radial_distortion_self_calibration — Calibrate the radial distortion.
radial_distortion_self_calibration(Contours : SelectedContours : Width, Height, InlierThreshold, RandSeed, DistortionModel, DistortionCenter, PrincipalPointVar : CameraParam)
radial_distortion_self_calibration estimates the distortion
parameters and the distortion center of a lens from a set of XLD
Contours.
The distortion parameters are returned in CameraParam.
Because no other parameters are estimated - particularly not the focal
length or the magnification - a telecentric camera model is returned with
Magnification 1 and scale factor 1 for and
.
See Calibration for more information on the different
camera models.
Application
Based on the result of radial_distortion_self_calibration, you
can remove lens distortions from images by passing the parameter
CameraParam, which contains the distortion parameters, to the
operators change_radial_distortion_cam_par and
change_radial_distortion_image.
Basic principle
The estimation of the distortions is based on the assumption that a significant number of straight lines are visible in the image. Because of lens distortions, these lines will be projected to curved contours. The operator now determines suitable parameters by which the curved contours can be straightened again, thus compensating the lens distortions.
Extract input contours
To get suitable input contours Contours, you can, e.g., use
edges_sub_pix or lines_gauss.
The contours should be equally distributed
and should lie near the image border because there the degree of
distortion is at its maximum and therefore the calibration is most
stable. To improve speed and robustness, you can try to
to obtain long linear or circular segments, e.g., with
segment_contours_xld, union_collinear_contours_xld,
union_cocircular_contours_xld, or select_shape_xld.
If a single image does
not contain enough straight contours in the scene,
you can use the contours of multiple images (concat_obj).
Set parameters for contour selection
The operator automatically estimates those contours from
Contours that are images of straigt lines in the scene using
the robust RANSAC method. The contours that do not fulfill this
condition and hence are not suited for the calibration process are
called outliers. The operator can cope with a maximum outlier
percentage of 50 percent. A contour is classified as an outlier if
the mean deviation of the contour from its associated straight line
is, after the distortion correction, higher than a given threshold
T.
The value InlierThreshold describes the mean deviation of a
contour from its associated line in pixels for a contour that
contains 100 points. The actual threshold T is derived from
InlierThreshold by scaling it with the reference length
(100) and the number of contour points m. Therefore, similar
contours are classified alike. Typical values of
InlierThreshold range from 0.05 to 0.5. The higher the
value, the more deviation is tolerated. By choosing the value 0, all
the contours of Contours are used for the calibration
process. The RANSAC contour selection will then be suppressed to
enable a manual contour selection. This can be helpful if the
outlier percentage is higher than 50 percent.
With the parameter RandSeed, you can control the randomized
behavior of the RANSAC algorithm and force it to return reproducible
results. The parameter is passed as initial value to the internally
used random number generator. If it is set to a positive value, the
operator returns identical results for each call with identical
parameter values.
radial_distortion_self_calibration returns the contours
that were chosen for the calibration process in SelectedContours.
Select distortion model
The distortion model used in the calibration can be selected with
the parameter DistortionModel. By choosing the division model
(DistortionModel = 'division'), the distortions are
modeled by the distortion parameter .
By choosing the polynomial model
(DistortionModel = 'polynomial'), the
distortions are modeled by the radial distortion parameters
and the decentering distortion
parameters .
See Calibration for details on the different camera
models.
Set parameters for the distortion center estimation
The starting value for the estimation of the distortion center
is the center of the image;
the image size is defined by Width and Height.
The distortion parameters
or
, respectively, are estimated via the
methods 'variable', 'adaptive', or
'fixed', which are specified via the parameter
DistortionCenter:
In the default mode 'variable', the distortion center c is estimated with all the other calibration parameters at the same time. Here, many contours should lie equally distributed near the image borders or the distortion should be high. Otherwise, the search for the distortion center could be ill-posed, which results in instability.
With the method 'adaptive',
the distortion center c is at first fixed in the image center.
Then, the outliers are eliminated by using the
InlierThreshold. Finally, the calibration process is rerun
by estimating or
, respectively, which will be accepted
if results from a stable
calibration and lies near the image center. Otherwise, c will be
assumed to lie in the image center. This method should be used if
the distortion center can be assumed to lie near the image center
and if very few contours are available or the position of other
contours is bad (e.g., the contours have the same direction or lie
in the same image region).
By choosing the method 'fixed', the distortion center will be assumed fixed in the image center and only or , respectively, will be estimated. This method should be used in case of very weak distortions or few contours in bad position.
In order to control the deviation of c from the image center, the
parameter PrincipalPointVar can be used in the methods
'adaptive' and 'variable'. If the deviation from
the image center should be controlled, PrincipalPointVar
must lie between 1 and 100. The higher the value, the more the
distortion center can deviate from the image center. By choosing
the value 0, the principal point is not controlled, i.e., the
principal point is determined solely based on the contours. The
parameter PrincipalPointVar should be used in cases of weak
distortions or similarly oriented contours. Otherwise, a stable
solution cannot be guaranteed.
Runtime
The runtime of
radial_distortion_self_calibration is shortest for
DistortionCenter = 'variable' and
PrincipalPointVar = 0. The runtime for
DistortionCenter = 'variable' and
PrincipalPointVar > 0 increases significantly
for smaller values of PrincipalPointVar. The runtimes for
DistortionCenter = 'adaptive' and
DistortionCenter = 'fixed' are also
significantly higher than for DistortionCenter =
'variable' and PrincipalPointVar =
0.
Since the polynomial model
(DistortionModel = 'polynomial') uses more parameters
than the division model (DistortionModel = 'division')
the calibration using the polynomial model can be slightly less stable than
the calibration using the division model, which becomes noticeable in the
accuracy of the decentering distortion parameters .
To improve the stability, contours of multiple images can be used.
Additional stability can be achieved by setting
DistortionCenter = 'fixed',
DistortionCenter = 'adaptive', or
PrincipalPointVar > 0, which was already mentioned
above.
Contours (input_object) xld_cont-array → object
Contours that are available for the calibration.
SelectedContours (output_object) xld_cont-array → object
Contours that were used for the calibration
Width (input_control) extent.x → (integer)
Width of the images from which the contours were extracted.
Default value: 640
Suggested values: 640, 768
Restriction: Width > 0
Height (input_control) extent.y → (integer)
Height of the images from which the contours were extracted.
Default value: 480
Suggested values: 480, 576
Restriction: Height > 0
InlierThreshold (input_control) real → (real)
Threshold for the classification of outliers.
Default value: 0.05
Suggested values: 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1
Restriction: InlierThreshold >= 0
RandSeed (input_control) integer → (integer)
Seed value for the random number generator.
Default value: 42
DistortionModel (input_control) string → (string)
Determines the distortion model.
Default value: 'division'
List of values: 'division', 'polynomial'
DistortionCenter (input_control) string → (string)
Determines how the distortion center will be estimated.
Default value: 'variable'
List of values: 'adaptive', 'fixed', 'variable'
PrincipalPointVar (input_control) real → (real)
Controls the deviation of the distortion center from the image center; larger values allow larger deviations from the image center; 0 switches the penalty term off.
Default value: 0.0
Suggested values: 0.0, 5.0, 10.0, 20.0, 50.0, 100.0
Restriction: PrincipalPointVar >= 0.0 && PrincipalPointVar <= 100.0
CameraParam (output_control) campar → (real / integer / string)
Internal camera parameters.
* Assume that GrayImage is one image in gray values with a
* resolution of 640 x 480 and a suitable number of contours. Then
* the following example performs the calibration using these
* contours and corrects the image with the estimated distortion
* parameters.
edges_sub_pix (GrayImage, Edges, 'canny', 1.0, 20, 40)
segment_contours_xld (Edges, ContoursSplit, 'lines_circles', 5, 8, 4)
radial_distortion_self_calibration (ContoursSplit, SelectedContours, \
640, 480, 0.08, 42, 'division', \
'variable', 0, CameraParam)
get_domain (GrayImage, Domain)
change_radial_distortion_cam_par ('fullsize', CameraParam, 0, CamParamOut)
change_radial_distortion_image (GrayImage, Domain, ImageRectified, \
CameraParam, CamParamOut)
If the parameters are valid, the operator
radial_distortion_self_calibration returns the value 2 (H_MSG_TRUE).
If necessary an exception is raised.
edges_sub_pix,
segment_contours_xld
change_radial_distortion_cam_par,
change_radial_distortion_image
T. Thormälen, H. Broszio: “Automatic line-based estimation of radial lens distortion”; in: Integrated Computer-Aided Engineering; vol. 12; pp. 177-190; 2005.
Calibration