Another Way of Looking at Plane-Based Calibration: The Centre Circle Constraint

Abstract

The plane-based calibration consists in recovering the internal parameters of the camera from the views of a planar pattern with a known geometric structure. The existing direct algorithms use a problem formulation based on the properties of basis vectors. They minimize algebraic distances and may require a ‘good’ choice of system normalization. Our contribution is to put this problem into a more intuitive geometric framework. A solution can be obtained by intersecting circles, called Centre Circles, whose parameters are computed from the world-to-image homographies. The Centre Circle is the camera centre locus when planar figures are in perpective correspondence, in accordance with a Poncelet’s theorem. An interesting aspect of our formulation, using the Centre Circle constraint, is that we can easily transform the cost function into a sum of squared Euclidean distances. The simulations on synthetic data and an application with real images confirm the strong points of our method.