Circle-Marker Detection Method for Omnidirectional Images and its Application to Robot Positioning

Introduction In this paper, we develop an algorithm for the detection of circles from an image captured by a monocular omnidirectional camera system. We assume that an image captured by an omnidirectional camera system is normalised to a spherical image, the image on the unit sphere. Using this geometrical property of the omnidirectional images, we introduce a method for marker-based positioning and navigation of autonomous mobile robots which mounts a monocular omnidirectional camera system. We first clarify the geometric properties of the spherical image of a circle marker placed on the ground plane, and we show that, for the detection of a plane from circle markers, we are required to capture at least two coplanar circle markers. We prove that the image of a circle on the spherical image is a fourth-order algebraic curve, which is the intersection of a sphere and an oblique elliptic cone. For the detection of marker images on the spherical images, we introduce a method for transforming the detection of this fourth-order algebraic curve to the detection of a spatial conic, which is quadric. Second, we develop a voting method for the extraction of images of planar circle markers on a spherical image, using the spatial-quadric detection strategy. Finally, using the assumption for the geometrical configuration of the camera system and the circle markers on the plane on which the robot moves, we derive a positioning algorithm. This positioning method for the robot mounting a monocular omnidirectional camera system allows us to navigate a robot using our circle-detection algorithm. We show some numerical examples both for synthetic and real images.