vector_to_poseT_vector_to_poseVectorToPoseVectorToPosevector_to_pose (Operator)

Name

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

Signature

vector_to_pose( : : WorldX, WorldY, WorldZ, ImageRow, ImageColumn, CameraParam, Method, QualityType : Pose, Quality)

Herror T_vector_to_pose(const Htuple WorldX, const Htuple WorldY, const Htuple WorldZ, const Htuple ImageRow, const Htuple ImageColumn, const Htuple CameraParam, const Htuple Method, const Htuple QualityType, Htuple* Pose, Htuple* Quality)

void VectorToPose(const HTuple& WorldX, const HTuple& WorldY, const HTuple& WorldZ, const HTuple& ImageRow, const HTuple& ImageColumn, const HTuple& CameraParam, const HTuple& Method, const HTuple& QualityType, HTuple* Pose, HTuple* Quality)

static HPose HImage::VectorToPose(const HTuple& WorldX, const HTuple& WorldY, const HTuple& WorldZ, const HTuple& ImageRow, const HTuple& ImageColumn, const HCamPar& CameraParam, const HString& Method, const HTuple& QualityType, HTuple* Quality)

static HPose HImage::VectorToPose(const HTuple& WorldX, const HTuple& WorldY, const HTuple& WorldZ, const HTuple& ImageRow, const HTuple& ImageColumn, const HCamPar& CameraParam, const HString& Method, const HString& QualityType, double* Quality)

static HPose HImage::VectorToPose(const HTuple& WorldX, const HTuple& WorldY, const HTuple& WorldZ, const HTuple& ImageRow, const HTuple& ImageColumn, const HCamPar& CameraParam, const char* Method, const char* QualityType, double* Quality)

static HPose HImage::VectorToPose(const HTuple& WorldX, const HTuple& WorldY, const HTuple& WorldZ, const HTuple& ImageRow, const HTuple& ImageColumn, const HCamPar& CameraParam, const wchar_t* Method, const wchar_t* QualityType, double* Quality)   (Windows only)

HPose HCamPar::VectorToPose(const HTuple& WorldX, const HTuple& WorldY, const HTuple& WorldZ, const HTuple& ImageRow, const HTuple& ImageColumn, const HString& Method, const HTuple& QualityType, HTuple* Quality) const

HPose HCamPar::VectorToPose(const HTuple& WorldX, const HTuple& WorldY, const HTuple& WorldZ, const HTuple& ImageRow, const HTuple& ImageColumn, const HString& Method, const HString& QualityType, double* Quality) const

HPose HCamPar::VectorToPose(const HTuple& WorldX, const HTuple& WorldY, const HTuple& WorldZ, const HTuple& ImageRow, const HTuple& ImageColumn, const char* Method, const char* QualityType, double* Quality) const

HPose HCamPar::VectorToPose(const HTuple& WorldX, const HTuple& WorldY, const HTuple& WorldZ, const HTuple& ImageRow, const HTuple& ImageColumn, const wchar_t* Method, const wchar_t* QualityType, double* Quality) const   (Windows only)

HTuple HPose::VectorToPose(const HTuple& WorldX, const HTuple& WorldY, const HTuple& WorldZ, const HTuple& ImageRow, const HTuple& ImageColumn, const HCamPar& CameraParam, const HString& Method, const HTuple& QualityType)

double HPose::VectorToPose(const HTuple& WorldX, const HTuple& WorldY, const HTuple& WorldZ, const HTuple& ImageRow, const HTuple& ImageColumn, const HCamPar& CameraParam, const HString& Method, const HString& QualityType)

double HPose::VectorToPose(const HTuple& WorldX, const HTuple& WorldY, const HTuple& WorldZ, const HTuple& ImageRow, const HTuple& ImageColumn, const HCamPar& CameraParam, const char* Method, const char* QualityType)

double HPose::VectorToPose(const HTuple& WorldX, const HTuple& WorldY, const HTuple& WorldZ, const HTuple& ImageRow, const HTuple& ImageColumn, const HCamPar& CameraParam, const wchar_t* Method, const wchar_t* QualityType)   (Windows only)

static void HOperatorSet.VectorToPose(HTuple worldX, HTuple worldY, HTuple worldZ, HTuple imageRow, HTuple imageColumn, HTuple cameraParam, HTuple method, HTuple qualityType, out HTuple pose, out HTuple quality)

static HPose HImage.VectorToPose(HTuple worldX, HTuple worldY, HTuple worldZ, HTuple imageRow, HTuple imageColumn, HCamPar cameraParam, string method, HTuple qualityType, out HTuple quality)

static HPose HImage.VectorToPose(HTuple worldX, HTuple worldY, HTuple worldZ, HTuple imageRow, HTuple imageColumn, HCamPar cameraParam, string method, string qualityType, out double quality)

HPose HCamPar.VectorToPose(HTuple worldX, HTuple worldY, HTuple worldZ, HTuple imageRow, HTuple imageColumn, string method, HTuple qualityType, out HTuple quality)

HPose HCamPar.VectorToPose(HTuple worldX, HTuple worldY, HTuple worldZ, HTuple imageRow, HTuple imageColumn, string method, string qualityType, out double quality)

HTuple HPose.VectorToPose(HTuple worldX, HTuple worldY, HTuple worldZ, HTuple imageRow, HTuple imageColumn, HCamPar cameraParam, string method, HTuple qualityType)

double HPose.VectorToPose(HTuple worldX, HTuple worldY, HTuple worldZ, HTuple imageRow, HTuple imageColumn, HCamPar cameraParam, string method, string qualityType)

def vector_to_pose(world_x: Sequence[Union[float, int]], world_y: Sequence[Union[float, int]], world_z: Sequence[Union[float, int]], image_row: Sequence[Union[float, int]], image_column: Sequence[Union[float, int]], camera_param: Sequence[Union[float, int, str]], method: str, quality_type: MaybeSequence[str]) -> Tuple[Sequence[Union[float, int]], Sequence[Union[float, int]]]

def vector_to_pose_s(world_x: Sequence[Union[float, int]], world_y: Sequence[Union[float, int]], world_z: Sequence[Union[float, int]], image_row: Sequence[Union[float, int]], image_column: Sequence[Union[float, int]], camera_param: Sequence[Union[float, int, str]], method: str, quality_type: MaybeSequence[str]) -> Tuple[Sequence[Union[float, int]], Union[float, int]]

Description

The operator vector_to_posevector_to_poseVectorToPoseVectorToPoseVectorToPosevector_to_pose computes a pose out of at least three or four (depending on MethodMethodMethodMethodmethodmethod) point correspondences of 3D world coordinates (WorldXWorldXWorldXWorldXworldXworld_x, WorldYWorldYWorldYWorldYworldYworld_y, WorldZWorldZWorldZWorldZworldZworld_z), given in meters, and 2D image coordinates (ImageRowImageRowImageRowImageRowimageRowimage_row, ImageColumnImageColumnImageColumnImageColumnimageColumnimage_column), given in pixels, as well as the internal camera parameters (CameraParamCameraParamCameraParamCameraParamcameraParamcamera_param). Thereby the pose (the external camera parameters) is in the form , 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 MethodMethodMethodMethodmethodmethod, it is possible to choose what kind of algorithm is used for the pose computation.

Methods supported for perspective area scan cameras:

MethodMethodMethodMethodmethodmethod When to use Minimum number of point correspondences
'analytic'"analytic""analytic""analytic""analytic""analytic" [1] Default method for general cases 4
'iterative'"iterative""iterative""iterative""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""planar_analytic""planar_analytic""planar_analytic""planar_analytic" [4] If the world points lie in a horizontal plane ( ) 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:

MethodMethodMethodMethodmethodmethod When to use Minimum number of point correspondences
'telecentric'"telecentric""telecentric""telecentric""telecentric""telecentric" [3] Default method for general cases 4
'telecentric_robust'"telecentric_robust""telecentric_robust""telecentric_robust""telecentric_robust""telecentric_robust" [3] For very ill-posed point configurations where QualityQualityQualityQualityqualityquality has an unlikely large value 4
'telecentric_planar'"telecentric_planar""telecentric_planar""telecentric_planar""telecentric_planar""telecentric_planar" [3] If the world points lie in a horizontal plane ( ) 3
'telecentric_planar_robust'"telecentric_planar_robust""telecentric_planar_robust""telecentric_planar_robust""telecentric_planar_robust""telecentric_planar_robust" [3] For very ill-posed point configurations where the world points lie in a horizontal plane ( ) and QualityQualityQualityQualityqualityquality 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:

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

Parameters CameraParam and Quality

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

The user can specify in QualityTypeQualityTypeQualityTypeQualityTypequalityTypequality_type one or more quality measures of the pose to be evaluated. The resulting quality evaluations are returned concatenated in QualityQualityQualityQualityqualityquality. Currently, only 'error'"error""error""error""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 . Therefore, the z-component of the world coordinates can be left empty (WorldZWorldZWorldZWorldZworldZworld_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 0 in PosePosePosePoseposepose.

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_posevector_to_poseVectorToPoseVectorToPoseVectorToPosevector_to_pose returns an arbitrary solution of the two possible solutions in this case. The other solution can be calculated easily by replacing the values of and in PosePosePosePoseposepose by and .

For perspective line scan cameras, the call to vector_to_posevector_to_poseVectorToPoseVectorToPoseVectorToPosevector_to_pose corresponds to the following operator sequence:
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)GetLineOfSight(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)
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)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)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)
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)PointPlueckerLineToHomMat3d("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)
hom_mat3d_to_pose(HomMat3D, Pose)hom_mat3d_to_pose(HomMat3D, Pose)HomMat3dToPose(HomMat3D, Pose)HomMat3dToPose(HomMat3D, Pose)HomMat3dToPose(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_mat3dpoint_pluecker_line_to_hom_mat3dPointPlueckerLineToHomMat3dPointPlueckerLineToHomMat3dPointPlueckerLineToHomMat3dpoint_pluecker_line_to_hom_mat3d). 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""analytic""analytic""analytic""analytic" only allows a maximum number of 32767 point correspondences.

Execution Information

Parameters

WorldXWorldXWorldXWorldXworldXworld_x (input_control)  number-array HTupleSequence[Union[float, int]]HTupleHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong)

X-Component of world coordinates.

Number of elements: WorldX >= 4

WorldYWorldYWorldYWorldYworldYworld_y (input_control)  number-array HTupleSequence[Union[float, int]]HTupleHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong)

Y-Component of world coordinates.

Number of elements: WorldY == WorldX

WorldZWorldZWorldZWorldZworldZworld_z (input_control)  number-array HTupleSequence[Union[float, int]]HTupleHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong)

Z-Component of world coordinates.

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

ImageRowImageRowImageRowImageRowimageRowimage_row (input_control)  number-array HTupleSequence[Union[float, int]]HTupleHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong)

Row-Component of image coordinates.

Number of elements: ImageRow == WorldX

ImageColumnImageColumnImageColumnImageColumnimageColumnimage_column (input_control)  number-array HTupleSequence[Union[float, int]]HTupleHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong)

Column-Component of image coordinates.

Number of elements: ImageColumn == WorldX

CameraParamCameraParamCameraParamCameraParamcameraParamcamera_param (input_control)  campar HCamPar, HTupleSequence[Union[float, int, str]]HTupleHtuple (real / integer / string) (double / int / long / string) (double / Hlong / HString) (double / Hlong / char*)

The inner camera parameters from camera calibration.

MethodMethodMethodMethodmethodmethod (input_control)  string HTuplestrHTupleHtuple (string) (string) (HString) (char*)

Kind of algorithm

Default value: 'iterative' "iterative" "iterative" "iterative" "iterative" "iterative"

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

QualityTypeQualityTypeQualityTypeQualityTypequalityTypequality_type (input_control)  string(-array) HTupleMaybeSequence[str]HTupleHtuple (string) (string) (HString) (char*)

Type of pose quality to be returned in Quality.

Default value: 'error' "error" "error" "error" "error" "error"

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

PosePosePosePoseposepose (output_control)  pose HPose, HTupleSequence[Union[float, int]]HTupleHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong)

Pose.

QualityQualityQualityQualityqualityquality (output_control)  number(-array) HTupleSequence[Union[float, int]]HTupleHtuple (real / integer) (double / int / long) (double / Hlong) (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_posevector_to_poseVectorToPoseVectorToPoseVectorToPosevector_to_pose returns TRUE if all parameter values are correct.

See also

proj_hom_mat2d_to_poseproj_hom_mat2d_to_poseProjHomMat2dToPoseProjHomMat2dToPoseProjHomMat2dToPoseproj_hom_mat2d_to_pose, vector_to_rel_posevector_to_rel_poseVectorToRelPoseVectorToRelPoseVectorToRelPosevector_to_rel_pose, camera_calibrationcamera_calibrationCameraCalibrationCameraCalibrationCameraCalibrationcamera_calibration

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