Pi-Tag: a fast image-space marker design based on projective invariants

Visual marker systems have become an ubiquitous tool to supply a reference frame onto otherwise uncontrolled scenes. Throughout the last decades, a wide range of different approaches have emerged, each with different strengths and limitations. Some tags are optimized to reach a high accuracy in the recovered camera pose, others are based on designs that aim to maximizing the detection speed or minimizing the effect of occlusion on the detection process. Most of them, however, employ a two-step procedure where an initial homography estimation is used to translate the marker from the image plane to an orthonormal world, where it is validated and recognized. In this paper, we present a general purpose fiducial marker system that performs both steps directly in image-space. Specifically, by exploiting projective invariants such as collinearity and cross-ratios, we introduce a detection and recognition algorithm that is fast, accurate and moderately robust to occlusion. The overall performance of the system is evaluated in an extensive experimental section, where a comparison with a well-known baseline technique is presented. Additionally, several real-world applications are proposed, ranging from camera calibration to projector-based augmented reality.