get_rectangle_pose — Determine the 3D pose of a rectangle from its perspective 2D projection
A rectangle in space is projected as a general quadrangle into the image. get_rectangle_pose determines the Pose of the rectangle from this projection (Contour).
The algorithm works as follows: First, Contour is segmented into four line segments and their intersections are considered as corners of the contour. The corners together with the internal camera parameters (CameraParam) and the rectangle size in meters (Width, Height) are used for an initial estimation of the rectangle pose. Then, the final Pose is refined with a non-linear optimization by minimizing the geometrical distance of the contour points from the back projection of the rectangle in the image.
The operator supports only area-scan pinhole (projective) cameras. An error is returned if CameraParam specifies a line-scan or a telecentric camera (see also calibrate_cameras).
Width and Height specify the size of the rectangle in x and y dimensions, respectively, in its coordinate system. The origin of this coordinate system is in the center of the rectangle. The z axis points away from the camera.
The arguments WeightingMode and ClippingFactor can be used to damp the impact of outliers on the algorithm. If WeightingMode is set to 'tukey' or 'huber', the contour points are weighted based on the approach of Tukey or Huber respectively. In such a case a robust error statistics is used to estimate the standard deviation of the distances of the contour points from the backprojected rectangle excluding outliers. The parameter ClippingFactor (a scaling factor for the standard deviation) controls the amount of damping outliers: The smaller the value chosen for ClippingFactor the more outliers are detected. See a discussion about the properties of the different weighting modes in fit_line_contour_xld. Note that, unlike by fit_line_contour_xld, for the rectangle pose estimation the approach of Huber is recommended.
The resulting Pose is of code-0 (see create_pose) and represents the pose of the center of the rectangle. You can compute the pose of the corners of the rectangle as follows:
set_origin_pose (Pose, Width/2, -Height/2, 0, PoseCorner1) set_origin_pose (Pose, Width/2, Height/2, 0, PoseCorner2) set_origin_pose (Pose, -Width/2, Height/2, 0, PoseCorner3) set_origin_pose (Pose, -Width/2, -Height/2, 0, PoseCorner4)
A rectangle is symmetric with respect to its x, y, and z axis and one and the same contour can represent a rectangle in 4 different poses. The angles in Pose are normalized to be in the range [-90; 90] degrees and the rest of the 4 possible poses can be computed by combining flips around the corresponding axis:
* NOTE: the following code works ONLY for pose of code-0 * as it is returned by get_rectangle_pose * * flip around z-axis PoseFlippedZ := Pose PoseFlippedZ := PoseFlippedZ+180 * flip around y-axis PoseFlippedY := Pose PoseFlippedY := PoseFlippedY+180 PoseFlippedY := -PoseFlippedY * flip around x-axis PoseFlippedX := Pose PoseFlippedX := PoseFlippedX+180 PoseFlippedX := -PoseFlippedX PoseFlippedX := -PoseFlippedX
Note that if the rectangle is a square (Width == Height) the number of alternative poses is 8.
If more than one contour are given in Contour, a corresponding tuple of values for both Width and Height has to be provided as well. Yet, if only one value is provided for each of these arguments, then this value is applied for each processed contour. A pose is estimated for each processed contour and all poses are concatenated in Pose (see the example below).
The accuracy of the estimated pose depends on the following three factors:
In order to achieve an accurate pose estimation, there are three corresponding criteria that should be considered:
The ratio Width/Height should fulfill
1/3 < Width/Height < 3
For a rectangular object deviating from this criterion, its longer side dominates the determination of its pose. This causes instability in the estimation of the angle around the longer rectangle's axis. In the extreme case when one of the dimensions is 0, the rectangle is in fact a line segment, whose pose cannot be estimated.
Secondly, the lengths of each side of the contour should be at least 20 pixels. An error is returned if a side of the contour is less than 5 pixels long.
Thirdly, the more the contour appears projectively distorted, the more stable the algorithm works. Therefore, the pose of a rectangle tilted with respect to the image plane can be estimated accurately, whereas the pose of an rectangle parallel to the image plane of the camera could be unstable. This is further discussed in the next paragraph. Additionally, there is a rule of thumb that ensures projective distortion: the rectangle should be placed in space such that its size in x and y dimension in the camera coordinate system should not be less than 1/10th of its distance from the camera in z direction.
get_rectangle_pose provides two measures for the accuracy of the estimated Pose. Error is the average pixel error between the contour points and the modeled rectangle backprojected on the image. If Error is exceeding 0.5, this is an indication that the algorithm did not converge properly, and the resulting Pose should not be used. CovPose contains 36 entries representing the 6×6 covariance matrix of the first 6 entries of Pose. The above mentioned case of instability of the angle about the longer rectangle's axis be detected by checking that the absolute values of the variances and covariances of the rotations around the x and y axis (CovPose,CovPose, and CovPose == CovPose) do not exceed 0.05. Further, unusually increased values of any of the covariances and especially of the variances (the 6 values on the diagonal of CovPose with indices 0, 7, 14, 21, 28 and 35, respectively) indicate a poor quality of Pose.
Contour(s) to be examined.
Internal camera parameters.
Number of elements: CameraParam == 8 || CameraParam == 12
Width of the rectangle in meters.
Restriction: Width > 0
Height of the rectangle in meters.
Restriction: Height > 0
Weighting mode for the optimization phase.
Default value: 'nonweighted'
List of values: 'huber', 'nonweighted', 'tukey'
Clipping factor for the elimination of outliers (typical: 1.0 for 'huber' and 3.0 for 'tukey').
Default value: 2.0
Suggested values: 1.0, 1.5, 2.0, 2.5, 3.0
Restriction: ClippingFactor > 0
3D pose of the rectangle.
Number of elements: Pose == 7 * Contour
Covariances of the pose values.
Number of elements: CovPose == 36 * Contour
Root-mean-square value of the final residual error.
Number of elements: Error == Contour
* Process an image with several rectangles of the same size appearing * as light objects * * RectWidth := 0.04 RectHeight := 0.025 read_cam_par ('campar.dat', CameraParam) read_image (Image, 'tea_boxes') * find light objects in the image mean_image (Image, ImageMean, 201, 201) dyn_threshold (Image, ImageMean, Region, 5, 'light') * fill gaps in the objects fill_up (Region, RegionFillUp) * extract rectangular contours * NOTE: for a real application, this step might require some additional * pre- or postprocessing reduce_domain (Image, RegionSelected, ImageReduced) edges_sub_pix (ImageReduced, Edges, 'canny', 0.7, 20, 30) * get the pose of all contours found get_rectangle_pose (Edges, CameraParam, RectWidth, RectHeight, 'huber', 2, \ Poses, CovPose, Error) NumPoses := |Poses|/7 for I := 0 to NumPoses-1 by 1 Pose := Poses[I*7:I*7+6] * use the Pose here * ... endfor
get_rectangle_pose returns 2 (H_MSG_TRUE) if all parameter values are correct and the position of the rectangle has been determined successfully. If the provided contour(s) cannot be segmented as a quadrangle get_rectangle_pose returns H_ERR_FIT_QUADRANGLE. If further necessary, an exception is raised.
get_circle_pose, set_origin_pose, camera_calibration
G.Schweighofer and A.Pinz: “Robust Pose Estimation from a Planar Target”; Transactions on Pattern Analysis and Machine Intelligence (PAMI), 28(12):2024-2030, 2006