Planar scenes would appear to be ideally suited for self-calibration because, by eliminating the problems of occlusion and parallax, high accuracy two-view relationships can be calculated without restricting motion to pure rotation. Unfortunately, the only monocular solutions so far devised involve costly nonlinear minimizations, which must be initialized with educated guesses for the calibration parameters. So far, this problem has been circumvented by using stereo or a known calibration object. In this work we show that when there is some control over the motion of the camera, a fast linear solution is available without these restrictions. For a camera undergoing a motion about a plane-normal rotation axis (typified for instance by a motion in the plane of the scene), the complex eigenvectors of a plane-induced homography are coincident with the circular points of the motion. Three such homographies provide sufficient information to solve for the image of the absolute conic (IAC), and therefore the calibration parameters. The required situation arises most commonly when the camera is viewing the ground plane, and either moving along it, or rotating about some vertical axis. We demonstrate a number of useful applications, and show the algorithm to be simple, fast, and accurate.

Many recent approaches to simultaneous localisation and mapping (SLAM) use an extended Kalman filter (EKF) to update and maintain a map of vehicle location. and multiple feature positions as a sensor moves through a scene. Although it is a highly powerful and well-used tool, it suffers from a well-known complexity problem. In this paper we outline the postponement technique which allows for much greater flexibility on when to use the available processing time, while not affecting the optimality of the filter. It works by updating a constant-sized data set based on current measurements, which can be used to affect the updates on all unobserved parts of the map at a later stage. By expanding the set of updated features when each new feature is observed we show that the full map update can be postponed indefinitely. We also demonstrate how postponement can be used to improve the performance of sub-optimal algorithms by applying it to a simple constant time method.

In this paper we will show how rotation matrices obtained from image measurements, for instance via self-calibration of rotating cameras, may be used to self-align an active stereo head such that the optic axes of the cameras are parallel, horizontal and perpendicular to the elevation axis. Whereas general rotation matrices have three degrees of freedom, with robot heads we may generate motions with fewer degrees of freedom, and use prior knowledge of the kinematic chain to constrain the rotation matrices to have a particular form. We demonstrate how these constraints provide sufficient alignment information, and we provide fast, accurate and stable algorithms to achieve this task. Both a linear method, which minimizes an algebraic error, and two nonlinear methods which minimize meaningful errors, are presented, and we show in theory and experiments that they give virtually identical results. Results from both simulated data and from real images obtained from an active stereo head are presented.

We present a very simple and effective method for eliminating the degeneracy inherent in a planar scene, and demonstrate its performance in a useful application - binocular self-calibration. The projective geometry of planar scenes suffers from a two-fold ambiguity: projective structure cannot be recovered from a pair of images of the scene, and transformations in projective 3-space are underconstrained for features lying on a plane. We overcome these problems by combining the feature data from different pairs of images where we know the relationship between the images is identical. In essence this generates images of a non-degenerate scene which can then be processed using standard algorithms. The only constraint is that the binocular head must be able to make repeated identical rotations about its axes. The benefits of this technique are demonstrated by its use in solving the problem of self-calibration. The use of data combination enables standard general scene stereo calibration algorithms to be used.

We present a complete system for automatic alignment and calibration of a stereo pan-tilt camera platform on a mobile robot. The system uses visual data from one or two controlled rotations of the head, and a single forward motion of the robot. We show how the images alone provide head alignment information, camera calibration, and head geometry. We also discuss automatic zeroing of steering angle for a single steering wheel AGV. Results are provided from tests on the working system.