erosion1 ( Region, StructElement : RegionErosion : Iterations : )

Erode a region.

erosion1 erodes the input regions with a structuring element. By applying erosion1 to a region, its boundary is 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 (Region) be two regions, where M is the ``structuring element'' and R is the region to be precessed. Furthermore, let m be a point in M. Then the displacement vector v(m) = (dx,dy) is defined as the difference of the center of gravity of M and the vector v(m). Let t(v(m))(R) denote the translation of a region R by a vector v(m). Then

                        __
                       /  \
      erosion1(R,M) := |  | t     (R)
                       |  |  -v(m)
                      m in M

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 operator minkowski_sub1, the difference being 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 circle, rectangle1, rectangle2, ellipse, draw_region, store_polygon, store_coord, etc.


Parameters

Region (input_object)
region(-array) -> object
Regions to be eroded.

StructElement (input_object)
region -> object
Structuring element.

RegionErosion (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
Range of values: 1 <= Iterations
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. The the runtime complexity for one region is:

    O(sqrt(F1) * sqrt(F2) * Iterations) .


Result

erosion1 returns TRUE if all parameters are correct. The behavior in case of empty or no input region can be set via:

  a) no region:    set_system(::'no_object_result',<RegionResult>:)
  b) empty region: set_system(::'empty_region_result',<RegionResult>:)
Otherwise, an exception is raised.


Possible Predecessors

threshold__, regiongrowing__, watersheds, class_ndim1__, circle, ellipse, rectangle1, rectangle2, draw_region, store_coord, struct_elements, store_filled_polygon


Possible Successors

connection, reduce_domain, select_shape, area_center


Alternatives

minkowski_sub1, minkowski_sub2, erosion2, erosion_golay, erosion_seq


See also

transpose



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