dilation1 — Dilate a region.
dilation1 dilates the input regions with a structuring
element. By applying
dilation1 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 dilation is
a set-theoretic region operation. It uses the union operation.
Let M (
StructElement) and R (
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 dilation of
R with M.
dilation1 is similar to the
minkowski_add1, the difference is that in
dilation1 the structuring element is mirrored at the
origin. The position of
meaningless, since the displacement vectors are determined with
respect to the center of gravity of M.
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
A dilation 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.
Regions to be dilated.
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:
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:
dilation1 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.