A three-dimensional position and orientation tracking system comprises one or more pattern tags (77), each comprising a plurality of contrasting portions (1222, 1322, 1332), a tracker (508, 610) for obtaining image information about the pattem tags, a database with geometric information describing patterns on pattem tags; and a controller (210) for receiving and processing the image information from the tracker, accessing the database to retrieve geometric information, and comparing the image information. The contrasting portions are arranged in a rotationally asymmetric pattern (1224) and at least one of the contrasting portions on a pattern tag has a perimeter that has a mathematically describable curved section (1236, 1326, 1336). The perimeter of the contrasting portion may comprise a conic section, including for example an ellipse or a circle. The pattern tags may be borne on tracking markers (12) that have a three-dimensional shaped surface. The tracking system may be implemented in a surgical monitoring system in which the pattern tags are attached to tracking markers or are themselves tracking markers. In other embodiments, the contrasting portions are implemented as contrasting pattern elements (333) on a close-packed tiled background (35) of tiles (334) of at least two mutually contrasting colors.