Two Separate Circles With Same-Radius: Projective Geometric Properties and Applicability in Camera Calibration

Abstract

In the domain of computer vision, camera calibration is a key step in recovering the twodimensional Euclidean structure. Circles are considered important image features similar to points, lines, and conics. In this paper, a novel linear calibration method is proposed using two separate same-radius (SSR) circles as the calibration pattern. We show that the distinct pair of dual circles encodes three lines, two of which are parallel to each other and perpendicular to the remaining line. When any two coplanar or parallel circles degenerate to SSR circles, a solution can be found to recover another pair of parallel lines based on the geometric properties of the SSR circles. Using the vanishing points obtained as the key helper for determining the imaged circular points and the orthogonal vanishing points, we deduce the constraints on the image of the absolute conic (IAC) and then employ it for complete camera calibration. Furthermore, a closed-form solution for the extrinsic parameters can be obtained based on the projective invariance of the conic dual to the circular points. Evaluations based on simulated and real data confirmed the effectiveness and feasibility of the proposed algorithms. INDEX TERMS Camera calibration, conic dual, image of circular points, parallel lines, SSR circles.

The general method of the tanker car mouth pose measurement

“…Furthermore, because the circle lacks any distinctive features, measuring its pose accurately is challenging. Various fields require high-precision measurements of spatial circle pose, including robot assembly (Ogun et al , 2015; Wen et al , 2017), spacecraft pose measurement (Liu et al , 2020; Jiang et al , 2021; Liu and Hu, 2014) and camera calibration (Yang et al , 2020). Currently, there are visual technique of monocular method and binocular method to measure the pose of the space circle.…”