This chapter provides information regarding camera calibration.
To achieve maximum accuracy of measurement for your camera setup, you have to calibrate it accordingly. Therefore, a camera model is determined, which describes the projection of a 3D world point into a (sub-)pixel in the image.
HALCON provides a wide range of operators to approach diverse tasks related to calibration, such as
describing and finding a calibration object (Calibration / Calibration Object),
the projection of points from the 3D scene onto the image plane and the other way around (Calibration / Projection, Calibration / Inverse Projection),
compensating perspective and radial distortions (Calibration / Rectification),
handling the camera parameters (Calibration / Camera Parameters),
performing a self-calibration (Calibration / Self-Calibration), and
calibrating different setups consisting of
one camera (Calibration / Monocular),
multiple cameras (Calibration / Binocular, Calibration / Multi-View), or
a camera in combination with a robot (Calibration / Hand-Eye).
This chapter gives guidance regarding the basic concept of retrieving the internal and external parameters of your camera. The following paragraphs state how to successfully calibrate a camera. In particular, they describe
the needed calibration object,
the individual steps to calibrate the cameras, including
how to prepare the calibration input data,
how to perform the actual calibration with
, and
calibrate_cameras
how to check the success of the calibration,
the camera parameters,
additional information about the calibration process, including
how to obtain an appropriate calibration plate,
how to take a set of suitable images, and
which distortion model to use,
the available 3D camera models and how 3D points are transformed into the image coordinate system, and
limitations related to specific camera types.
For a successful calibration of your camera setup, at least one calibration object with accurately known metric properties is needed, e.g., a HALCON calibration plate. For the calibration, take a series of images of the calibration object in different positions and orientations. The success of the calibration highly depends on the quality of the calibration object and the images. So you might want to exercise special diligence during the acquisition of the calibration images. See the section “How to take a set of suitable images?” for further information.
A calibration plate is covered by multiple calibration marks, which are extracted in the calibration images in order to retrieve their coordinates. The orientation of the plate has to be known distinctively, hence, a finder pattern is also part of the imprint.
Your distributor can provide you with two different types of standard HALCON calibration plates:
As finder pattern, there are special groups of mark hexagons where some of
the marks contain dot-shaped holes (see
).
One finder pattern has to be visible to locate the calibration plate.
To make sure the plate is not inverted, at least a second one needs to be
seen, but the plate does not have to be fully visible in the image.
The origin of the coordinate system is located at the center of the central
mark of the first finder pattern.
The z-axis of the coordinate system is pointing into
the calibration plate, its x-axis is pointing to the right, and
its y-axis is pointing downwards with the direction of view along
the z-axis.
create_caltab
camera_calibration
instead of
calibrate_cameras
, this calibration plate is not applicable.
gen_caltab
).
Thus, the plate has to be fully visible in the image.
The origin is located in the middle of the surface of the calibration plate.
The z-axis of the coordinate system is pointing into
the calibration plate, its x-axis is pointing to the right, and
its y-axis is pointing downwards with the direction of view along
the z-axis.
When acquiring your calibration images, note that there are different recommendations on how to take them, depending on your used calibration plate (see section “How to take a set of suitable images?”).
Before calling a calibration operator (e.g.,
), you
must create and adapt the calibration data model with the following steps:
calibrate_cameras
Create a calibration data model with the operator
, specifying the number of cameras in the
setup and the number of used calibration objects.
create_calib_data
Specify the camera type and the initial internal
camera parameters with the operator
.
set_calib_data_cam_param
Specify the description of all calibration objects
with the operator
.
set_calib_data_calib_object
Collect observation data with the operators
or find_calib_object
,
i.e., obtain the image coordinates of the extracted calibration marks of
the calibration object and a roughly estimated pose of the
calibration object relative to the observing camera.
set_calib_data_observ_points
set_calib_data
.
For example, if the image sensor cell size of camera 0 is known precisely
and only the rest of the parameters needs to be calibrated, you call
Using all the information stored within the calibration data model, the
actual calibration can be performed calling
.
Thereby, the input model is modified by optimizing the initial internal
camera parameters, computing and adding further data like the external
camera parameters or standard deviations.
Furthermore, the standard deviations and covariances of the calibrated
internal parameters and the root mean square error of the back projection
are calculated in order to check the success of the calibration.
calibrate_cameras
The results can then be queried with the operator
.
get_calib_data
After a successful calibration, the root mean square error (RMSE) of
the back projection of the optimization is returned in
(in pixels). The error gives a general indication
whether the optimization was successful as it corresponds to the average
distance (in pixels) between the back projected calibration points and their
extracted image coordinates.
Error
If only a single camera is calibrated, an
in the
order of 0.1 pixel (the typical detection error by extraction of the
coordinates of the projected calibration markers) is an indication
that the optimization fits the observation data well. If
Error
strongly differs from 0.1 pixels, the calibration did
not perform well. Reasons for this might be, e.g., a poor image
quality, an insufficient number of calibration images, or an
inaccurate calibration plate.
Error
For information about how to check the success of the calibration using a multi-view camera setup, see the respective section in the chapter Calibration / Multi-View.
Regarding camera parameters, you can distinguish between internal and external camera parameters.
These parameters describe the characteristics of the used camera,
especially the dimension of the sensor itself and the projection
properties of the used combination of lens, camera, and frame
grabber. Below is an overview of all available camera types and
their respective parameters CameraParam
. In the list,
“projective cameras” refers to the property that the lens
performs a perspective projection on the object-side of the lens,
while “telecentric cameras” refers to the property that the lens
performs a telecentric projection on the object-side of the lens.
have 9 to 16 internal parameters depending on the camera type.
For reasons explained below, parameters that are marked with an * asterisk are fixed and not estimated by the algorithm.
Projective area scan cameras with regular lenses
'area_scan_division'
:
['area_scan_division', Focus, Kappa, Sx, Sy*, Cx,
Cy, ImageWidth, ImageHeight]
'area_scan_polynomial'
:
['area_scan_polynomial', Focus, K1, K2, K3, P1, P2,
Sx, Sy*, Cx, Cy, ImageWidth, ImageHeight]
Telecentric area scan cameras with regular lenses
'area_scan_telecentric_division'
:
['area_scan_telecentric_division', Magnification,
Kappa, Sx, Sy*, Cx, Cy, ImageWidth, ImageHeight]
'area_scan_telecentric_polynomial'
:
['area_scan_telecentric_polynomial', Magnification,
K1, K2, K3, P1, P2, Sx, Sy*, Cx, Cy, ImageWidth, ImageHeight]
Projective area scan cameras with tilt lenses
'area_scan_tilt_division'
:
['area_scan_tilt_division', Focus, Kappa,
ImagePlaneDist, Tilt, Rot, Sx, Sy*, Cx, Cy, ImageWidth, ImageHeight]
'area_scan_tilt_polynomial'
:
['area_scan_tilt_polynomial', Focus, K1, K2, K3, P1,
P2, ImagePlaneDist, Tilt, Rot, Sx, Sy*, Cx, Cy, ImageWidth,
ImageHeight]
'area_scan_tilt_image_side_telecentric_division'
:
['area_scan_tilt_image_side_telecentric_division',
Focus, Kappa, Tilt, Rot, Sx*, Sy*, Cx, Cy, ImageWidth, ImageHeight]
'area_scan_tilt_image_side_telecentric_polynomial'
:
['area_scan_tilt_image_side_telecentric_polynomial',
Focus, K1, K2, K3, P1, P2, Tilt, Rot, Sx*, Sy*, Cx, Cy,
ImageWidth, ImageHeight]
Telecentric area scan cameras with tilt lenses
'area_scan_tilt_bilateral_telecentric_division'
:
['area_scan_tilt_bilateral_telecentric_division',
Magnification, Kappa, Tilt, Rot, Sx*, Sy*, Cx, Cy,
ImageWidth, ImageHeight]
'area_scan_tilt_bilateral_telecentric_polynomial'
:
['area_scan_tilt_bilateral_telecentric_polynomial',
Magnification, K1, K2, K3, P1, P2, Tilt, Rot, Sx*, Sy*, Cx,
Cy, ImageWidth, ImageHeight]
'area_scan_tilt_object_side_telecentric_division'
:
['area_scan_tilt_object_side_telecentric_division',
Magnification, Kappa, ImagePlaneDist, Tilt, Rot, Sx, Sy*,
Cx, Cy, ImageWidth, ImageHeight]
'area_scan_tilt_object_side_telecentric_polynomial'
:
['area_scan_tilt_object_side_telecentric_polynomial',
Magnification, K1, K2, K3, P1, P2, ImagePlaneDist, Tilt,
Rot, Sx, Sy*, Cx, Cy, ImageWidth, ImageHeight]
Projective area scan cameras with hypercentric lenses
'area_scan_hypercentric_division'
:
['area_scan_hypercentric_division', Focus, Kappa, Sx, Sy*,
Cx, Cy, ImageWidth, ImageHeight]
'area_scan_hypercentric_polynomial'
:
['area_scan_hypercentric_polynomial', Focus, K1, K2, K3, P1,
P2, Sx, Sy*, Cx, Cy, ImageWidth, ImageHeight]
Type of the camera, as listed above.
Focal length of the lens (only for lenses that perform a perspective projection on the object side of the lens).
The initial value is the nominal focal length of the used lens, e.g., 0.008m.
Magnification of the lens (only for lenses that perform a telecentric projection on the object side of the lens).
The initial value is the nominal magnification of the used telecentric lens (the image size divided by the object size), e.g., 0.2.
Distortion coefficient to model the radial lens distortions (only for the division model).
Use 0.0 as initial value.
Distortion coefficients to model the radial and decentering lens distortions (only for the polynomial model).
Use 0.0 as initial value for all five coefficients.
Distance of the exit pupil of the lens to the image plane. The exit pupil is the (virtual) image of the aperture stop (typically the diaphragm), as viewed from the image side of the lens. Typical values are in the order of a few centimeters to very large values if the lens is close to being image-side telecentric.
The tilt angle describes the angle by which the optical axis is tilted with respect to the normal of the sensor plane (corresponds to a rotation around the x-axis). The rotation angle describes the rotation around the optical axis (z-axis). For a rotation the optical axis gets tilted vertically down with respect to the camera housing, corresponds to the optical axis being tilted horizontally to the left (direction of view along the z-axis), corresponds to the optical axis being tilted vertically up, and corresponds to the optical axis being tilted horizontally to the right.
These parameters are only used if a tilt lens is part of the camera setup.These angles are typically roughly known based on the considerations that led to the use of the tilt lens or can be read off from the mechanism by which the lens is tilted.
Scale factors. They correspond to the horizontal and vertical distance between two neighboring cells on the sensor. Since in most cases the image signal is sampled line-synchronously, is determined by the dimension of the sensor and does not need to be estimated by the calibration process.
The initial values depend on the dimensions of the used chip of the camera. See the technical specification of your camera for the actual values. Attention: These values increase if the image is subsampled!
As projective cameras are described through the pinhole camera
model, it is impossible to determine
, , and simultaneously.
Therefore, the algorithm will keep fixed.Focus
For telecentric lenses, it is
impossible to determine Magnification
,
, and simultaneously. Therefore,
the algorithm will keep fixed.
For image-side telecentric tilt lenses (see chapter “Basics”,
section “Camera Model and Parameters” in the
“Solution Guide III-C 3D Vision”
for an overview of different
types of tilt lenses), it is impossible
to determine
, , ,
and the tilt parameters and
simultaneously. Therefore, additionally to , the
algorithm will keep fixed. Focus
For bilateral telecentric tilt lenses,
it is impossible to determine Magnification
,
, , and the tilt parameters
and simultaneously. Therefore,
additionally to , the algorithm will keep
fixed.
Column () and row () coordinate of the principal point of the image (center of the radial distortion).
Use the half image width and height as initial values. Attention: These values decrease if the image is subsampled!
Width and height of the sampled image. Attention: These values decrease if the image is subsampled!
have 12 or 16 internal parameters depending on the camera type.
For reasons explained below, parameters that are marked with an * asterisk are fixed and not estimated by the algorithm.
Projective line scan cameras with regular lenses
'line_scan_division'
:
['line_scan_division', Focus, Kappa, Sx*, Sy*, Cx,
Cy, ImageWidth, ImageHeight, Vx, Vy, Vz]
'line_scan_polynomial'
:
['line_scan_polynomial', Focus, K1, K2, K3, P1, P2,
Sx*, Sy*, Cx, Cy, ImageWidth, ImageHeight, Vx, Vy, Vz]
Telecentric line scan cameras with regular lenses
'line_scan_telecentric_division'
:
['line_scan_telecentric_division', Magnification,
Kappa, Sx*, Sy*, Cx, Cy, ImageWidth, ImageHeight, Vx, Vy, Vz*]
'line_scan_telecentric_polynomial'
:
['line_scan_telecentric_polynomail', Magnification,
K1, K2, K3, P1, P2, Sx*, Sy*, Cx, Cy, ImageWidth,
ImageHeight, Vx, Vy, Vz*]
Type of the camera, as listed above.
Focal length of the lens (only for lenses that perform a perspective projection on the object side of the lens).
The initial value is the nominal focal length of the used lens, e.g., 0.008m.
Magnification of the lens (only for lenses that perform a telecentric projection on the object side of the lens).
The initial value is the nominal magnification of the used telecentric lens (the image size divided by the object size), e.g., 0.2.
Distortion coefficient of the division model to model the radial lens distortions.
Use 0.0 as initial value.
Distortion coefficients to model the radial and decentering lens distortions (only for the polynomial model).
Use 0.0 as initial value for all five coefficients.
Scale factor. Corresponds to the horizontal distance between two
neighboring cells on the sensor. Note that Focus
or
Magnification
, respectively, and cannot
be determined simultaneously. Therefore, is
kept fixed in the calibration. The initial value for
can be taken from the technical specifications
of the camera. Attention: This value increases if the image is
subsampled!
Scale factor. During the calibration, it appears only in the form . Consequently, and cannot be determined simultaneously. Therefore, in the calibration, is kept fixed. describes the distance of the image center point from the sensor line in meters. The initial value for can be taken from the technical specifications of the camera. Attention: This value increases if the image is subsampled!
Column coordinate of the image center point (center of the radial distortions). Use half of the image width as the initial value for . Attention: This value decreases if the image is subsampled!
Distance of the image center point (center of the radial distortions) from the sensor line in scanlines. The initial value can normally be set to 0.
Width and height of the sampled image. Attention: These values decrease if the image is subsampled!
X-, Y-, and Z-component of the motion vector.
The initial values for the x-, y-, and z-component of the motion vector depend on the image acquisition setup. Assuming a camera that looks perpendicularly onto a conveyor belt and that is rotated around its optical axis such that the sensor line is perpendicular to the conveyor belt, i.e., the y-axis of the camera coordinate system is parallel to the conveyor belt, use the initial values . The initial value for can then be determined, e.g., from a line scan image of an object with known size (e.g., calibration plate, ruler):
With
If, compared to the above setup, the camera is rotated 30 degrees around its optical axis, i.e., around the z-axis of the camera coordinate system, the above determined initial values must be changed as follows:
If, compared to the first setup, the camera is rotated -20 degrees around the x-axis of the camera coordinate system, the following initial values result:
The quality of the initial values for , , and are crucial for the success of the whole calibration. If they are not precise enough, the calibration may fail.
Note that for telecentric line scan cameras, the value of has no influence on the image position of 3D points and therefore cannot be determined. Consequently, is not optimized and left at its initial value for telecentric line scan cameras. Therefore, the initial value of should be set to 0. For setups with multiple telecentric line scan cameras that share a common motion vector (for a detailed explanation, see Calibration / Multi-View), however, can be determined based on the camera poses. Therefore, in this case is optimized.
Note that the term focal length is not quite correct and would be appropriate only for an infinite object distance. To simplify matters, always the term focal length is used even if the image distance is meant.
For all operators that use camera parameters as input the respective parameter values are checked as to whether they fulfill the following restrictions:
For some operators the restrictions differ slightly. In particular, for operators that do not support line scan cameras the following restriction applies:
The following 6 parameters describe the 3D pose, i.e., the position and orientation of the world coordinate system relative to the camera coordinate system. The x- and y-axis of the camera coordinate system are parallel to the column and row axes of the image, while the z-axis is perpendicular to the image plane. For line scan cameras, the pose of the world coordinate system refers to the camera coordinate system of the first image line.
Translation along the x-axis of the camera coordinate system.
Translation along the y-axis of the camera coordinate system.
Translation along the z-axis of the camera coordinate system.
Rotation around the x-axis of the camera coordinate system.
Rotation around the y-axis of the camera coordinate system.
Rotation around the z-axis of the camera coordinate system.
The pose tuple contains one more element, which is the
representation type of the pose. It codes the combination of the
parameters
, OrderOfTransform
, and
OrderOfRotation
. See ViewOfTransform
for more information
about 3D poses.
create_pose
When using a standard HALCON calibration plate, the world coordinate system is defined by the coordinate system of the calibration plate. See the section “Calibration Object” above for further information.
If a HALCON calibration plate is used, you can use the operator
to determine initial values for all
parameters. Using HALCON calibration plates with rectangularly
arranged marks, a combination of the two operators find_calib_object
and find_caltab
will have the same effect.
find_marks_and_pose
HALCON calibration plates use meters as unit. The camera parameters use corresponding units. Of course, calibration can be done using different units, but in this case the related parameters have to be adapted. Here, we list the HALCON default units for the different camera parameters:
Parameter | Unit | |
---|---|---|
External | RotX, RotY, RotZ | , , |
TransX, TransY, TransZ | , , | |
Internal | Cx, Cy | , |
Focus | ||
ImagePlaneDist | ||
ImageWidth, ImageHeight | , | |
K1, K2, K3 | , , | |
Kappa |