Operators

# dilation1 (Operator)

## Name

dilation1 — Dilate a region.

## Signature

dilation1(Region, StructElement : RegionDilation : Iterations : )

## Description

dilation1 dilates the input regions with a structuring element. By applying dilation1 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 (StructElement) and R (Region) 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 dilation of R with M. dilation1 is similar to the operator minkowski_add1, the difference is that in dilation1 the structuring element is mirrored at the origin. The position of StructElement is meaningless, since the displacement vectors are determined with respect to the center of gravity of M.

The parameter Iterations 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 (StructElement) can be generated with operators such as gen_circle, gen_rectangle1, gen_rectangle2, gen_ellipse, draw_region, gen_region_polygon, gen_region_points, 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 union1 has to be called first.

## Parallelization

• Multithreading type: reentrant (runs in parallel with non-exclusive operators).
• Automatically parallelized on tuple level.

## Parameters

Region (input_object)  region(-array) object

Regions to be dilated.

StructElement (input_object)  region object

Structuring element.

RegionDilation (output_object)  region(-array) object

Dilated regions.

Iterations (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 (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

dilation1 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.