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Detection of co-planar circle pair of same radius from a single image

This paper describes a method that detects two co-planar circular shaped objects having the same radius from an image with clutter background. We propose an unique RANSAC based method for detecting the candidates of ellipses that divides the circular region centered at the assumed ellipse center into N equal sectors, then fits the edge points selected randomly from each sector. We propose three geometrical constraints of a pair of co-planar circles having the same radius by considering the normal vectors of the supporting plane estimated from each ellipse and the 3D coordinates of the centers of the two circles. From the detected candidates of ellipses, we select the co-planar circle pairs having the same radius by checking how well they fit the proposed geometrical constraints. The output of this method can be used as inputs of many camera calibration and/or 3D structure recovery algorithms that require parallel or co-planar circles. Our method can also applied to the mobile robots to determine their position by monitoring the two co-planar circular objects in the environment.