fit_rectangle2_contour_xld — Fit rectangles to XLD contours.
fit_rectangle2_contour_xld fits rectangles to the
rectangular XLD contours given by
Contours and returns the
parameters of the rectangles in
Phi (orientation), as well as
Length2 (half edge lengths). The angle
returned in radians and specifies the angle between the horizontal
axis and the edge with the half length
Length1 in the
mathematically positive direction (counterclockwise). In addition,
the point order of the contour is returned in
PointOrder = 'positive' means that the contour
is traversed in the mathematically positive direction
The algorithm used for the fitting of the rectangles can be selected
Standard least-squares line fitting.
Weighted least-squares line fitting, where the impact of outliers is decreased based on the approach of Huber (see below).
Weighted least-squares line fitting, where outliers are ignored based on the approach of Tukey(see below).
For 'huber' and 'tukey', a robust error statistics is used
to estimate the standard deviation of the distances of the contour points
from the approximating sides of the rectangle while ignoring outliers. The
standard deviation is computed separately for each side of the rectangle to
allow the processing of rectangles whose sides are not exactly perpendicular
to each other. The parameter
ClippingFactor (a scaling factor
relative to the standard deviation) controls the amount of outliers:
The smaller the value chosen for
ClippingFactor the more outliers
are detected. The detection of outliers is iterated. The parameter
Iterations specifies the number of iterations. For
Algorithm = 'regression', the values of the last two
parameters are ignored. Note that in the approach of Tukey ('*tukey'), the
outliers are removed before performing the approximation and all other points
are weighted, whereas in the approach of Huber ('*huber'), the outliers still
have a small influence. Particularly, for outliers the optimization is
influenced linearly and for points with a smaller distance it is influenced
to the squre. For the algebraic approach, all distances of the points
influence the optimization to the square and thus are not robust against
outliers. In practice, the approach of Tukey is recommended.
To reduce the computational load, the fitting of rectangles can be
restricted to a subset of the contour points: If a value other than
-1 is assigned to
MaxNumPoints, only up to
MaxNumPoints points, uniformly distributed across the
contour, are used.
Depending on the processing used to create
start and end points of a contour may contain positional errors.
Therefore, it is possible to exclude
points at the beginning and at the end of a contour from the
Contours, for which the distance between their start points and
their end points is <=
considered to be closed. For closed contours, the end point of the
contour is not used for the rectangle fitting because it would
receive twice the weight of the remaining points in the fit.
The fitting of the rectangle to the contour is based on finding the
correspondence between the contour points and the four sides of the
rectangle. To enable a successful fit, there must be at least one
point that lies in the interior of the line segment that represents
the respective rectangle side, i.e., the point must not lie at the
ends of the line segment. Because of this, at least eight contour
points are necessary to fit the rectangle. A point is internally
assigned to the side of the rectangle to which it has the minimum
distance. For this, the currently optimal rectangle parameters,
i.e., the parameters used for the current iteration step, are used
internally. If no corresponding points are found for at least one
side of the rectangle, the rectangle parameters cannot be determined
uniquely. In this case, the error 3266 is returned. Because of
this, the caller of
fit_rectangle2_contour_xld must ensure
that the input contours sufficiently resemble a rectangle. In
particular, none of the interior angles of the contour, if the
contour was approximated by four lines, should be smaller than 45
degrees or larger than 135 degrees. Because of the assignment of
contour points to the closest side of the rectangle this would mean
that at least one side of the rectangle would have no corresponding
ClippingFactor should not be chosen
too small to avoid that the outlier suppression creates rectangle
sides without corresponding contour points. This can only happen
Algorithm = 'tukey'. If the above
conditions are observed,
highly accurate rectangle parameters. If the outlier suppression
according to Tukey is used,
be used to robustly fit rectangles, e.g., to rectangular contours
with rounded corners.
Algorithm for fitting the rectangles.
Default value: 'regression'
List of values: 'huber', 'regression', 'tukey'
Maximum number of contour points used for the computation (-1 for all points).
Default value: -1
MaxNumPoints == -1 || MaxNumPoints >= 8
Maximum distance between the end points of a contour to be considered as closed.
Default value: 0.0
MaxClosureDist >= 0.0
Number of points at the beginning and at the end of the contours to be ignored for the fitting.
Default value: 0
Suggested values: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
ClippingEndPoints >= 0
Maximum number of iterations (not used for 'regression').
Default value: 3
Iterations >= 0
Clipping factor for the elimination of outliers (typical values: 1.0 for 'huber' and 2.0 for 'tukey').
Default value: 2.0
Suggested values: 1.0, 1.5, 2.0, 2.5, 3.0
ClippingFactor > 0
Row coordinate of the center of the rectangle.
Column coordinate of the center of the rectangle.
Orientation of the main axis of the rectangle [rad].
First radius (half length) of the rectangle.
Second radius (half width) of the rectangle.
Point order of the contour.
List of values: 'negative', 'positive'
fit_rectangle2_contour_xld returns TRUE if all parameter
values are correct, and rectangles could be fitted to the input
contours. If the input is empty the behavior can be set via
set_system('no_object_result',<Result>). If necessary, an
exception is raised. If the parameter
chosen too small, i.e., all points are classified as outliers, the
error 3266 is raised. If no points could be found for at least one
side of the rectangle, the error 3266 is raised as well.