vector_to_poseVectorToPoseVectorToPosevector_to_poseT_vector_to_pose🔗

Short description🔗

vector_to_poseVectorToPoseVectorToPosevector_to_poseT_vector_to_pose — Compute an absolute pose out of point correspondences between world and image coordinates.

Signature🔗

vector_to_pose( number WorldX, number WorldY, number WorldZ, number ImageRow, number ImageColumn, campar CameraParam, string Method, string QualityType, out pose Pose, out number Quality )

Description🔗

The operator vector_to_poseVectorToPose computes a pose out of at least three or four (depending on Methodmethodmethod) point correspondences of 3D world coordinates (WorldXworldXworld_x, WorldYworldYworld_y, WorldZworldZworld_z), given in meters, and 2D image coordinates (ImageRowimageRowimage_row, ImageColumnimageColumnimage_column), given in pixels, as well as the internal camera parameters (CameraParamcameraParamcamera_param). Thereby the pose (the external camera parameters) is in the form \(\mvPoseVar{{ccs}}{wcs}\), where ccs denotes the camera coordinate system and wcs the world coordinate system (see Transformations / Poses and “Solution Guide III-C - 3D Vision”).

Parameter Method🔗

By setting the parameter Methodmethodmethod, it is possible to choose what kind of algorithm is used for the pose computation.

Methods supported for perspective area scan cameras:

`Methodmethodmethod`	When to use	Minimum number of point correspondences
'analytic'"analytic" [1]	Default method for general cases	4
'iterative'"iterative" [2]	If only three or four point correspondences are used or if the world points are close to being planar	3
'planar_analytic'"planar_analytic" [4]	If the world points lie in a horizontal plane (\(\textrm{WorldZ} = 0\))	4

The numbers in square brackets in the table above refer to the publications the implementations of the corresponding methods are based on.

Methods supported for telecentric area or line scan cameras:

`Methodmethodmethod`	When to use	Minimum number of point correspondences
'telecentric'"telecentric" [3]	Default method for general cases	4
'telecentric_robust'"telecentric_robust" [3]	For very ill-posed point configurations where `Qualityqualityquality` has an unlikely large value	4
'telecentric_planar'"telecentric_planar" [3]	If the world points lie in a horizontal plane (\(\textrm{WorldZ} = 0\))	3
'telecentric_planar_robust'"telecentric_planar_robust" [3]	For very ill-posed point configurations where the world points lie in a horizontal plane (\(\textrm{WorldZ} = 0\)) and `Qualityqualityquality` has an unlikely large value	3

The numbers in square brackets in the table above refer to the publications the implementations of the corresponding methods are based on.

Methods supported for perspective line scan cameras:

`Methodmethodmethod`	When to use	Minimum number of point correspondences
'line_scan'"line_scan"	Default method for general cases	3

Parameters CameraParam and Quality🔗

All methods need the inner camera parameters obtained from camera_calibrationCameraCalibration to solve the pose estimation problem. They must be passed in CameraParamcameraParamcamera_param.

The user can specify in QualityTypequalityTypequality_type one or more quality measures of the pose to be evaluated. The resulting quality evaluations are returned concatenated in Qualityqualityquality. Currently, only 'error'"error" is supported. It corresponds to the root-mean-square error in pixels of the projected 3D world coordinates.

General Remarks🔗

If a method for planar world points is chosen, all world points are assumed to lie in the plane \(\textrm{WorldZ} = 0\). Therefore, the z-component of the world coordinates can be left empty (WorldZworldZworld_z = [][]) since only 2D correspondences are used in this case.

For telecentric cameras, the translation in z obviously cannot be determined. It is set to 00 in Poseposepose.

For planar world points and telecentric cameras, there are always two possible equivalent poses. This ambiguity can only be resolved by some additional knowledge. vector_to_poseVectorToPose returns an arbitrary solution of the two possible solutions in this case. The other solution can be calculated easily by replacing the values of \(\alpha\) and \(\beta\) in Poseposepose by \(360-\alpha\) and \(360-\beta\).

For perspective line scan cameras, the call to vector_to_poseVectorToPose corresponds to the following operator sequence:


`get_line_of_sight(ImageRow, ImageColumn, CameraParam, PX, PY, PZ, QX, QY, QZ)GetLineOfSight(ImageRow, ImageColumn, CameraParam, PX, PY, PZ, QX, QY, QZ)GetLineOfSight(ImageRow, ImageColumn, CameraParam, PX, PY, PZ, QX, QY, QZ)get_line_of_sight(ImageRow, ImageColumn, CameraParam, PX, PY, PZ, QX, QY, QZ)get_line_of_sight(ImageRow, ImageColumn, CameraParam, PX, PY, PZ, QX, QY, QZ)`
`points_to_pluecker_line(PX, PY, PZ, QX, QY, QZ, LX, LY, LZ, MX, MY, MZ)PointsToPlueckerLine(PX, PY, PZ, QX, QY, QZ, LX, LY, LZ, MX, MY, MZ)PointsToPlueckerLine(PX, PY, PZ, QX, QY, QZ, LX, LY, LZ, MX, MY, MZ)points_to_pluecker_line(PX, PY, PZ, QX, QY, QZ, LX, LY, LZ, MX, MY, MZ)points_to_pluecker_line(PX, PY, PZ, QX, QY, QZ, LX, LY, LZ, MX, MY, MZ)`
point_pluecker_line_to_hom_mat3d('rigid', WorldX, WorldY, WorldZ, LX, LY, LZ, MX, MY, MZ, HomMat3D)PointPlueckerLineToHomMat3d("rigid", WorldX, WorldY, WorldZ, LX, LY, LZ, MX, MY, MZ, HomMat3D)PointPlueckerLineToHomMat3d("rigid", WorldX, WorldY, WorldZ, LX, LY, LZ, MX, MY, MZ, HomMat3D)point_pluecker_line_to_hom_mat3d("rigid", WorldX, WorldY, WorldZ, LX, LY, LZ, MX, MY, MZ, HomMat3D)point_pluecker_line_to_hom_mat3d("rigid", WorldX, WorldY, WorldZ, LX, LY, LZ, MX, MY, MZ, HomMat3D)
`hom_mat3d_to_pose(HomMat3D, Pose)HomMat3dToPose(HomMat3D, Pose)HomMat3dToPose(HomMat3D, Pose)hom_mat3d_to_pose(HomMat3D, Pose)hom_mat3d_to_pose(HomMat3D, Pose)`

In contrast to the methods for other camera types, an error in 3D space is minimized in this case (see point_pluecker_line_to_hom_mat3dPointPlueckerLineToHomMat3d). However, like for all other methods, the quality evaluation is performed in pixels. If it is essential that a pixel error is optimized, this can be done as shown in the example below.

Attention🔗

The method 'analytic'"analytic" only allows a maximum number of 32767 point correspondences.

Execution information🔗

Execution information

Multithreading type: reentrant (runs in parallel with non-exclusive operators).
Multithreading scope: global (may be called from any thread).
Processed without parallelization.

Parameters🔗

WorldXworldXworld_x (input_control) number-array → (real / integer)HTuple (double / Hlong)HTuple (double / int / long)Sequence[Union[float, int]]Htuple (double / Hlong)

X-Component of world coordinates.

Number of elements: WorldX >= 4

WorldYworldYworld_y (input_control) number-array → (real / integer)HTuple (double / Hlong)HTuple (double / int / long)Sequence[Union[float, int]]Htuple (double / Hlong)

Y-Component of world coordinates.

Number of elements: WorldY == WorldX

WorldZworldZworld_z (input_control) number-array → (real / integer)HTuple (double / Hlong)HTuple (double / int / long)Sequence[Union[float, int]]Htuple (double / Hlong)

Z-Component of world coordinates.

Number of elements: WorldZ == WorldX || WorldZ == 0

ImageRowimageRowimage_row (input_control) number-array → (real / integer)HTuple (double / Hlong)HTuple (double / int / long)Sequence[Union[float, int]]Htuple (double / Hlong)

Row-Component of image coordinates.

Number of elements: ImageRow == WorldX

ImageColumnimageColumnimage_column (input_control) number-array → (real / integer)HTuple (double / Hlong)HTuple (double / int / long)Sequence[Union[float, int]]Htuple (double / Hlong)

Column-Component of image coordinates.

Number of elements: ImageColumn == WorldX

CameraParamcameraParamcamera_param (input_control) campar → (real / integer / string)HTuple (double / Hlong / HString)Sequence[Union[float, int, str]]Htuple (double / Hlong / char*)

The inner camera parameters from camera calibration.

Methodmethodmethod (input_control) string → (string)HTuple (HString)HTuple (string)strHtuple (char*)

Kind of algorithm

Default: 'iterative'"iterative"
List of values: 'analytic', 'iterative', 'line_scan', 'planar_analytic', 'telecentric', 'telecentric_planar', 'telecentric_planar_robust', 'telecentric_robust'

QualityTypequalityTypequality_type (input_control) string(-array) → (string)HTuple (HString)HTuple (string)MaybeSequence[str]Htuple (char*)

Type of pose quality to be returned in Quality.

Default: 'error'"error"
List of values: 'error'"error"

Poseposepose (output_control) pose → (real / integer)HTuple (double / Hlong)HPose, HTuple (double / int / long)Sequence[Union[float, int]]Htuple (double / Hlong)

Pose.

Qualityqualityquality (output_control) number(-array) → (real / integer)HTuple (double / Hlong)HTuple (double / int / long)Sequence[Union[float, int]]Htuple (double / Hlong)

Pose quality.

Example🔗

(HDevelop)

* Optimize the pixel error line scan cameras. We assume that the
* point correspondences (Row, Col) - (PX, PY, PZ) have already been
* computed and the internal camera parameters CamParam have already
* been calibrated.
vector_to_pose (PX, PY, PZ, Row, Col, CamParam, 'line_scan', \
                'error', PoseObjectSpace, RMS)
* Use PoseObjectSpace as the starting value for a camera calibration
* that only optimizes the pose.
create_calib_data ('calibration_object', 1, 1, CalibDataID)
set_calib_data_cam_param (CalibDataID, 0, [], CamParam)
set_calib_data_calib_object (CalibDataID, 0, [PX, PY, PZ])
set_calib_data (CalibDataID, 'camera', 0, \
                'excluded_settings', 'params')
set_calib_data_observ_points (CalibDataID, 0, 0, 0, Row, Col, \
                              'all', PoseObjectSpace)
calibrate_cameras (CalibDataID, Error)
get_calib_data (CalibDataID, 'calib_obj_pose', [0, 0], 'pose', Pose)
clear_calib_data (CalibDataID)
* As an alternative, the following one-line code can be used.
camera_calibration (PX, PY, PZ, Row, Col, CamParam, PoseObjectSpace, \
                    'pose', _, Pose, Error)

Result🔗

vector_to_poseVectorToPose returns 2 (H_MSG_TRUE) if all parameter values are correct.

Combinations with other operators🔗

Combinations

References🔗

[1] Francesc Moreno-Noguer, Vincent Lepetit, and Pascal Fua: “Accurate Non-Iterative O(n) Solution to the PnP Problem”; Eleventh IEEE International Conference on Computer Vision, 2007.

[2] Gerald Schweighofer, and Axel Pinz: ``Robust Pose Estimation from a Planar Target’‘; Transactions on Pattern Analysis and Machine Intelligence (PAMI), 28(12):2024-2030, 2006.

[3] Carsten Steger: “Algorithms for the Orthographic-n-Point Problem”; Journal of Mathematical Imaging and Vision, vol. 60, no. 2, pp. 246-266, 2018.

[4] Zhengyou Zhang: “A flexible new technique for camera calibration.”; Transactions on Pattern Analysis and Machine Intelligence (PAMI), 22(11):1330-1334, 2000.

Module🔗

Calibration