Abstract

This paper presents an approach for calibrating omnidirectional single-viewpoint sensors using the central catadioptric projection properties of parallel lines. Single-viewpoint sensors are widely used in robot navigation and driverless cars; thus, a high degree of calibration accuracy is needed. In the unit viewing sphere model of central catadioptric cameras, a line in a three-dimensional space is projected to a great circle, resulting in the projections of a group of parallel lines intersecting only at the endpoints of the diameter of the great circle. Based on this property, when there are multiple groups of parallel lines, a group of orthogonal directions can be determined by a rectangle constructed by two groups of parallel lines in different directions. When there is a single group of parallel lines in space, the diameter and tangents at their endpoints determine a group of orthogonal directions for the plane containing the great circle. The intrinsic parameters of the camera can be obtained from the orthogonal vanishing points in the central catadioptric image plane. An optimization algorithm for line image fitting based on the properties of antipodal points is proposed. The performance of the algorithm is verified using simulated setups. Our calibration method was validated though simulations and real experiments with a catadioptric camera.

Highlights

  • With the rapid development of computer vision technology, requirements for visual performance have become increasingly stringent

  • According to the properties of antipodal points, the orthogonal vanishing points can be determined on the image plane to obtain the intrinsic parameters of the camera (II) A group of parallel lines is projected to a group of great circles on the unit viewing sphere

  • The diameter of the circles and tangents at their endpoints determine a group of orthogonal directions for the support plane containing each great circle to obtain the intrinsic parameters of the camera (III) An optimization algorithm for line image fitting is proposed based on the relationship between the antipodal points

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Summary

Introduction

With the rapid development of computer vision technology, requirements for visual performance have become increasingly stringent. This study considers the applications of the projection properties of parallel lines in the unit viewing sphere model to calibrate central catadioptric cameras; these methods could apply to any of the mirror-type cameras. According to the properties of antipodal points, the orthogonal vanishing points can be determined on the image plane to obtain the intrinsic parameters of the camera (II) A group of parallel lines is projected to a group of great circles on the unit viewing sphere. The diameter of the circles and tangents at their endpoints determine a group of orthogonal directions for the support plane containing each great circle to obtain the intrinsic parameters of the camera (III) An optimization algorithm for line image fitting is proposed based on the relationship between the antipodal points.

Preliminaries
Camera Calibration Using a Group of Parallel Lines
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Experiments
Calibration methods
Conclusions
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