get_rectangle_pose — Determine the 3D pose of a rectangle from its perspective 2D
projection
get_rectangle_pose(Contour : : CameraParam, Width, Height, WeightingMode, ClippingFactor : Pose, CovPose, Error)
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
Calibration / Multi-View).
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[5] := PoseFlippedZ[5]+180
* flip around y-axis
PoseFlippedY := Pose
PoseFlippedY[4] := PoseFlippedY[4]+180
PoseFlippedY[5] := -PoseFlippedY[5]
* flip around x-axis
PoseFlippedX := Pose
PoseFlippedX[3] := PoseFlippedX[3]+180
PoseFlippedX[4] := -PoseFlippedX[4]
PoseFlippedX[5] := -PoseFlippedX[5]
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
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[21],CovPose[28], and
CovPose[22] == CovPose[27]) 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 (input_object) xld(-array) → object
Contour(s) to be examined.
CameraParam (input_control) campar → (real / integer / string)
Internal camera parameters.
Width (input_control) number(-array) → (real)
Width of the rectangle in meters.
Restriction: Width > 0
Height (input_control) number(-array) → (real)
Height of the rectangle in meters.
Restriction: Height > 0
WeightingMode (input_control) string → (string)
Weighting mode for the optimization phase.
Default value: 'nonweighted'
List of values: 'huber', 'nonweighted', 'tukey'
ClippingFactor (input_control) number → (real)
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
Pose (output_control) pose(-array) → (real / integer)
3D pose of the rectangle.
Number of elements: Pose == 7 * Contour
CovPose (output_control) number-array → (real)
Covariances of the pose values.
Number of elements: CovPose == 36 * Contour
Error (output_control) number-array → (real)
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
gen_cam_par_area_scan_division (0.014, 830, 4.58e-006, 4.65e-006, \
509, 488, 800, 800, CameraParam)
read_image (Image, 'barcode/ean13/tea_box_01')
* 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.
connection (RegionFillUp, ConnectedRegions)
select_shape (ConnectedRegions, SelectedRegions, ['area','rectangularity'], \
'and', [50000,0.9], [640000,1])
boundary (SelectedRegions, RegionBorder, 'inner')
dilation_circle (RegionBorder, RegionDilation, 3.5)
* NOTE: for a real application, this step might require some additional
* pre- or postprocessing.
reduce_domain (Image, RegionDilation, ImageReduced)
edges_sub_pix (ImageReduced, Edges, 'canny', 1, 20, 40)
* 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
3D Metrology