erosion1 — Erode a region.
erosion1 erodes the input regions with a structuring
element. By applying
erosion1 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 erosion is a set-theoretic region
operation. It uses the intersection 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 intersection of all these translations is the
erosion of R with M.
erosion1 is similar to the
minkowski_sub1, 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.
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
Regions to be eroded.
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:
erosion1 returns TRUE if all parameters are correct.
The behavior in case of empty or no input region can be set via:
Otherwise, an exception is raised.