Square markers are a widespread tool to find correspondences for camera localization because of their robustness, accuracy, and detection speed. Their identification is usually based on a binary encoding that accounts for the different rotations of the marker; however, most systems do not consider the possibility of observing reflected markers. This case is possible in environments containing mirrors or reflective surfaces, and its lack of consideration is a source of detection errors, which is contrary to the robustness expected from square markers. This is the first work in the literature that focuses on reflection-aware square marker dictionaries. We present the derivation of the inter-marker distance of a reflection-aware dictionary and propose new algorithms for generating and identifying such dictionaries. Additionally, part of the proposed method can be used to optimize preexisting dictionaries to take reflection into account. The experimentation carried out demonstrates how our proposal greatly outperforms the most popular predefined dictionaries in terms of inter-marker distance and how the optimization process significantly improves them.
Keywords: augmented reality; camera localization; fiducial markers; object tracking; square markers.