sborník

25. KONFERENCE O GEOMETRII A POČÍTAČOVÉ GRAFICE
Henryk Gliński
CORRECTION OF RADIAL DISTORTION IN
PHOTOGRAPHS
Abstract
The paper presents a proposal of radial distortion correction method
in photographs. At the first stage, based on specially prepared pattern,
the location of the photo center is determined. Then, based on the
photographs of another pattern, the coefficients of the multinomial
correcting the radial distortion are determined, with the use
of projective geometry.
Keywords
Radial distortion, photography, computer graphics, projective
geometry.
1 Radial distortion
Radial distortion is a typical geometric deformation of photographic
pictures caused by photographic camera lenses, the wide angle lenses in
particular. The deformation consists in the fact that straight lines are imaged
in the pictures as curved ones (Photo 1 and 4). Radial distortion grows along
with the distance from the center of distortion, generally the principal point
of the photograph and is particularly visible near the photograph’s border.
Radial distortion may be removed by appropriate transformation of the
photographs, upon converting it into the digital form. Radial distortion is
mainly described by the equation:
r d = r(1+k 1 r 2 +k 2 r 4 +…),
where r d is the distance of the distorted point from the distortion center, r is
the real distance and k 1 , k 2, … are the coefficients of the even grade
polynomial.
The principal issue is obviously to settle the location of distortion center
and polynomial coefficients. Normally they are determined based on the
photographs of well-known and appropriately selected pattern, in general
the various types of orthogonal grids. Then upon measurement of selected
points in the photographs and carrying out relevant calculations, the
locations of the distortion center and distortion coefficients are fixed
approximately. The simultaneous determination of the distortion center and
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