Accurate chequerboard corner localisation for camera calibration

In this article we describe a novel approach to obtain the position of a chequerboard corner at sub-pixel accuracy from digital images. Applications of this method include photogrammetric scene reconstruction, pose estimation, self localisation of (mobile) robots, and camera calibration. Chequerboard patterns are especially suitable for calibrating non-pinhole cameras such as fisheye or catadioptric cameras. We model the grey values of an imaged corner by a simulated imaging process. In order to obtain an efficient implementation on standard hardware, several approximations are presented. The grey value model is used to perform a least-squares fit to the input image using a Levenberg–Marquardt optimisation. The model is described by four geometric parameters (position, rotation, and skew angle of the chequerboard corner), the width of the point spread function, and two photometric parameters (gain and offset). We compare our non-linear algorithm with two linear chequerboard corner localisation algorithms and the classical localisation of photogrammetric circular targets. Ground truth is obtained by mechanically moving a target pattern in front of the camera at sub-pixel accuracy. The corner localisation algorithm is then used to measure the displacement. On the average, our algorithm achieves a displacement error (half the difference between the 75% and 25% quantiles) of 0.032 pixels, while it becomes 0.024 pixels for high contrast and 0.043 pixels for low contrast conditions. The classical photogrammetric method based on circular targets achieves 0.045 pixels in the average case, 0.017 pixels under high contrast and 0.132 pixels under low contrast conditions. The actual positional errors of the corner point positions are lower by a factor of 1/2 than the measured displacement errors.

► Precise determination of the position of chequerboard corners in images.
► Approach: Simulation of the imaging process.
► Higher accuracy than for “classical” circular targets.
► Application: Camera calibration (especially non-pinhole cameras).