union_collinear_contours_xld — Unite approximately collinear contours.
union_collinear_contours_xld(Contours : UnionContours : MaxDistAbs, MaxDistRel, MaxShift, MaxAngle, Mode : )
The operator union_collinear_contours_xld unites all contours
of the input XLD contour array Contours that are
approximately collinear, i.e., which lie approximately on the same
straight line. The united contours consist of the concatenation of
the contour points of the respective input contours. They are returned,
together with the contours that could not be united with any other
contour, in the output XLD contour array UnionContours.
Typical applications
union_collinear_contours_xld can be used to bridge gaps in
extracted edges or lines, which may be caused, e.g., by locally low
image contrast. It can also be used to unite collinear edge or line
segments that are separated, e.g., because of junctions. Typically,
union_collinear_contours_xld is part of the process of
grouping and selecting extracted edges or lines to achieve meaningful
entities.
Example
The following example shows the effect of
union_collinear_contours_xld. On the left hand side, a set of
disconnected input contours is shown. The contours that lie on the
same border of the rectangle are approximately collinear. On the right
hand side, the result of union_collinear_contours_xld shows
that the contours that were approximately collinear have been united.
Note that the contours that are approximately perpendicular to each
other have not been united.
| (1) | (2) |
Parameters
The parameters MaxDistAbs, MaxDistRel,
MaxShift, and MaxAngle are used to define the
conditions for the collinearity of two contours. The parameter
Mode controls the handling of the attributes of the input
contours.
In principle, the measures for the first three parameters depend on the order in which each pair of contours is evaluated, i.e., which contour is used as reference contour that is to be joined with the second contour. To avoid this dependency, the respective measures are evaluated in both directions and the order of contours is chosen that results in the smaller value for these measures. Note that in the illustrations below, the contour on the left is always used as the reference contour.
MaxDistAbsThe parameter MaxDistAbs defines the maximum accepted
absolute distance between the two contours. The distance is
measured along the regression line of the reference contour. Thus, it
is the length of the projection of the gap between the two contours
onto the regression line of the reference contour.
MaxDistRelThe parameter MaxDistRel defines the maximum accepted
relative distance between the two contours. The relative distance is
calculated by dividing the distance a (see the description of the
parameter MaxDistAbs) by the length b of the reference
contour.
MaxShiftThe parameter MaxShift defines the maximum distance of the
second contour from the regression line of the reference contour.
This distance is measured perpendicular to the regression line of
the reference contour.
MaxAngleThe parameter MaxAngle defines the maximum angle (in
radians) between the regression lines of the two contours.
ModeThe parameter Mode controls the handling of the attributes
that may be available for the input contours, e.g., if the contours
have been created by edges_sub_pix.
All attributes are copied to the output contours.
Global attributes are only kept for those contours that are not united with other contours. In general, it is not possible to determine the global attributes of a united contour from the global attributes of the individual contours.
The output contours will not contain any attributes. This mode may be chosen for performance reasons if the attributes will not be required for further calculations.
To query, which attributes are available,
query_contour_attribs_xld can be used.
Implementation details
The input contours are analyzed and united pairwise. This pairwise process is repeated until there are no more unconnected collinear contours left. If necessary, the order of the input contour points is flipped, so that the end points of the contours that have been connected are direct neighbors in the resulting point list.
Two contours are united only if all criteria are fulfilled, i.e., all
values must be lower than the specified thresholds. As another
precondition, contours must not overlap each other significantly (see
union_collinear_contours_ext_xld for an illustration of overlap).
An overlap of at most 0.5 pixels is tolerated. To allow a larger overlap,
union_collinear_contours_ext_xld can be used.
Besides finding pairs of contours to be united, it is
important for the behavior of union_collinear_contours_xld to
determine the order in which contours are united.
For this, all contour pairs that may be united are rated by
calculating costs for their unification.
The costs are the sum of the measures, each normalized by the
respective threshold, defined by the parameters MaxDistAbs,
MaxDistRel, MaxShift, and MaxAngle.
The contour pair with the
lowest costs is united first. Then, the costs are updated with
respect to the newly created contour and the contour list is searched
for the next best pair of contours to be united.
Note that the definition of collinearity as used in
union_collinear_contours_xld depends on the regression lines
of the input contours. To avoid unexpected results, make sure that the
input contours are approximately straight lines, e.g., by splitting
them into line segments with segment_contours_xld. Note also
that closed contours are not united with any other contour.
Limitations and alternatives
union_collinear_contours_xld can only be used if the contours
that should be joined lie approximately on a straight line. If the
contours lie approximately on a circle,
union_cocircular_contours_xld can be used instead. If the
contours represent a free-form,
union_cotangential_contours_xld can be used. If only very
small gaps between the contours should be closed, regardless of the
orientation of the contours, union_adjacent_contours_xld can
be used.
If the parameter adjustments available with
union_collinear_contours_xld are not sufficient,
union_collinear_contours_ext_xld can be used to define the
criteria for the unification more specifically. Among others,
union_collinear_contours_ext_xld allows to set the tolerance
for the overlap of contours as well as a limit for the total costs to
avoid the connection of contours that are close to the limits of all
criteria.
Contours (input_object) xld_cont-array → object
Input XLD contours.
UnionContours (output_object) xld_cont-array → object
Output XLD contours.
MaxDistAbs (input_control) real → (real)
Maximum length of the gap between two contours, measured along the regression line of the reference contour.
Default value: 10.0
Typical range of values: 0.0
≤
MaxDistAbs
MaxDistRel (input_control) real → (real)
Maximum length of the gap between two contours, relative to the length of the reference contour, both measured along the regression line of the reference contour.
Default value: 1.0
Typical range of values: 0.0
≤
MaxDistRel
MaxShift (input_control) real → (real)
Maximum distance of the second contour from the regression line of the reference contour.
Default value: 2.0
Typical range of values: 0.0
≤
MaxShift
MaxAngle (input_control) real → (real)
Maximum angle between the regression lines of two contours.
Default value: 0.1
Typical range of values: 0.0
≤
MaxAngle
≤
0.78539816339
Mode (input_control) string → (string)
Mode that defines the treatment of contour attributes, i.e., if the contour attributes are kept or discarded.
Default value: 'attr_keep'
List of values: 'attr_forget', 'attr_keep'
edges_sub_pix,
lines_gauss,
segment_contours_xld,
select_contours_xld,
select_shape_xld,
split_contours_xld,
threshold_sub_pix
fit_line_contour_xld,
select_contours_xld,
select_shape_xld
union_collinear_contours_ext_xld,
union_straight_contours_xld,
union_cocircular_contours_xld,
union_cotangential_contours_xld,
union_adjacent_contours_xld
get_contour_xld,
get_contour_attrib_xld,
query_contour_attribs_xld
Foundation