dilation1Dilation1Dilation1dilation1dilation1🔗

Short description🔗

dilation1Dilation1Dilation1dilation1dilation1 — Dilate a region.

Signature🔗

dilation1( region Region, region StructElement, out region RegionDilation, integer Iterations )

Description🔗

dilation1Dilation1 dilates the input regions with a structuring element. By applying dilation1Dilation1 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 dilation is a set-theoretic region operation. It uses the union operation.

Let \(M\) (StructElementstructElementstruct_element) and \(R\) (Regionregionregion) 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 \({{\vec{v}}_{m}} = (dx,dy)\) is defined as the difference of the center of gravity of \(M\) and the vector \(\vec{m}\). Let \(t_{\vec{v}_{m}}(R)\) denote the translation of a region \(R\) by a vector \(\vec{v}\). Then

\[\begin{eqnarray*} \textrm{dilation1}(R,M) := \bigcup_{m \in M} {t_{{-\vec{v}}_{m}} (R)} \end{eqnarray*}\]

For each point \(m\) in \(M\) a translation of the region \(R\) is performed. The union of all these translations is the dilation of \(R\) with \(M\). dilation1Dilation1 is similar to the operator minkowski_add1MinkowskiAdd1, the difference is that in dilation1Dilation1 the structuring element is mirrored at the origin. The position of StructElementstructElementstruct_element is meaningless, since the displacement vectors are determined with respect to the center of gravity of \(M\).

The parameter Iterationsiterationsiterations 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 (StructElementstructElementstruct_element) can be generated with operators such as gen_circleGenCircle, gen_rectangle1GenRectangle1, gen_rectangle2GenRectangle2, gen_ellipseGenEllipse, draw_regionDrawRegion, gen_region_polygonGenRegionPolygon, gen_region_pointsGenRegionPoints, etc.

Attention🔗

A dilation 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 union1Union1 has to be called first.

Execution information🔗

Execution information

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

Parameters🔗

Regionregionregion (input_object) region(-array) → objectHObjectHRegionHObjectHobject

Regions to be dilated.

StructElementstructElementstruct_element (input_object) region → objectHObjectHRegionHObjectHobject

Structuring element.

RegionDilationregionDilationregion_dilation (output_object) region(-array) → objectHObjectHRegionHObjectHobject *

Dilated regions.

Iterationsiterationsiterations (input_control) integer → (integer)HTuple (Hlong)HTuple (int / long)intHtuple (Hlong)

Number of iterations.

Default: 11
Suggested values: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 17, 20, 30, 40, 50
Value range: 1 ≤ 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:

\[\begin{eqnarray*} O(\sqrt{F1} \cdot \sqrt{F2} \cdot \textrm{Iterations}) \enspace . \end{eqnarray*}\]

Result🔗

dilation1Dilation1 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.

Combinations with other operators🔗

Combinations

Possible predecessors

thresholdThreshold, regiongrowingRegiongrowing, connectionConnection, union1Union1, watershedsWatersheds, class_ndim_normClassNdimNorm, gen_circleGenCircle, gen_ellipseGenEllipse, gen_rectangle1GenRectangle1, gen_rectangle2GenRectangle2, draw_regionDrawRegion, gen_region_pointsGenRegionPoints, gen_region_polygon_filledGenRegionPolygonFilled

Possible successors

reduce_domainReduceDomain, add_channelsAddChannels, select_shapeSelectShape, area_centerAreaCenter, connectionConnection

Alternatives

minkowski_add1MinkowskiAdd1, minkowski_add2MinkowskiAdd2, dilation2Dilation2

Module🔗

Foundation