Introduction In the past years real-time object tracking in a closed loop of image acquisition and camera movement has become more and more important. Real-time object tracking algo- rithms are applied to the area of autonomous mobile systems [1], service and cleaning robots and surveillance systems [2]. The typical environment of such systems con- sists of a dynamically changing world due to motion and actions of objects in the world and due to the movement of the system itself. Thus, no offline processing of the image data is possible. The results of a motion tracking module must be available in time, to suitably react to events in the world. One example is service robots, which must track moving people in hospitals to avoid collisions with them. The tracking algorithm provides information about moving persons, which is used by another module to decide whether a person might be an obstacle or not. If the moving object is on the movement path of the service robot, the robot must avoid the collision. Up to now, many different algorithms have been devel- oped to detect and track motion in image sequences [3]. Some of the work was concentrated on offline processing of pre-recorded image sequences [4]. This means that no interaction in a closed loop of image acquisition and camera movement is possible. Real-time object tracking has been the goal of several researchers. Some of them use 1077-2014/99/030203 + 11 $30.00/0 © 1999 Academic Press Active Rays: Polar-transformed Active Contours for Real-Time Contour Tracking n this paper we describe a new approach to contour extraction and tracking, which is based on the principles of active contour models and overcomes its shortcomings. We formally introduce active Irays, describe the contour extraction as an energy minimization problem and discuss what active contours and active rays have in common. The main difference is that for active rays a unique ordering of the contour elements in the 2D image plane is given, which cannot be found for active contours. This is advantageous for predicting the con- tour elements’ position and prevents crossings in the contour. Furthermore, another advantage is that instead of an energy minimization in the 2D image plane the minimization is reduced to a 1D search problem. The approach also shows any-time behavior, which is important with respect to real-time applications. Finally, the method allows for the management of multiple hypotheses of the object’s boundary. This is an important aspect if concave contours are to be tracked. Results on real image sequences (tracking a toy train in a laboratory scene, tracking pedestrians in an outdoor scene) show the suitability of this approach for real-time object tracking in a closed loop between image acquisition and camera movement. The contour tracking can be done within the image frame rate (25 fps) on standard Unix workstations (HP 735) without any specialized hardware. © 1999 Academic Press J. Denzler and H. Niemann Lehrstuhl für Mustererkennung Universität Erlangen/Nürnberg D-91058 Erlangen, Germany Real-Time Imaging 5, 203–213 (1999) Article No. rtim.1997.0116, available online at http://www.idealibrary.com on