minkowski_add2minkowski_add2minkowski_add2MinkowskiAdd2MinkowskiAdd2 (Operator)

Name

minkowski_add2minkowski_add2minkowski_add2MinkowskiAdd2MinkowskiAdd2 — Dilate a region (using a reference point).

Signature

Description

minkowski_add2minkowski_add2minkowski_add2MinkowskiAdd2MinkowskiAdd2 computes the Minkowski addition of the input regions with a structuring element (StructElementStructElementStructElementStructElementstructElement) having the reference point (RowRowRowRowrow,ColumnColumnColumnColumncolumn). minkowski_add2minkowski_add2minkowski_add2MinkowskiAdd2MinkowskiAdd2 has a similar effect as minkowski_add1minkowski_add1minkowski_add1MinkowskiAdd1MinkowskiAdd1, the difference is that the reference point of the structuring element can be chosen arbitrarily. 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.

An empty region is generated in case of an empty structuring element.

Structuring elements (StructElementStructElementStructElementStructElementstructElement) can be generated with operators such as gen_circlegen_circlegen_circleGenCircleGenCircle, gen_rectangle1gen_rectangle1gen_rectangle1GenRectangle1GenRectangle1, gen_rectangle2gen_rectangle2gen_rectangle2GenRectangle2GenRectangle2, gen_ellipsegen_ellipsegen_ellipseGenEllipseGenEllipse, draw_regiondraw_regiondraw_regionDrawRegionDrawRegion, gen_region_polygongen_region_polygongen_region_polygonGenRegionPolygonGenRegionPolygon, gen_region_pointsgen_region_pointsgen_region_pointsGenRegionPointsGenRegionPoints, 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.

Parallelization

• 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

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:

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

Result

minkowski_add2minkowski_add2minkowski_add2MinkowskiAdd2MinkowskiAdd2 returns 2 (H_MSG_TRUE) if all parameters are correct. The behavior in case of empty or no input region can be set via:

• no region: set_system('no_object_result',<RegionResult>)

• empty region: set_system('empty_region_result',<RegionResult>)

Otherwise, an exception is raised.

Possible Predecessors

thresholdthresholdthresholdThresholdThreshold, regiongrowingregiongrowingregiongrowingRegiongrowingRegiongrowing, connectionconnectionconnectionConnectionConnection, union1union1union1Union1Union1, watershedswatershedswatershedsWatershedsWatersheds, class_ndim_normclass_ndim_normclass_ndim_normClassNdimNormClassNdimNorm, gen_circlegen_circlegen_circleGenCircleGenCircle, gen_ellipsegen_ellipsegen_ellipseGenEllipseGenEllipse, gen_rectangle1gen_rectangle1gen_rectangle1GenRectangle1GenRectangle1, gen_rectangle2gen_rectangle2gen_rectangle2GenRectangle2GenRectangle2, draw_regiondraw_regiondraw_regionDrawRegionDrawRegion, gen_region_pointsgen_region_pointsgen_region_pointsGenRegionPointsGenRegionPoints, gen_struct_elementsgen_struct_elementsgen_struct_elementsGenStructElementsGenStructElements, gen_region_polygon_filledgen_region_polygon_filledgen_region_polygon_filledGenRegionPolygonFilledGenRegionPolygonFilled

Possible Successors

reduce_domainreduce_domainreduce_domainReduceDomainReduceDomain, select_shapeselect_shapeselect_shapeSelectShapeSelectShape, area_centerarea_centerarea_centerAreaCenterAreaCenter, connectionconnectionconnectionConnectionConnection

Alternatives

minkowski_add1minkowski_add1minkowski_add1MinkowskiAdd1MinkowskiAdd1, dilation1dilation1dilation1Dilation1Dilation1

See also

transpose_regiontranspose_regiontranspose_regionTransposeRegionTransposeRegion

Module

Foundation