erosion1erosion1Erosion1Erosion1erosion1 (Operator)

Name

erosion1erosion1Erosion1Erosion1erosion1 — Erode a region.

Signature

erosion1(Region, StructElement : RegionErosion : Iterations : )

Description

erosion1erosion1Erosion1Erosion1Erosion1erosion1 erodes the input regions with a structuring element. By applying erosion1erosion1Erosion1Erosion1Erosion1erosion1 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 (StructElementStructElementStructElementStructElementstructElementstruct_element) and R (RegionRegionRegionRegionregionregion) 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 erosion of R with M. erosion1erosion1Erosion1Erosion1Erosion1erosion1 is similar to the operator minkowski_sub1minkowski_sub1MinkowskiSub1MinkowskiSub1MinkowskiSub1minkowski_sub1, the difference is that in erosion1erosion1Erosion1Erosion1Erosion1erosion1 the structuring element is mirrored at the origin. The position of StructElementStructElementStructElementStructElementstructElementstruct_element is meaningless, since the displacement vectors are determined with respect to the center of gravity of M.

The parameter IterationsIterationsIterationsIterationsiterationsiterations 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 (StructElementStructElementStructElementStructElementstructElementstruct_element) can be generated with operators such as gen_circlegen_circleGenCircleGenCircleGenCirclegen_circle, gen_rectangle1gen_rectangle1GenRectangle1GenRectangle1GenRectangle1gen_rectangle1, gen_rectangle2gen_rectangle2GenRectangle2GenRectangle2GenRectangle2gen_rectangle2, gen_ellipsegen_ellipseGenEllipseGenEllipseGenEllipsegen_ellipse, draw_regiondraw_regionDrawRegionDrawRegionDrawRegiondraw_region, gen_region_polygongen_region_polygonGenRegionPolygonGenRegionPolygonGenRegionPolygongen_region_polygon, gen_region_pointsgen_region_pointsGenRegionPointsGenRegionPointsGenRegionPointsgen_region_points, etc.

Execution Information

Multithreading type: reentrant (runs in parallel with non-exclusive operators).
Multithreading scope: global (may be called from any thread).
Automatically parallelized on tuple level.

Parameters

RegionRegionRegionRegionregionregion (input_object) region(-array) → object

Regions to be eroded.

StructElementStructElementStructElementStructElementstructElementstruct_element (input_object) region → object

Structuring element.

RegionErosionRegionErosionRegionErosionRegionErosionregionErosionregion_erosion (output_object) region(-array) → object

Eroded regions.

IterationsIterationsIterationsIterationsiterationsiterations (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 Iterations Iterations Iterations iterations iterations (lin)

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. Then the runtime complexity for one region is:

Result

erosion1erosion1Erosion1Erosion1Erosion1erosion1 returns TRUE if all parameters are correct. The behavior in case of empty or no input region can be set via: