minkowski_add1minkowski_add1MinkowskiAdd1MinkowskiAdd1 (Operator)

Name

minkowski_add1minkowski_add1MinkowskiAdd1MinkowskiAdd1 — Perform a Minkowski addition on a region.

Signature

minkowski_add1(Region, StructElement : RegionMinkAdd : Iterations : )

Herror minkowski_add1(const Hobject Region, const Hobject StructElement, Hobject* RegionMinkAdd, const Hlong Iterations)

Herror T_minkowski_add1(const Hobject Region, const Hobject StructElement, Hobject* RegionMinkAdd, const Htuple Iterations)

void MinkowskiAdd1(const HObject& Region, const HObject& StructElement, HObject* RegionMinkAdd, const HTuple& Iterations)

HRegion HRegion::MinkowskiAdd1(const HRegion& StructElement, Hlong Iterations) const

static void HOperatorSet.MinkowskiAdd1(HObject region, HObject structElement, out HObject regionMinkAdd, HTuple iterations)

HRegion HRegion.MinkowskiAdd1(HRegion structElement, int iterations)

Description

minkowski_add1minkowski_add1MinkowskiAdd1MinkowskiAdd1MinkowskiAdd1 dilates the input regions with a structuring element. By applying minkowski_add1minkowski_add1MinkowskiAdd1MinkowskiAdd1MinkowskiAdd1 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 (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 union of all these translations is the Minkowski addition of R with M. minkowski_add1minkowski_add1MinkowskiAdd1MinkowskiAdd1MinkowskiAdd1 is similar to the operator dilation1dilation1Dilation1Dilation1Dilation1, the difference is that in dilation1dilation1Dilation1Dilation1Dilation1 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 an empty 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.

Attention

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 union1union1Union1Union1Union1 has to be called first.

Execution Information

Parameters

RegionRegionRegionRegionregion (input_object)  region(-array) objectHRegionHRegionHobject

Regions to be dilated.

StructElementStructElementStructElementStructElementstructElement (input_object)  region objectHRegionHRegionHobject

Structuring element.

RegionMinkAddRegionMinkAddRegionMinkAddRegionMinkAddregionMinkAdd (output_object)  region(-array) objectHRegionHRegionHobject *

Dilated 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

minkowski_add1minkowski_add1MinkowskiAdd1MinkowskiAdd1MinkowskiAdd1 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, connectionconnectionConnectionConnectionConnection, union1union1Union1Union1Union1, 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

reduce_domainreduce_domainReduceDomainReduceDomainReduceDomain, select_shapeselect_shapeSelectShapeSelectShapeSelectShape, area_centerarea_centerAreaCenterAreaCenterAreaCenter, connectionconnectionConnectionConnectionConnection

Alternatives

minkowski_add2minkowski_add2MinkowskiAdd2MinkowskiAdd2MinkowskiAdd2, dilation1dilation1Dilation1Dilation1Dilation1

See also

transpose_regiontranspose_regionTransposeRegionTransposeRegionTransposeRegion, minkowski_sub1minkowski_sub1MinkowskiSub1MinkowskiSub1MinkowskiSub1

Module

Foundation