The Geometry of Colorful, Lenticular Fiducial Markers

Understanding the pose of an object is fundamental to a variety of visual tasks, from trajectory estimation of UAVs to object tracking for augmented reality. Fiducial markers are visual targets designed to simplify this process by being easy to detect, recognize, and track. They are often based on features that are partially invariant to lighting, pose and scale. Here we explore the opposite approach and design passive calibration patterns that explicitly change appearance as a function of pose. We propose a new, simple fiducial marker made with a small lenticular array, which changes its apparent color based on the angle at which it is viewed. This allows full six degree-of-freedom pose estimation with just two markers and an optimization that fully decouples the estimate of rotation from translation. We derive the geometric constraints that these fiducial markers provide, and show improved pose estimation performance over standard markers through experiments with a physical prototype for form factors that are not well supported by standard markers (such as long skinny objects). In addition, we experimentally evaluate heuristics and optimizations that give robustness to real-world lighting variations.