A simplified method of endoscopic image distortion correction based on grey level registration

Abstract

We present a new method of endoscopic camera calibration for non-linear radial distortion correction. The algorithm implemented computes both projective (camera) and polynomial (distortion) transformations. The optimization process registrates the corrected distorted pattern image with the non-distorted one. Mutual information was used as measure of similarity and stochastic gradient descent method for optimization.The algorithm was tested with two blw (chessboard, concentric circles) and one grey level patterns, For 3 angular positions of the endoscope (0", 5" and IO" to perpendicular). Convergence time increased with the angle. Maximal mean correction error was less than 0.45 % with optimized distortion parameters calculated for the grey level pattern. Tested inclinations did not have significant effects on errnrs. Results obtained show the interest of the method proposed that requires only approximative perpendicular positioning of the endoscope and simple grey levcl calibration patterns without precise geometrical characteristics.0-7803-8SS4-3/04/%20.00 0 2 0 0 4 IEEE.

Flexible projector calibration for active stereoscopic systems

“…The second step models the radial lens distortion. It was shown in [6] that two polynomial coefficients (k 1 and k 2 ) are sufficient to model precisely strong distortions:…”

Flexible calibration of structured-light systems projecting point patterns

“…This model is well suited to camera optics involving strong barrel distortion [25]. The last step brings c P d in the image coordinate system ðO im ;x im ;ỹ im Þ taking the upper left corner of the image as origin (see Fig.…”

“…The second step models the radial lens distortion according to a polynomial model [24, p. 191] in r, where r is the distance from c P u to the projection of the optical cen- ter on the image plane. Following [25], we use a fourth order polynomial obtained by removing the monomials of larger degrees:…”

From 2D towards 3D cartography of hollow organs

“…In (8), ∂g/∂a rs corresponds to the grey level variations with respect to the a rs value modifications. G x and G y are the components along x and y of the grey level gradient of the point with coordinates (x, y) in T k,k+1,j…”

“…The registration process optimizes the parameters of T k,k+1 2D such as the M I (mutual information, see [7]) measure reaches a maximum. The I ov k images do not include barrel distortion and light inhomogeneities since these radial distortions and shading effects affecting endoscopic data are corrected with the algorithms described in [8], [9]. Moreover, as detailed in [10], the bladder being filled up with physiological serum during an examination, and due to the high acquisition rate (25 images/s), the bladder can be considered as being rigid between two acquisitions k and k + 1.…”