minkowski_sub1 — Erode a region.
minkowski_sub1(Region, StructElement : RegionMinkSub : Iterations : )
minkowski_sub1 computes the Minkowski subtraction of the
input regions with a structuring element. By applying
minkowski_sub1 to a region, its boundary gets smoothed.
In the process, the area of the region is reduced. Furthermore,
connected regions may be split. Such regions, however, remain
logically one region. The Minkowski subtraction is a set-theoretic
region operation. It uses the intersection operation.
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 intersection of all these translations is the
Minkowski subtraction of R with M. minkowski_sub1
is similar to the operator erosion1, the difference
is that in erosion1 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 the maximum 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.
Region (input_object) region(-array) → object
Regions to be eroded.
StructElement (input_object) region → object
Structuring element.
RegionMinkSub (output_object) region(-array) → object
Eroded regions.
Iterations (input_control) integer → (integer)
Number of iterations.
Default value: 1
Suggested values: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 17, 20, 30, 40, 50
Typical range of values: 1
≤
Iterations
(lin)
Minimum increment: 1
Recommended increment: 1
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:
minkowski_sub1 returns TRUE if all parameters are
correct. The behavior in case of empty or no input region can be
set via:
no region: set_system('no_object_result',<RegionResult>)
empty region: set_system('empty_region_result',<RegionResult>)
Otherwise, an exception is raised.
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
reduce_domain,
select_shape,
area_center,
connection
Foundation