minkowski_sub1 (Operator)

Name

`minkowski_sub1` — Erode a region.

Signature

`minkowski_sub1(Region, StructElement : RegionMinkSub : Iterations : )`

Description

`minkowski_sub1` computes the Minkowski subtraction of the input regions with a structuring element. By applying `minkowski_sub1` 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 Minkowski subtraction is a set-theoretic region operation. It uses the intersection 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 intersection of all these translations is the Minkowski subtraction of R with M. `minkowski_sub1` is similar to the operator `erosion1`, the difference is that in `erosion1` 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 the maximum 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.

Execution Information

• 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 eroded.

`StructElement` (input_object)  region `→` object

Structuring element.

`RegionMinkSub` (output_object)  region(-array) `→` object

Eroded 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

`minkowski_sub1` returns 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

`threshold`, `regiongrowing`, `connection`, `union1`, `watersheds`, `class_ndim_norm`, `gen_circle`, `gen_ellipse`, `gen_rectangle1`, `gen_rectangle2`, `draw_region`, `gen_region_points`, `gen_region_polygon_filled`

Possible Successors

`reduce_domain`, `select_shape`, `area_center`, `connection`

Alternatives

`minkowski_sub2`, `erosion1`

`transpose_region`