minkowski_add1 — Perform a Minkowski addition on a region.
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 (
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
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.
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 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.
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:
minkowski_add1 returns TRUE if all parameters are
correct. The behavior in case of empty or no input region can be
Otherwise, an exception is raised.