ClassesClassesClassesClasses | | | | Operators

calibrate_camerascalibrate_camerasCalibrateCamerascalibrate_camerasCalibrateCamerasCalibrateCameras (Operator)

Name

calibrate_camerascalibrate_camerasCalibrateCamerascalibrate_camerasCalibrateCamerasCalibrateCameras — Determine all camera parameters by a simultaneous minimization process.

Signature

calibrate_cameras( : : CalibDataID : Error)

Herror calibrate_cameras(const Hlong CalibDataID, double* Error)

Herror T_calibrate_cameras(const Htuple CalibDataID, Htuple* Error)

Herror calibrate_cameras(const HTuple& CalibDataID, double* Error)

double HCalibData::CalibrateCameras() const

void CalibrateCameras(const HTuple& CalibDataID, HTuple* Error)

double HCalibData::CalibrateCameras() const

void HOperatorSetX.CalibrateCameras(
[in] VARIANT CalibDataID, [out] VARIANT* Error)

double HCalibDataX.CalibrateCameras()

static void HOperatorSet.CalibrateCameras(HTuple calibDataID, out HTuple error)

double HCalibData.CalibrateCameras()

Description

The operator calibrate_camerascalibrate_camerasCalibrateCamerascalibrate_camerasCalibrateCamerasCalibrateCameras calculates the internal and external camera parameters of a calibration data model specified in CalibDataIDCalibDataIDCalibDataIDCalibDataIDCalibDataIDcalibDataID. 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 ErrorErrorErrorErrorErrorerror (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_camerascalibrate_camerasCalibrateCamerascalibrate_camerasCalibrateCamerasCalibrateCameras, 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 acquisiton 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:

Preparing the calibration input data

Before calling calibrate_camerascalibrate_camerasCalibrateCamerascalibrate_camerasCalibrateCamerasCalibrateCameras, you must create and fill the calibration data model with the following steps:

  1. Create a calibration data model with the operator create_calib_datacreate_calib_dataCreateCalibDatacreate_calib_dataCreateCalibDataCreateCalibData, specifying the number of cameras in the setup and the number of used calibration objects.

  2. Specify the camera type and the initial internal camera parameters for all cameras with the operator set_calib_data_cam_paramset_calib_data_cam_paramSetCalibDataCamParamset_calib_data_cam_paramSetCalibDataCamParamSetCalibDataCamParam. Note that only cameras of the same type can be calibrated in a single setup.

  3. Specify the description of all calibration objects with the operator set_calib_data_calib_objectset_calib_data_calib_objectSetCalibDataCalibObjectset_calib_data_calib_objectSetCalibDataCalibObjectSetCalibDataCalibObject.

  4. Collect observation data with the operators find_calib_objectfind_calib_objectFindCalibObjectfind_calib_objectFindCalibObjectFindCalibObject or set_calib_data_observ_pointsset_calib_data_observ_pointsSetCalibDataObservPointsset_calib_data_observ_pointsSetCalibDataObservPointsSetCalibDataObservPoints, 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.

  5. 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_dataset_calib_dataSetCalibDataset_calib_dataSetCalibDataSetCalibData, 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']).
      

Performing the actual camera calibration

Depending on the camera type being calibrated in the setup, calibrate_camerascalibrate_camerasCalibrateCamerascalibrate_camerasCalibrateCamerasCalibrateCameras performs the calibration in three different ways.

For projective area-scan cameras ('area_scan_division'"area_scan_division""area_scan_division""area_scan_division""area_scan_division""area_scan_division", 'area_scan_polynomial'"area_scan_polynomial""area_scan_polynomial""area_scan_polynomial""area_scan_polynomial""area_scan_polynomial", 'area_scan_tilt_division'"area_scan_tilt_division""area_scan_tilt_division""area_scan_tilt_division""area_scan_tilt_division""area_scan_tilt_division", and 'area_scan_tilt_polynomial'"area_scan_tilt_polynomial""area_scan_tilt_polynomial""area_scan_tilt_polynomial""area_scan_tilt_polynomial""area_scan_tilt_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.

image/svg+xml image/svg+xml
(1) (2)
(1) All cameras can be connected by a chain of observation poses. (2) The leftmost camera is isolated, because the left calibration plate cannot be seen by any other camera.

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_camerascalibrate_camerasCalibrateCamerascalibrate_camerasCalibrateCamerasCalibrateCameras 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_objectfind_calib_objectFindCalibObjectfind_calib_objectFindCalibObjectFindCalibObject). 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_camerascalibrate_camerasCalibrateCamerascalibrate_camerasCalibrateCamerasCalibrateCameras computes the standard deviations and the covariances of the calibrated internal camera parameters.

For telecentric area-scan cameras ('area_scan_telecentric_division'"area_scan_telecentric_division""area_scan_telecentric_division""area_scan_telecentric_division""area_scan_telecentric_division""area_scan_telecentric_division", 'area_scan_telecentric_polynomial'"area_scan_telecentric_polynomial""area_scan_telecentric_polynomial""area_scan_telecentric_polynomial""area_scan_telecentric_polynomial""area_scan_telecentric_polynomial", 'area_scan_telecentric_tilt_division'"area_scan_telecentric_tilt_division""area_scan_telecentric_tilt_division""area_scan_telecentric_tilt_division""area_scan_telecentric_tilt_division""area_scan_telecentric_tilt_division", or 'area_scan_telecentric_tilt_polynomial'"area_scan_telecentric_tilt_polynomial""area_scan_telecentric_tilt_polynomial""area_scan_telecentric_tilt_polynomial""area_scan_telecentric_tilt_polynomial""area_scan_telecentric_tilt_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 line-scan cameras ('line_scan'"line_scan""line_scan""line_scan""line_scan""line_scan"), the operator internally calls camera_calibrationcamera_calibrationCameraCalibrationcamera_calibrationCameraCalibrationCameraCalibration. Therefore, some of the restrictions of camera_calibrationcamera_calibrationCameraCalibrationcamera_calibrationCameraCalibrationCameraCalibration are inherited as well: in addition to the restriction of only one camera and only one calibration object per setup, there is a further restriction that the calibration does not deliver information about standard deviations and covariances for the estimated parameters. Furthermore, for calibration plates with rectangularly arranged marks (see gen_caltabgen_caltabGenCaltabgen_caltabGenCaltabGenCaltab) all observations must contain the projection coordinates of all calibration marks of the calibration object. For calibration plates with hexagonally arranged marks (see create_caltabcreate_caltabCreateCaltabcreate_caltabCreateCaltabCreateCaltab) this restriction is not applied.

Checking the success of the calibration

After a successful calibration, the root mean square error (RMSE) of the back projection of the optimization is returned in ErrorErrorErrorErrorErrorerror (in pixels). The error gives a general indication whether the optimization was successful.

If only a single camera is calibrated, an ErrorErrorErrorErrorErrorerror 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 ErrorErrorErrorErrorErrorerror 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 ErrorErrorErrorErrorErrorerror is more difficult to judge. As a rule of thumb, ErrorErrorErrorErrorErrorerror 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_dataget_calib_dataGetCalibDataget_calib_dataGetCalibDataGetCalibData).

Getting the calibration results

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_dataget_calib_dataGetCalibDataget_calib_dataGetCalibDataGetCalibData. 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.

Camera parameters

The camera parameters can be divided into the internal and external camera parameters.

Internal 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.

Area scan cameras have 8 to 14 internal parameters depending on the camera type.

CameraType CameraParam #
'area_scan_division'"area_scan_division""area_scan_division""area_scan_division""area_scan_division""area_scan_division" [Focus, Kappa, Sx, Sy, Cx, Cy, ImageWidth, ImageHeight] 8
'area_scan_telecentric_division'"area_scan_telecentric_division""area_scan_telecentric_division""area_scan_telecentric_division""area_scan_telecentric_division""area_scan_telecentric_division" [0, Kappa, Sx, Sy, Cx, Cy, ImageWidth, ImageHeight] 8
'area_scan_tilt_division'"area_scan_tilt_division""area_scan_tilt_division""area_scan_tilt_division""area_scan_tilt_division""area_scan_tilt_division" [Focus, Kappa, Tilt, Rot, Sx, Sy, Cx, Cy, ImageWidth, ImageHeight] 10
'area_scan_telecentric_tilt_division'"area_scan_telecentric_tilt_division""area_scan_telecentric_tilt_division""area_scan_telecentric_tilt_division""area_scan_telecentric_tilt_division""area_scan_telecentric_tilt_division" [0, Kappa, Tilt, Rot, Sx, Sy, Cx, Cy, ImageWidth, ImageHeight] 10
'area_scan_polynomial'"area_scan_polynomial""area_scan_polynomial""area_scan_polynomial""area_scan_polynomial""area_scan_polynomial" [Focus, K1, K2, K3, P1, P2, Sx, Sy, Cx, Cy, ImageWidth, ImageHeight] 12
'area_scan_telecentric_polynomial'"area_scan_telecentric_polynomial""area_scan_telecentric_polynomial""area_scan_telecentric_polynomial""area_scan_telecentric_polynomial""area_scan_telecentric_polynomial" [0, K1, K2, K3, P1, P2, Sx, Sy, Cx, Cy, ImageWidth, ImageHeight] 12
'area_scan_tilt_polynomial'"area_scan_tilt_polynomial""area_scan_tilt_polynomial""area_scan_tilt_polynomial""area_scan_tilt_polynomial""area_scan_tilt_polynomial" [Focus, K1, K2, K3, P1, P2, Tilt, Rot, Sx, Sy, Cx, Cy, ImageWidth, ImageHeight] 14
'area_scan_telecentric_tilt_polynomial'"area_scan_telecentric_tilt_polynomial""area_scan_telecentric_tilt_polynomial""area_scan_telecentric_tilt_polynomial""area_scan_telecentric_tilt_polynomial""area_scan_telecentric_tilt_polynomial" [0, K1, K2, K3, P1, P2, Tilt, Rot, Sx, Sy, Cx, Cy, ImageWidth, ImageHeight] 14
'line_scan'"line_scan""line_scan""line_scan""line_scan""line_scan" [Focus, Kappa, Sx, Sy, Cx, Cy, ImageWidth, ImageHeight, Vx, Vy, Vz] 11

Focus:

Focal length of the lens. 0 for telecentric lenses.

The initial value is the nominal focal length of the used lens, e.g., 0.008m

Kappa :

Distortion coefficient to model the radial lens distortions (only for division model).

Use 0.0 as initial value.

K1, K2, K3, P1, P2:

Distortion coefficients to model the radial and decentering lens distortions (only for polynomial model).

Use 0.0 as initial value for all five coefficents.

Tilt, Rot:

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.

image/svg+xml y x z y x z 2. tilt 1. rot
The tilt of the lens is described by the two parameters and . describes the orientation of the tilt axis in relation to the x-axis of the sensor. describes the actual tilt of the lens.

These angels 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.

Sx, Sy:

Scale factors. For pinhole cameras, this corresponds to the horizontal and vertical distance between two neighboring cells on the sensor. For telecentric cameras, this represents the horizontal and vertical size of a pixel in world coordinates (i.e., the distance of the cells on the sensor divided by the magnification of the lens). 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 for pinhole cameras 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!

Cx, Cy:

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!

ImageWidth, Image Height:

Width and height of the sampled image. Attention: These values decrease if the image is subsampled!

Line scan cameras have the following 11 internal parameters:

Focus:

Focal length of the lens.

The initial value is the nominal focal length of the used lens, e.g., 0.008m

Kappa :

Distortion coefficient of the division model to model the radial lens distortions. Use 0.0 as initial value.

Sx:

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!

Sy:

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!

Cx:

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!

Cy:

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.

ImageWidth, Image Height:

Width and height of the sampled image. Attention: These values decrease if the image is subsampled!

Vx, Vy, Vz:

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 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.

Note that for all operators that use camera parameters as input the parameter values are checked as to whether they fullfill the following restrictions:

For some operators the restrictions differ slightly. In particular, for operators that do not support telecentric cameras the following restriction applies:

For operators that do not support line scan cameras the following restriction applies:

External camera parameters:

TransX:

Translation along the x-axis of the camera coordinate system.

TransY:

Translation along the y-axis of the camera coordinate system.

TransZ:

Translation along the z-axis of the camera coordinate system.

RotX:

Rotation around the x-axis of the camera coordinate system.

RotY:

Rotation around the y-axis of the camera coordinate system.

RotZ:

Rotation around the z-axis of the camera coordinate system.

These 6 parameters describe the 3D pose, i.e., the position and orientation of the world coordinate system relative to the camera coordinate system. For line scan cameras, the pose of the world coordinate system refers to the camera coordinate system of the first image line. The three parameters (TransX, TransY and TransZ) describe the translation, the three parameters (RotX, RotY, RotZ) the rotation. See create_posecreate_poseCreatePosecreate_poseCreatePoseCreatePose for more information about 3D poses.

When using a standard HALCON calibration plate, the world coordinate system is defined by the coordinate system of the calibration plate. For calibration plates with hexagonally arranged marks (see create_caltabcreate_caltabCreateCaltabcreate_caltabCreateCaltabCreateCaltab), the origin of the coordinate system is located at the center of the central mark of the first finder pattern. For calibration plates with rectangularly arranged marks gen_caltabgen_caltabGenCaltabgen_caltabGenCaltabGenCaltab the origin is located in the middle of the surface of the calibration plate. In both cases, 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.

If a HALCON calibration plate is used, you can use the operator find_calib_objectfind_calib_objectFindCalibObjectfind_calib_objectFindCalibObjectFindCalibObject to determine initial values for all 6 parameters. Using HALCON calibration plates with rectangularly arranged marks (see gen_caltabgen_caltabGenCaltabgen_caltabGenCaltabGenCaltab), a combination of the two operators find_caltabfind_caltabFindCaltabfind_caltabFindCaltabFindCaltab and find_marks_and_posefind_marks_and_poseFindMarksAndPosefind_marks_and_poseFindMarksAndPoseFindMarksAndPose will have the same effect.

Additional information about the calibration process

The use of calibrate_camerascalibrate_camerasCalibrateCamerascalibrate_camerasCalibrateCamerasCalibrateCameras leads to some questions, which are addressed in the following sections:

How to generate an appropriate calibration plate?

You can obtain high-precision calibration plates in various sizes and materials from your local distributor. These calibration plates come with associated description files and can be easily extracted with find_calib_objectfind_calib_objectFindCalibObjectfind_calib_objectFindCalibObjectFindCalibObject.

It is also possible to use any arbitrary object for calibration. The only requirement is that the object has characteristic points that can be robustly detected in the image and that the 3D world position of these points is known with high accuracy. See the “Solution Guide III-C 3D Vision” for details.

Self-printed calibration objects are usually not accurate enough for high-precision applications.

How to take a set of suitable images?

If you use a HALCON calibration plate, you can proceed in the following way: With the combination of lens (fixed focus setting!), camera, and frame grabber to be calibrated, a set of images of the calibration plate must be taken (see open_framegrabberopen_framegrabberOpenFramegrabberopen_framegrabberOpenFramegrabberOpenFramegrabber and grab_imagegrab_imageGrabImagegrab_imageGrabImageGrabImage). The following items must be considered:

Your local distributor can provide you with two different types of HALCON calibration plates: Calibration plates with hexagonally arranged marks (see create_caltabcreate_caltabCreateCaltabcreate_caltabCreateCaltabCreateCaltab) and calibration plates with rectangularly arranged marks (see gen_caltabgen_caltabGenCaltabgen_caltabGenCaltabGenCaltab). Since these two calibration plates substantially differ from each other, additional particularities have to be considered beside the general advices (see also find_calib_objectfind_calib_objectFindCalibObjectfind_calib_objectFindCalibObjectFindCalibObject):

HALCON calibration plates with hexagonally arranged marks

HALCON calibration plates with rectangularly arranged marks

Which distortion model should be used?

For area scan cameras, two distortion models can be used: The division model and the polynomial model. The division model uses one parameter to model the radial distortions while the polynomial model uses five parameters to model radial and decentering distortions (see section “Camera parameters”).

The advantages of the division model are that the distortions can be applied faster, especially the inverse distortions, i.e., if world coordinates are projected into the image plane. Furthermore, if only few calibration images are used or if the field of view is not covered sufficiently, the division model typically yields more stable results than the polynomial model. The main advantage of the polynomial model is that it can model the distortions more accurately because it uses higher order terms to model the radial distortions and because it also models the decentering distortions. Note that the polynomial model cannot be inverted analytically. Therefore, the inverse distortions must be calculated iteratively, which is slower than the calculation of the inverse distortions with the (analytically invertible) division model.

Typically, the division model should be used for the calibration. If the accuracy of the calibration is not high enough, the polynomial model can be used. Note, however, that the calibration sequence used for the polynomial model must provide an even better coverage of the area in which measurements will later be performed. The distortions may be modeled inaccurately outside of the area that was covered by the calibration plate. This holds for the image border as well as for areas inside the field of view that were not covered by the calibration plate.

Used 3D camera model

In general, camera calibration means the exact determination of the parameters that model the (optical) projection of any 3D world point into a (sub-)pixel (r,c) in the image. This is important if the original 3D pose of an object must be computed from the image (e.g., measuring of industrial parts).

To transform a 3D point which is given in world coordinates, into a 2D point , which is given in pixel coordinates, a chain of transformations is needed:

First, is transformed into the camera coordinate system into . Then, is projected into the image plane, i.e., converted to the 2D point , still in metric coordinates. Then, lens distortion is applied to , transforming it into the distorted point . If a tilt lens is used, only lies on a virtual image plane of a system without tilt. This is corrected by projecting to the point on the tilted image plane. Finally, the coordinates of the distorted point (or ) are converted to pixel coordinates, which results in the final point .

The following describes these steps in more detail:

The point is transformed from world into camera coordinates by (points as homogeneous vectors, compare affine_trans_point_3daffine_trans_point_3dAffineTransPoint3daffine_trans_point_3dAffineTransPoint3dAffineTransPoint3d):

Then, the point is projected into the image plane, i.e., onto the sensor chip.

For the modeling of this projection process, which is determined by the used combination of camera, lens, and frame grabber, HALCON provides the following three 3D camera models:

Area scan pinhole camera:

The combination of an area scan camera with a lens that effects a perspective projection and that may show radial and decentering distortions. The lens may be a tilt lens, i.e., the optical axis of the lens may be tilted with respect to the camera's sensor (this is sometimes called a Scheimpflug lens).

Area scan telecentric camera:

The combination of an area scan camera with a telecentric lens that effects a parallel projection and that may show radial and decentering distortions. The lens may be a tilt lens. In this case, the lens must be bilaterally telecentric.

Line scan pinhole camera:

The combination of a line scan camera with a lens that effects a perspective projection and that may show radial distortions. Tilt lenses are currently not supported for line scan cameras.

If the underlying camera model is an area scan pinhole camera, the projection of into the image plane is described by the following equation:

If an area scan telecentric camera is used, the corresponding equation is:

For both types of area scan cameras, the lens distortions can be modeled either by the division model or by the polynomial model.

The division model uses one parameter ( ) to model the radial distortions.

The following equations transform the distorted image plane coordinates into undistorted image plane coordinates if the division model is used:

These equations can be inverted analytically, which leads to the following equations that transform undistorted coordinates into distorted coordinates:

The polynomial model uses three parameters ( ) to model the radial distortions and two parameters ( ) to model the decentering distortions.

The following equations transform the distorted image plane coordinates into undistorted image plane coordinates if the polynomial model is used:

with

These equations cannot be inverted analytically. Therefore, distorted image plane coordinates must be calculated from undistorted image plane coordinates numerically.

If the lens is a tilt lens, the tilt of the lens with respect to the image plane is described by two parameters: The rotation angle , which describes the direction of the tilt axis, and the tilt angle , by which the sensor plane is tilted with respect to the optical axis.

If the sensor is used as the reference, corresponds to the optical axis being tilted vertically down with respect to the sensor, corresponds to the optical axis being tilted horizontally to the left, corresponds to the optical axis being tilted vertically up, and corresponds to the optical axis being tilted horizontally to the right.

For projective tilt lenses, the projection of into the point , which lies in the tilted image plane, is described by a projective 2D transformation, i.e., by the homogeneous 3×3 matrix (see projective_trans_point_2dprojective_trans_point_2dProjectiveTransPoint2dprojective_trans_point_2dProjectiveTransPoint2dProjectiveTransPoint2d):

where
with
with and .

For telecentric tilt lenses, the projection onto the tilted image plane is described by a linear 2D transformation, i.e., by a 2×2 matrix:

where is defined as above for projective lenses.

Finally, the point (or if a tilt lens is present) is transformed from the image plane coordinate system into the image coordinate system (the pixel coordinate system):

For line scan cameras, also the relative motion between the camera and the object must be modeled. In HALCON, the following assumptions for this motion are made:

  1. The camera moves with constant velocity along a straight line.

  2. The orientation of the camera is constant.

  3. The motion is equal for all images.

The motion is described by the motion vector that must be given in [meter/scanline] in the camera coordinate system. The motion vector describes the motion of the camera, assuming a fixed object. In fact, this is equivalent to the assumption of a fixed camera with the object traveling along -V.

The camera coordinate system of line scan cameras is defined as follows: The origin of the coordinate system is the center of projection. The z-axis is identical to the optical axis and directed so that the visible points have positive z coordinates. The y-axis is perpendicular to the sensor line and to the z-axis. It is directed so that the motion vector has a positive y-component. The x-axis is perpendicular to the y- and z-axis, so that the x-, y-, and z-axis form a right-handed coordinate system.

As the camera moves over the object during the image acquisition, also the camera coordinate system moves relatively to the object, i.e., each image line has been imaged from a different position. This means there would be an individual pose for each image line. To make things easier, in HALCON all transformations from world coordinates into camera coordinates and vice versa are based on the pose of the first image line only. The motion V is taken into account during the projection of the point into the image. Consequently, only the pose of the first image line is computed by the operator find_calib_objectfind_calib_objectFindCalibObjectfind_calib_objectFindCalibObjectFindCalibObject (and stored by calibrate_camerascalibrate_camerasCalibrateCamerascalibrate_camerasCalibrateCamerasCalibrateCameras in the calibration results).

For line scan pinhole cameras, the projection of the point that is given in the camera coordinate system into (sub-)pixel coordinates (r,c) in the image is defined as follows:

Assuming

the following set of equations must be solved for m, , and t:
with

This already includes the compensation for radial distortions. Note that for line scan cameras, only the division model for radial distortions can be used.

Finally, the point is transformed into the image coordinate system, i.e., the pixel coordinate system:

Limitations

For pinhole cameras, it is impossible to determine Focus, , and simultaneously. Therefore, the algorithm will keep fixed.

In addition, if the calibration plates are parallel to each other in all images (in particular, if they all lie in the same plane), it is impossible to determine Focus together with all six of the external camera parameters. For example, it is impossible to determine Focus and the distance of the calibration plates to the camera in this case. To be able to calibrate all camera parameters uniquely, make sure that you acquire images of the calibration plate tilted in different orientations.

For telecentric lenses, the distance of the calibration plate from the camera cannot be determined. Therefore, the z-component of the resulting calibration plate pose is set to 1 in the calibration results.

For tilt lenses the greater the lens distortion is, the more accurately the tilt can be determined. For lenses with small distortions, the tilt cannot be determined robustly. Therefore, the optimized tilt parameters may differ significantly from the nominal tilt parameters of the setup. If this is the case, please check ErrorErrorErrorErrorErrorerror. If ErrorErrorErrorErrorErrorerror is small, the resulting camera parameters describe the imaging geometry consistently within the calibrated volume and can be used for accurate measurements.

The decentering (also called tangential) distortion parameters P1 and P2 of the polynomial model are capable of modeling tilt lenses to some extent. Conversely, the tilt parameters are capable of modeling P1 and P2 to some extent. Therefore, when using the polynomial model, it can happen that some of the tilt is modeled by P1 and P2 and some of the tilt by and . In this case, the resulting tilt parameters may deviate from the nominal values of the setup. Again, if ErrorErrorErrorErrorErrorerror is small, the optimized camera parameters describe the imaging geometry consistently and can be used. If it is important to obtain the actual values of the tilt parameters with the polynomial model, the parameters P1 and P2 should be excluded from the optimization by calling

   set_calib_data (CalibDataID, 'camera', 'general', \
                   'excluded_settings', 'poly_tan_2').

Additionally, note that for tilt lenses it is only possible to determine and simultaneously. This is an implementation choice that makes the optimization numerically more robust. Consequently, the parameters and are excluded simultaneously from the optimization by calling

   set_calib_data (CalibDataID, 'camera', 'general', \
                   'excluded_settings', 'tilt').

For telecentric tilt lenses, it is impossible to determine , , and the tilt parameters and simultaneously. Here, the calibration only determines an overall pixel scaling factor. The aspect ratio of the sensor's pixels given by the starting values of the camera parameters specified with set_calib_data_cam_paramset_calib_data_cam_paramSetCalibDataCamParamset_calib_data_cam_paramSetCalibDataCamParamSetCalibDataCamParam remains unchanged. This ensures that the optimized tilt parameters have meaningful values.

Pinhole cameras with tilt lenses with large focal lengths have nearly telecentric projection characteristics. Therefore, as described in the previous paragraph, and the tilt parameters and are correlated and can only be determined imprecisely simultaneously. In this case, it is advisable to exclude from the optimization by calling

   set_calib_data (CalibDataID, 'camera', 'general', \
                   'excluded_settings', 'sx').

For telecentric lenses, there are always two poses of a calibration plate whose image is identical. Therefore, it is not possible to decide which one of the two poses is actually present in the image. This ambiguity also effects the tilt parameters and of a telecentric tilt lens. Consequently, depending on the initial parameters for and the camera calibration may return the alternative parameters instead of the nominal ones. If this is the case, please check ErrorErrorErrorErrorErrorerror. If ErrorErrorErrorErrorErrorerror is small, the resulting camera parameters describe the imaging geometry consistently within the calibrated volume and can be used for accurate measurements.

Finally, for line scan cameras, it is impossible to determine and Focus simultaneously. Furthermore, it is impossible to determine and simultaneously. Therefore, and are not optimized.

Parallelization

This operator modifies the state of the following input parameter:

The value of this parameter may not be shared across multiple threads without external synchronization.

Parameters

CalibDataIDCalibDataIDCalibDataIDCalibDataIDCalibDataIDcalibDataID (input_control, state is modified)  calib_data HCalibData, HTupleHTupleHCalibData, HTupleHCalibDataX, VARIANTHtuple (integer) (IntPtr) (Hlong) (Hlong) (Hlong) (Hlong)

Handle of a calibration data model.

ErrorErrorErrorErrorErrorerror (output_control)  number HTupleHTupleHTupleVARIANTHtuple (real) (double) (double) (double) (double) (double)

Back projection root mean square error (RMSE) of the optimization.

Possible Predecessors

create_calib_datacreate_calib_dataCreateCalibDatacreate_calib_dataCreateCalibDataCreateCalibData, set_calib_data_cam_paramset_calib_data_cam_paramSetCalibDataCamParamset_calib_data_cam_paramSetCalibDataCamParamSetCalibDataCamParam, set_calib_data_calib_objectset_calib_data_calib_objectSetCalibDataCalibObjectset_calib_data_calib_objectSetCalibDataCalibObjectSetCalibDataCalibObject, set_calib_data_observ_pointsset_calib_data_observ_pointsSetCalibDataObservPointsset_calib_data_observ_pointsSetCalibDataObservPointsSetCalibDataObservPoints, find_calib_objectfind_calib_objectFindCalibObjectfind_calib_objectFindCalibObjectFindCalibObject, set_calib_dataset_calib_dataSetCalibDataset_calib_dataSetCalibDataSetCalibData, remove_calib_data_observremove_calib_data_observRemoveCalibDataObservremove_calib_data_observRemoveCalibDataObservRemoveCalibDataObserv

Possible Successors

get_calib_dataget_calib_dataGetCalibDataget_calib_dataGetCalibDataGetCalibData

References

J. Heikillä: “Geometric Camera Calibration Using Circular Control Points”; PAMI-22, no. 6; pp. 1066-1077; 2000.

Module

Calibration


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