sborník

CORRECTION OF RADIAL DISTORTION IN PHOTOGRAPHS
approximate location of the distortion center was determined (marked with
a black cross ” + “ in figure 1- right).
4 Determination of distortion coefficients
If we take a photograph of any flat pattern, located outside the plane
perpendicular to the lens axis, then its image on the photograph will be the
combination of the central projection and radial distortion.
Let us assume that the photographed pattern creates a series of collinear
points A, 1, 2, 3, …, O and B. Let us also assume that the standard was
photographed so that the O’ point (the image of the point O) is in the
distortion center and the images of A and B points are located in equal
distance from the distortion center. Distortion for points A’ and B’ is
identical, to simplify things, we may assume that it is equal to 0. The central
projection is a projection transformation for a series of collinear points, it is
determined through giving three points. Thus, knowing the location of
points A’, O’ and B’ we may determine the real, without distortion, location
of points 1’, 2’, 3’, … in the photograph.
5 Practical determination of distortion
coefficients
A pattern created by squares with 0,5 cm side was prepared and printed,
making a grid – 180 cm long and 8 cm wide (Figure 2). The grid was
photographed several times so that the picture of the longer lines of the
pattern was placed along the photograph’s diagonal. Each photograph was
rotated around the distortion center so that the adjacent (in relation to the
distortion center) longer lines of the pattern were parallel to the longer side
of the photograph. Then a horizontal straight line was drawn through the
distortion center, then, with the use of appropriate graphic procedures, the
intersection points between the straight lines and the shorter lines of the grid
were determined and their distances from the distortion center were
calculated. The picture where one of the points was located near the
distortion center and two other – almost at the same distance from the
distortion center – was selected for the further calculations. The selected
points correspond to points A’, O’ and B’, respectively, of chapter …, the
other to points 1’, 2’, 3’, … . Then, using the properties of the projection
transformation, the real distances of points 1’, 2’, 3’, …, (points 1”, 2”, 3”,
…) from the distortion center were calculated. In the end, using the Maple
software, the approximation of the (A’, A’), (1’,1”), (2’, 2”), (3’, 3”), … ,
(O’,O’) and (B’, B’) point sequence was made with the appropriate grade
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