Geometric camera calibration using circular control points

Abstract

Modern CCD cameras are usually capable of a spatial accuracy greater than 1/50 of the pixel size. However, such accuracy is not easily attained due to various error sources that can affect the image formation process. Current calibration methods typically assume that the observations are unbiased, the only error is the zero-mean independent and identically distributed random noise in the observed image coordinates, and the camera model completely explains the mapping between the 3-D coordinates and the image coordinates. In general, these conditions are not met, causing the calibration results to be less accurate than expected. In this paper, a calibration procedure for precise 3-D computer vision applications is described. It introduces bias correction for circular control points and a non-recursive method for reversing the distortion model. The accuracy analysis is presented and the error sources that can reduce the theoretical accuracy are discussed. The tests with synthetic images indicate improvements in the calibration results in limited error conditions. In real images, the suppression of external error sources becomes a prerequisite for successful calibration.

Visual and Acoustic Data Analysis for the Bridge Deck Inspection Robotic System

“…here R is a 3 × 3 rotation matrix which can be defined by the three Euler angles [6], and T = [t x , t y , t z ] T is the translation between two frames. We have the following transformation from the image coordinate to the camera coordinate.…”

Robust detection and ordering of ellipses on a calibration pattern

“…The method that we propose here deals with images like the one in Fig. 1 in which there is an image of a calibrator which is often used to calibrate a camera [7,14]. This is the original pattern and, in this case, it is composed of two orthogonal planes each containing twenty circles in known 3D positions.…”

Which pattern? Biasing aspects of planar calibration patterns and detection methods

“…In turn, the pattern also facilitates the recovery of the control point projections on the image plane. Patterns such as squares (Zhang, 2000;Weng et al, 1992), checkerboards (Lucchese and Mitra, 2002) and circles (Heikkila, 2000;Asari et al, 1999;Kannala and Brandt, 2006) have become popular as they can be readily manufactured to a sufficient precision, and their data points are recoverable through the use of standard image processing techniques.…”

“…This may not always be the case. Heikkila (2000) and Kannala and Brandt (2006) describe calibration techniques using circular control points including corrections for their perspective bias to improve the calibration accuracy.…”