On Constant Focal Length Self-Calibration from Multiple Views

Abstract

We investigate the problem of finding the metric structure of a general 3D scene viewed by a moving camera with square pixels and constant unknown focal length. While the problem has a concise and well-understood formulation in the stratified framework thanks to the absolute dual quadric, two open issues remain. The first issue concerns the generic Critical Motion Sequences, i.e. camera motions for which self-calibration is ambiguous. Most of the previous work focuses on the varying focal length case. We provide a thorough study of the constant focal length case. The second issue is to solve the nonlinear set of equations in four unknowns arising from the dual quadric formulation. Most of the previous work either does local nonlinear optimization, thereby requiring an initial solution, or linearizes the problem, which introduces artificial degeneracies, most of which likely to arise in practice. We use interval analysis to solve this problem. The resulting algorithm is guaranteed to find the solution and is not subject to artificial degeneracies. Directly using interval analysis usually results in computationally expensive algorithms. We propose a carefully chosen set of inclusion functions, making it possible to find the solution within few seconds. Comparisons of the proposed algorithm with existing ones are reported for simulated and real data.