| Operators |
calibrate_cameras — Determine all camera parameters by a simultaneous minimization process.
calibrate_cameras( : : CalibDataID : Error)
The operator calibrate_cameras calculates the internal and external camera parameters of a calibration data model specified in CalibDataID. For a detailed description of the camera parameters, see section “Camera parameters”.
The calibration data model describes a setup of one or more cameras and is specified during the creation of the data model. See section “Preparing the calibration input data” for details.
The root mean square error (RMSE) of the back projection of the optimization is returned in Error (in pixels). The error gives a general indication whether the optimization was successful. See section “Checking the success of the calibration” for details.
For a successful calibration, at least one calibration object with accurately known metric properties is needed, e.g., a HALCON calibration plate. Before calling calibrate_cameras, take a series of images of the calibration object in different orientations and make sure that the whole field of view or measurement volume is covered. 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 details.
In the following, the calibration process is explained in detail:
Before calling calibrate_cameras, you must create and fill the calibration data model with the following steps:
Create a calibration data model with the operator create_calib_data, specifying the number of cameras in the setup and the number of used calibration objects.
Specify the camera type and the initial internal camera parameters for all cameras with the operator set_calib_data_cam_param. Note that only cameras of the same type can be calibrated in a single setup.
Specify the description of all calibration objects with the operator set_calib_data_calib_object.
Collect observation data with the operators find_calib_object or set_calib_data_observ_points, i.e., 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.
Configure the calibration process, e.g., specify the reference camera or exclude certain internal or external camera parameters from the optimization. With the operator set_calib_data, you can specify parameters for the complete setup or configure parameters of individual cameras or calibration object poses in the setup. For example, if the image sensor cell size of camera 0 is known precisely and only the rest of the parameters need to be calibrated, you call
set_calib_data (CalibDataID, 'camera', 0, \
'excluded_settings', ['sx','sy']).
The calibration performed by calibrate_cameras depends on the camera types that are involved in the calibration setup.
For a setup with projective area-scan cameras ('area_scan_division', 'area_scan_polynomial', 'area_scan_tilt_division', 'area_scan_tilt_polynomial', 'area_scan_tilt_image_side_telecentric_division', 'area_scan_tilt_image_side_telecentric_polynomial', 'area_scan_hypercentric_division', and 'area_scan_hypercentric_polynomial'), the calibration is performed in four steps. First, the algorithm tries to build a chain of observation poses that connects all cameras and calibration object poses to the reference camera.
| (1) | (2) |
If there is a camera that cannot be reached (i.e., it is not observing any calibration object pose that can be connected in the chain), the calibration process is terminated with an error. Otherwise, the algorithm initializes all calibration items' poses by going down this chain. In the second step, calibrate_cameras performs the actual optimization for all optimization parameters that where not explicitly excluded from the calibration. Based on the so-far calibrated cameras, in the third step the algorithm corrects all observations that contain mark contour information (see find_calib_object). Then, the calibration setup is optimized anew for the corrections to take effect. If no contour information was available, this step is skipped. In the last step, calibrate_cameras computes the standard deviations and the covariances of the calibrated internal camera parameters.
For a setup with telecentric area-scan cameras ('area_scan_telecentric_division', 'area_scan_telecentric_polynomial', 'area_scan_tilt_bilateral_telecentric_division', 'area_scan_tilt_bilateral_telecentric_polynomial', 'area_scan_tilt_object_side_telecentric_division', or 'area_scan_tilt_object_side_telecentric_polynomial'), the same four steps are executed as for projective area-scan cameras. In the first step (building a chain of observation poses that connects all cameras and calibration objects), additional conditions must hold. Since the pose of an object can only be determined up to a translation along the optical axis, each calibration object must be observed by at least two cameras to determine its relative location. Otherwise, its pose is excluded from the calibration. Also, since a planar calibration object appears the same from two different observation angles, the relative pose of the cameras among each other cannot be determined unambiguously. There are always two valid alternative relative poses. Note that both alternatives result in a consistent camera setup which can be used for measuring. Since the ambiguity cannot be resolved, the first of the alternatives is returned. Note also that, if the returned pose is not the real pose but the alternative one, then this will result in a mirrored reconstruction.
For a mixed setup with projective and telecentric area-scan cameras, the algorithm performs the same four steps as for a setup with projective area-scan cameras. Possible ambiguities during the first step (building a chain of observation poses that connects all cameras and calibration objects), as described above for the setup with telecentric cameras, can be resolved as long as there exists a chain of observation poses consisting of all perspective cameras and a sufficient number of calibration objects. Here, sufficient number means that each telecentric camera observes at least two calibration objects of this chain.
| (1) | (2) |
For a setup with line-scan cameras ('line_scan'), some restrictions exist: First, only one camera can be calibrated and only one calibration object per setup can be used. Furthermore, the calibration does not deliver information about standard deviations and covariances for the estimated parameters. Finally, for calibration plates with rectangularly arranged marks (see gen_caltab) all observations must contain the projection coordinates of all calibration marks of the calibration object. For calibration plates with hexagonally arranged marks (see create_caltab) this restriction is not applied.
After a successful calibration, the root mean square error (RMSE) of the back projection of the optimization is returned in Error (in pixels). The error gives a general indication whether the optimization was successful.
If only a single camera is calibrated, an Error 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. If more than one camera is calibrated simultaneously, the value of Error is more difficult to judge. As a rule of thumb, Error should be as small as possible and at least smaller than 1.0, thus indicating that a subpixel precise evaluation of the data is possible with the calibrated parameters. This value might be difficult to reach in particular configurations. For further analysis of the quality of the calibration, refer to the standard deviations and covariances of the estimated parameters (currently for area-scan cameras only, see get_calib_data).
The results of the calibration, i.e., internal camera parameters, camera poses (external camera parameters), calibration objects poses etc., can be queried with get_calib_data. The poses of telecentric cameras can only be determined up to a displacement along the z-axis of the coordinate system of the respective camera. Therefore, all camera poses are moved along this axis until they all lie on a common sphere. The center of the sphere is defined by the pose of the first calibration object. The radius of the sphere depends on the calibration setup. If projective and telecentric area-scan cameras are calibrated, the radius is the maximum over all distances from the perspective cameras to the first calibration object. Otherwise, if only telecentric area-scan cameras are considered, the radius is equal to 1m.
The camera parameters can be divided into the 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 area-scan cameras” refers to the property that the lens performs a perspetive projection on the object-side of the lens, while “telecentric area-scan 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.
Area-scan cameras with regular lenses
Projective area-scan cameras
['area_scan_division', Focus, Kappa, Sx, Sy*, Cx, Cy, ImageWidth, ImageHeight]
['area_scan_polynomial', Focus, K1, K2, K3, P1, P2, Sx, Sy*, Cx, Cy, ImageWidth, ImageHeight]
Telecentric area-scan cameras
['area_scan_telecentric_division', Magnification, Kappa, Sx, Sy*, Cx, Cy, ImageWidth, ImageHeight]
['area_scan_telecentric_polynomial', Magnification, K1, K2, K3, P1, P2, Sx, Sy*, Cx, Cy, ImageWidth, ImageHeight]
Area-scan cameras with tilt lenses
Projective area-scan cameras
['area_scan_tilt_division', Focus, Kappa, ImagePlaneDist, Tilt, Rot, Sx, Sy*, Cx, Cy, ImageWidth, ImageHeight]
['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', Focus, Kappa, Tilt, Rot, Sx*, Sy*, Cx, Cy, ImageWidth, ImageHeight]
['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
['area_scan_tilt_bilateral_telecentric_division', Magnification, Kappa, Tilt, Rot, Sx*, Sy*, Cx, Cy, ImageWidth, ImageHeight]
['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', Magnification, Kappa, ImagePlaneDist, Tilt, Rot, Sx, Sy*, Cx, Cy, ImageWidth, ImageHeight]
['area_scan_tilt_object_side_telecentric_polynomial', Magnification, K1, K2, K3, P1, P2, ImagePlaneDist, Tilt, Rot, Sx, Sy*, Cx, Cy, ImageWidth, ImageHeight]
Area-scan cameras with hypercentric lenses
Projective area-scan cameras with hypercentric lenses
['area_scan_hypercentric_division', Focus, Kappa, Sx, Sy*, Cx, Cy, ImageWidth, ImageHeight]
['area_scan_hypercentric_polynomial', Focus, K1, K2, K3, P1, P2, Sx, Sy*, Cx, Cy, ImageWidth, ImageHeight]
For reasons explained below, parameters that are marked with an * asterisk are fixed and not estimated by the algorithm.
Description of the internal camera parameters:
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. The rotation angle describes the direction in which the optical axis is tilted. 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. This corresponds 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!
For pinhole cameras, it is impossible to determine Focus, , and simultaneously. Therefore, the algorithm will keep fixed. For telecentric lenses, it is impossible to determine Magnification, , and simultaneously. Therefore, the algorithm will keep fixed. For image-side telecentric tilt lenses, it is impossible to determine Focus, , , and the tilt parameters and simultaneously. Therefore, the algorithm will additionally keep fixed. For bilateral telecentric tilt lenses, it is impossible to determine Magnification, , , and the tilt parameters and simultaneously. Therefore, the algorithm will additionally 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!
Line scan cameras have the following 12 internal parameters: ['line_scan', Focus, Kappa, Sx*, Sy*, Cx, Cy, ImageWidth, ImageHeight, Vx, Vy, Vz]
* For reasons explained below, 'Sx' und 'Sy' are fixed and not estimated by the algorithm.
'line_scan'
Focal length of the lens.
The initial value is the nominal focal length of the used lens, e.g., 0.008m
Distortion coefficient of the division model to model the radial lens distortions. Use 0.0 as initial value.
Scale factor. Corresponds to the horizontal distance between two neighboring cells on the sensor. Note that Focus 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). The initial value for is the half image width. 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
l[m] = Length of the object in object coordinates [meter]
l[row] = Length of the object in image coordinates [rows]
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: