union_cotangential_contours_xld — Compute the union of cotangential contours.
union_cotangential_contours_xld(Contours : UnionContours : FitClippingLength, FitLength, MaxTangAngle, MaxDist, MaxDistPerp, MaxOverlap, Mode : )
The operator union_cotangential_contours_xld unifies contours
of the input XLD contour array Contours according to the local
curvatures at their endpoints.
Parameters
FitClippingLength
How does the union work?
First, endpieces for each input contour in Contours are
determined.
The parameter FitClippingLength specifies the Euclidean length
that is temporarily clipped at both ends of a contour. With this parameter,
it is possible to ignore artifacts at the endings of the input contours.
FitLength
With the parameter FitLength the Euclidean length of the endpieces
that will be examined for the union is given. At each
end of a contour at least that many points are assigned to an endpiece that
its length is greater or equal to FitLength. The value
'auto' can be used here. The operator then tries to segment
the contours into straights and arcs and takes the first and last segment
as endpieces. As this is computationally intensive, it is recommended to use
numerically specified values for the lengths whenever possible.
FitLength
The operator tries to fit a circle into each endpiece. Then, the endpoints of the input contours are determined that lie near enough to these circles (measured against the root mean square error of the circle fit). The tangents at these points correspond to the local curvature at the endings of the input contours.
If a circle fit fails, the operator tries to fit a regression line. Then, the local curvature of the endings of a contour corresponds to the direction of the regression line through the points of the endpieces.
The input contours are going to be unified according to the calculated local curvatures at their endpoints. Two contours are considered for the union if multiple thresholds are fulfilled at the same time:
MaxTangAngle
The parameter MaxTangAngle specifies the maximum angle between the
tangents of two contours.
MaxDist
The maximum distance of two endpoints is given with the parameter
MaxDist.
MaxDistPerp
The maximum distance perpendicular to the tangents is specified with the
parameter MaxDistPerp. This distance is the minimum of the
distances of the endpoints of the contours perpendicular to the other
contour.
MaxOverlap
As a last threshold, the overlap of the contours is considered.
The amount of the overlap is determined by the projection of one
endpoint onto the tangent of another contour and vice versa. The distances
between the endpoints and their projections
must be shorter than MaxOverlap. Contrary to the other threshold
values, MaxOverlap can become negative. Negative values denote
the minimum distance of the endpoints in the direction of the
tangents.
union_collinear_contours_ext_xld for an
illustration with positive values for 'a' and 'b'.
It is possible, that a single contour is closed by this operator or multiple contours are merged into a single closed contour, if the criteria named above are fulfilled for the endpieces. Be aware that already closed contours are not considered for a union anymore.
If all thresholds are fulfilled between contours, a score value is calculated. The closer the calculated values for the angles and distances are to 0, the higher is the score value. The unification is then executed in the order of the score values. Thus, if there are multiple candidates for the unification, the best fitting contours are merged first.
The parameter Mode states, whether existing attributes of the
input contours should be copied to the output contours. 'attr_keep'
copies the attributes, which can have negative impacts on the performance of
the operator.
'attr_forget' causes the operator to ignore existing attributes.
For further details see the description of the parameter Mode of the
operator union_adjacent_contours_xld.
Contours (input_object) xld_cont-array → object
Input XLD contours.
UnionContours (output_object) xld_cont-array → object
Output XLD contours.
FitClippingLength (input_control) real → (real)
Length of the part of a contour to skip for the determination of tangents.
Default value: 0.0
Typical range of values: 0.0
≤
FitClippingLength
FitLength (input_control) real → (real / string)
Length of the part of a contour to use for the determination of tangents.
Default value: 30.0
Suggested values: 10.0, 20.0, 30.0, 'auto'
Typical range of values: 0.0
≤
FitLength
MaxTangAngle (input_control) angle.rad → (real)
Maximum angle difference between two contours' tangents.
Default value: 0.78539816
Typical range of values: 0.0
≤
MaxTangAngle
≤
3.1415926
MaxDist (input_control) real → (real)
Maximum distance of the contours' end points.
Default value: 25.0
Suggested values: 5.0, 10.0, 25.0, 50.0
Typical range of values: 0.0
≤
MaxDist
MaxDistPerp (input_control) real → (real)
Maximum distance of the contours' end points perpendicular to their tangents.
Default value: 10.0
Suggested values: 2.0, 5.0, 10.0, 20.0
Typical range of values: 0.0
≤
MaxDistPerp
MaxOverlap (input_control) real → (real)
Maximum overlap of two contours.
Default value: 2.0
Suggested values: 2.0, 5.0, 10.0, 20.0
Mode (input_control) string → (string)
Mode describing the treatment of the contours' attributes.
Default value: 'attr_forget'
List of values: 'attr_forget', 'attr_keep'
split_contours_xld,
select_contours_xld
union_collinear_contours_xld,
union_collinear_contours_ext_xld,
union_cocircular_contours_xld,
union_straight_contours_xld,
union_adjacent_contours_xld
edges_sub_pix,
threshold_sub_pix,
gen_polygons_xld,
get_contour_xld,
get_contour_attrib_xld
Foundation