In this paper we describe an efficient software architecture for object-tracking, based on a stereoscopic vision system, that has been applied to a mobile robot controlled by a PC. After analyzing the epipolar rectification required to correct the original stereo-images, it is described a new valid and efficient algorithm for ball recognition (indeed circle detection) which is able to work in different lighting conditions and in a manner faster than some modified versions of Circle Hough Transform. Then, we show that stereo vision, besides giving an optimum estimation of the 3D position of the object, is useful to remove lots of the false identifications of the ball, thanks to the advantages of epipolar constraint. Finally, we describe a new strategy for ball following, by a mobile robot, which is able to ”look for” the object whenever it comes out of the cameras view, by taking advantage of a ”block matching” method similar to that of MPEG Video.