erosion1erosion1Erosion1Erosion1 (Operator)

Name

erosion1erosion1Erosion1Erosion1 — Erode a region.

Signature

erosion1(Region, StructElement : RegionErosion : Iterations : )

Herror erosion1(const Hobject Region, const Hobject StructElement, Hobject* RegionErosion, const Hlong Iterations)

Herror T_erosion1(const Hobject Region, const Hobject StructElement, Hobject* RegionErosion, const Htuple Iterations)

void Erosion1(const HObject& Region, const HObject& StructElement, HObject* RegionErosion, const HTuple& Iterations)

HRegion HRegion::Erosion1(const HRegion& StructElement, Hlong Iterations) const

static void HOperatorSet.Erosion1(HObject region, HObject structElement, out HObject regionErosion, HTuple iterations)

HRegion HRegion.Erosion1(HRegion structElement, int iterations)

Description

erosion1erosion1Erosion1Erosion1Erosion1 erodes the input regions with a structuring element. By applying erosion1erosion1Erosion1Erosion1Erosion1 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 (StructElementStructElementStructElementStructElementstructElement) and R (RegionRegionRegionRegionregion) 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. erosion1erosion1Erosion1Erosion1Erosion1 is similar to the operator minkowski_sub1minkowski_sub1MinkowskiSub1MinkowskiSub1MinkowskiSub1, the difference is that in erosion1erosion1Erosion1Erosion1Erosion1 the structuring element is mirrored at the origin. The position of StructElementStructElementStructElementStructElementstructElement is meaningless, since the displacement vectors are determined with respect to the center of gravity of M.

The parameter IterationsIterationsIterationsIterationsiterations 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 (StructElementStructElementStructElementStructElementstructElement) can be generated with operators such as gen_circlegen_circleGenCircleGenCircleGenCircle, gen_rectangle1gen_rectangle1GenRectangle1GenRectangle1GenRectangle1, gen_rectangle2gen_rectangle2GenRectangle2GenRectangle2GenRectangle2, gen_ellipsegen_ellipseGenEllipseGenEllipseGenEllipse, draw_regiondraw_regionDrawRegionDrawRegionDrawRegion, gen_region_polygongen_region_polygonGenRegionPolygonGenRegionPolygonGenRegionPolygon, gen_region_pointsgen_region_pointsGenRegionPointsGenRegionPointsGenRegionPoints, etc.

Execution Information

Parameters

RegionRegionRegionRegionregion (input_object)  region(-array) objectHRegionHRegionHobject

Regions to be eroded.

StructElementStructElementStructElementStructElementstructElement (input_object)  region objectHRegionHRegionHobject

Structuring element.

RegionErosionRegionErosionRegionErosionRegionErosionregionErosion (output_object)  region(-array) objectHRegionHRegionHobject *

Eroded regions.

IterationsIterationsIterationsIterationsiterations (input_control)  integer HTupleHTupleHtuple (integer) (int / long) (Hlong) (Hlong)

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 (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

erosion1erosion1Erosion1Erosion1Erosion1 returns 2 (H_MSG_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.

Possible Predecessors

thresholdthresholdThresholdThresholdThreshold, regiongrowingregiongrowingRegiongrowingRegiongrowingRegiongrowing, watershedswatershedsWatershedsWatershedsWatersheds, class_ndim_normclass_ndim_normClassNdimNormClassNdimNormClassNdimNorm, gen_circlegen_circleGenCircleGenCircleGenCircle, gen_ellipsegen_ellipseGenEllipseGenEllipseGenEllipse, gen_rectangle1gen_rectangle1GenRectangle1GenRectangle1GenRectangle1, gen_rectangle2gen_rectangle2GenRectangle2GenRectangle2GenRectangle2, draw_regiondraw_regionDrawRegionDrawRegionDrawRegion, gen_region_pointsgen_region_pointsGenRegionPointsGenRegionPointsGenRegionPoints, gen_region_polygon_filledgen_region_polygon_filledGenRegionPolygonFilledGenRegionPolygonFilledGenRegionPolygonFilled

Possible Successors

connectionconnectionConnectionConnectionConnection, reduce_domainreduce_domainReduceDomainReduceDomainReduceDomain, select_shapeselect_shapeSelectShapeSelectShapeSelectShape, area_centerarea_centerAreaCenterAreaCenterAreaCenter

Alternatives

minkowski_sub1minkowski_sub1MinkowskiSub1MinkowskiSub1MinkowskiSub1, minkowski_sub2minkowski_sub2MinkowskiSub2MinkowskiSub2MinkowskiSub2, erosion2erosion2Erosion2Erosion2Erosion2

See also

transpose_regiontranspose_regionTransposeRegionTransposeRegionTransposeRegion

Module

Foundation