Uniform Marker Fields: Camera localization by orientable De Bruijn tori

In various applications, a wider area needs to be covered by fiduciary markers but a large marker cannot be used because only a fraction of the area is to be viewed by the camera. Such an area can be covered by a number of small markers with unique identifiers. However, with the camera freely moving in the scene and with occluders present, it is difficult to ensure that at least one of the individual markers is completely visible, unless the markers are small and numerous. In that case, the markers are not recognizable from larger distances. In this paper we introduce the concept of Marker Fields which overcome this limitation. The Marker Field covers a large-scale planar (or non-planar) area and it is composed of mutually overlapping partial markers. We propose a particular arrangement of the Marker Field: a Uniform Checker-Board Marker Field, which is a black- and-white checkerboard whose square modules are defined by aperiodic 4-orientable binary n²-window arrays (De Bruijn tori). We propose a genetic algorithm for construction of 4-orientable n²window arrays. We used a supercomputer to synthesize large 4-orientable 4²window arrays and offer them publicly for downloading. We prototyped an algorithm for detection of the checkerboard marker fields and measured its performance. When processing input video from a cellphone camera, the algorithm visits only about 5 % of image pixels for reliable detection and the processing time is about 1 ms on a mid-range PC processor. The Uniform Marker Field increases freedom of camera movement, especially with occluders present in the scene. The detection algorithm is efficient and real-time marker field detection will be feasible on ultramobile devices.