A non-metric pan-tilt stereo head consists of a weakly calibrated stereo rig mounted on a pan-tilt mechanism. It is called non-metric since neither the kinematics of the mechanism, nor the camera calibration are required. The Lie group of "projective rotations"-homographies of projective space corresponding to rotational displacements is a new, formalism that is introduced in this article to model the geometry of such a pan-tilt system. A Rodrigues-like formula as well as a minimal parameterization of projective rotations are introduced. Based on this, the practical part of the article devises a numerical optimization technique for accurately estimating projective rotations from stereo point correspondences along trial motions. This procedure recovers sufficient geometry to operate the system. The experiments validate and evaluate the proposed approach on real image data. They evaluate weak calibration, image prediction, and homing of a non-metric pan-tilt stereo head.

This paper establishes a link between uncalibrated stereo vision and the motion of rigid and articulated bodies. The variation in the projective reconstruction of a dynamic scene over time allows an uncalibrated stereo rig to be used as a faithful motion capturing device. We introduce an original theoretical framework-projective kinematics-which allows rigid and articulated motion to be represented within the transformation group of projective space. Corresponding projective velocities are defined in the tangent space. Most importantly, these projective motions inherit the Lie-group structure of the displacement group. These theoretical results lead immediately to non-metric formulations of visual servoing, tracking, motion capturing and motion synthesis systems, that no longer require the metric geometry of a stereo camera or of the articulated body to be known. We report on such a non-metric formulation of a visual servoing system and present simulated experimental results.

This paper investigates the structure of projective translations-rigid translations expressed as homographies in projective space. A seven parameter representation is proposed, which explicitly represents the geometric entities constraining and defining the translation. A practical algebraic method for estimating these parameters is developed. It provides affine calibration of a stereo rig, determines the translation axis, and allows projective translations to be composed. The practical effectiveness of the calibration is evaluated on synthetic and real image data.

Presents results of a model-based approach to visual tracking and pose estimation for a moving polyhedral tool in position-based visual servoing. This enables the control of a robot in look-and-move mode to achieve six degree of freedom goal configurations. Robust solutions of the correspondence problem-known as "matching" in the static case and "tracking" in the dynamic one-are crucial to the feasibility of such an approach in real-world environments. The object's motion along an arbitrary trajectory in space is tracked using visual pose estimates through consecutive images. Subsequent positions are predicted from robot joint angle measurements. To deal with inaccurate models and to relax calibration requirements, adaptive online calibration of the kinematic chain is proposed. The kinematic predictions enable unambiguous feature matching by a pessimistic algorithm. The performance of the suggested algorithms and the robustness of the proposed system are evaluated on real image sequences of a moving gripper. The results fulfill the requirements of visual servoing, and the computational demands are sufficiently low to allow for real-time implementation.