Operator Reference
minkowski_add1 (Operator)
minkowski_add1 — Perform a Minkowski addition on a region.
Signature
minkowski_add1(Region, StructElement : RegionMinkAdd : Iterations : )
Description
minkowski_add1 dilates the input regions with a
structuring element. By applying minkowski_add1 to a
region, its boundary gets smoothed. In the process, the area of the
region is enlarged. Furthermore, disconnected regions may be
merged. Such regions, however, remain logically distinct region.
The Minkowski addition is a set-theoretic region operation. It is
based on translations and union operations.
Let M (StructElement) and R (Region) be
two regions, where M is the structuring element and R is the
region to be processed. Furthermore, let m be a point in M.
Then the displacement vector is defined as the difference of the
center of gravity of M and the vector . Let
denote the translation of a
region R by a vector . Then
For each point m in M a translation of the region R is
performed. The union of all these translations is the Minkowski
addition of R with M. minkowski_add1 is similar to
the operator dilation1, the difference is that in
dilation1 the structuring element is mirrored at the
origin. The position of StructElement is meaningless,
since the displacement vectors are determined with respect to the
center of gravity of M.
The parameter Iterations determines the number of
iterations which are to be performed with the structuring element.
The result of iteration n-1 is used as input for iteration n.
From the above definition it follows that an empty region is
generated in case of an empty structuring element.
Structuring elements (StructElement) can be generated
with operators such as gen_circle, gen_rectangle1,
gen_rectangle2, gen_ellipse,
draw_region, gen_region_polygon,
gen_region_points, etc.
Attention
A Minkowski addition always results in enlarged regions.
Closely spaced regions which may touch or overlap as a result of the
dilation are still treated as two separate regions. If the desired
behavior is to merge them into one region, the operator
union1 has to be called first.
Execution Information
- Multithreading type: reentrant (runs in parallel with non-exclusive operators).
- Multithreading scope: global (may be called from any thread).
- Automatically parallelized on tuple level.
Parameters
Region (input_object) region(-array) → object
Regions to be dilated.
StructElement (input_object) region → object
Structuring element.
RegionMinkAdd (output_object) region(-array) → object
Dilated regions.
Iterations (input_control) integer → (integer)
Number of iterations.
Default: 1
Suggested values: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 17, 20, 30, 40, 50
Value range:
1
≤
Iterations
(lin)
Minimum increment: 1
Recommended increment: 1
Complexity
Let F1 be the area of the input region, and F2 be the area of the structuring element. Then the runtime complexity for one region is:
Result
minkowski_add1 returns 2 (
H_MSG_TRUE)
if all parameters are
correct. The behavior in case of empty or no input region can be
set via:
-
empty region:
set_system('empty_region_result',<RegionResult>)
Otherwise, an exception is raised.
Possible Predecessors
threshold,
regiongrowing,
connection,
union1,
watersheds,
class_ndim_norm,
gen_circle,
gen_ellipse,
gen_rectangle1,
gen_rectangle2,
draw_region,
gen_region_points,
gen_region_polygon_filled
Possible Successors
reduce_domain,
select_shape,
area_center,
connection
Alternatives
See also
transpose_region,
minkowski_sub1
Module
Foundation