Radial Distortion Correction
Modern camera lenses
are relatively free of geometric distortion. However, there is always a
small remaining amount even with the most expensive lenses.
Radial distortion is
most visible when taking pictures of vertical structures having
straight lines which then appear curved. This kind of distortion
appears most visibly when the widest angle (shortest focal length) is
selected either with a fixed or a zoom lens. It may be adequately
corrected by applying a simple polynomial transformation due to the
19th century mathematician and astronomer Philipp Ludwig von Seidel
(1821-1896) published by him in 1856 which requires three constants
affecting the image content as a function of the distance from the
center and symmetrical about it, hence the name radial distortion. A very complete discussion with full mathematical background, is given in this link
These constants may
be computed by photographing a structure or a target containing known
straight lines, both vertically and horizontally. They depend on the
focal length of the lens relative to the length of the diagonal of the
image sensor and vary from lens to lens. For cameras with
interchangeable lenses, separate calibration is required for each lens
and for a selection of typical focal lengths relative to a given
camera. For a less expensive digital camera with a non-interchangeable
lens, calibration is required only for a selection of focal lengths.
accesses a database called PTLens.dat to correct distortion. To use
recent entries in the database you must purchase a license from the
Purchase page at http://epaperpress.com/ptlens.
Updates to the database may be found on the Download page at same site.
Instructions for installing the license in RadCor are in a readme file
that accompanies the license. If you have any questions about the
database contact Tom Niemann (http://epaperpress.com/whoami).
Because of the many
cameras and lenses on the market which are constantly being added to,
it is not possible to have a profile for every camera and every lens.
Therefore, this programme offers simple tools for calibrating any
camera-lens combination if a suitable image is available. Here, this
process is called manual correction..
Some cheaper cameras
have distortion which varies with colour. This is chromatic
aberration. In this programme, a facility is offered for selection of
the correction constants for the red, green and blue components of a
colour calibration image in the chromatic correction option.
In addition to
radial distortion and chromatic aberration, there are other types of
lens distortion which affect the quality and geometry of an image which
are not radially symmetric. This type of distortion (tangential)
is not corrected in this programme, since it is usually small compared
with that due to radial lens distortion at the typical image
resolutions of digital cameras. Perspective distortion, which is
introduced by the camera pointing obliquely at the subject of interest,
will be addressed in another programme.
If the distribution
of light at the sides of the image is not the same as nearer to the
center, these portions of an image appear to be darker. The programme
can correct for simple symmetrical radial vignetting sometimes present
at very wide angles or when lens hoods are used.