Technique of distortion correction in endoscopic images using a polynomialexpansion

A new technique to correct non-linear distortion of endoscopic images based on L-2-norm approximation is proposed. A mathematical model is defined tha t maps the endoscopic images from the distorted image plane onto an undisto rted image plane. A set of model parameters is defined, consisting of the i mage distortion centre, corrected centre and expansion polynomial coefficie nts representing radial distortion correction. A new method to find the ima ge distortion centre based on a curvature criterion is also developed. The expansion coefficients are estimated on the basis of the degree of straight ness of the grid lines in an image of a test grid consisting of dots in a r ectangular pattern. The corrected image centre is computed by ensuring that the distances between neighbouring test dots of different grid lines in th e corrected image are the same. The quantitative data providing the results and errors of the expansion characteristics are presented. The performance of the proposed distortion correction algorithm is validated with grid pat terns of different orientations. The algorithm is also applied to typical e ndoscopic images, and the results are presented. The high-speed response of the proposed technique is a key step towards on-line camera calibration.