equation is defined which relates the camera pose to one conic correspondence and the normal vector defining the scene plane. Through the assumptions, we simplify the system of polynomials in such a way that the task involving solution to a set of seven simultaneous polynomials in seven equations, is transformed into a task of solving only two polynomials in two variables, at the same time. For this we design a geometric construction. This method gives a set of finitely many camera pose solutions. We test our propositions through synthetic datasets and suggest an observation which helps in selecting a unique solution from the finite set of pose solutions. For synthetic dataset, the solution so obtained is quite accurate with an error of 10��4, and for real datasets, the solution is erroneous due to errors in camera calibration data we have. We justify this fact through an experiment. Additionally, the formulation of above mentioned seven equations relating the pose to conic correspondence and scene plane position, helps to understand that, how does the relative pose establish point and conic correspondences between the two images. We then compare the performance of our geometric approach with the conventional way of optimizing a cost function and show that the geometric approach gives us more accurate pose solutions.