# Documentation

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# offsetstrel

Morphological offset structuring element

## Description

An `offsetstrel` object represents a nonflat morphological structuring element, which is an essential part of morphological dilation and erosion operations.

A nonflat structuring element is a matrix that identifies the pixel in the image being processed and defines the neighborhood used in the processing of that pixel. A nonflat structuring element contains finite values used as additive offsets in the morphological computation. The center pixel of the matrix, called the origin, identifies the pixel in the image that is being processed. Pixels in the neighborhood with the value `-Inf` are not used in the computation.

You can only use `offsetstrel` objects with grayscale images. The matrix is of type `double`.

To create a flat structuring element, use `strel`.

## Creation

### Syntax

``SE = offsetstrel('ball',r,h)``
``SE = offsetstrel('ball',r,h,n)``
``SE = offsetstrel(offset)``

### Description

example

````SE = offsetstrel('ball',r,h)` creates a nonflat, ball-shaped structuring element whose radius in the x-y plane is `r` and whose maximum offset height is `h`. For improved performance, `offsetstrel` approximates this shape by a sequence of eight nonflat line-shaped structuring elements.```
````SE = offsetstrel('ball',r,h,n)` creates a nonflat ball-shaped structuring element, where `n` specifies the number of nonflat, line-shaped structuring elements that `offsetstrel` uses to approximate the shape. Morphological operations using ball approximations run much faster when you specify a value for `n` greater than `0`.```
````SE = offsetstrel(offset)` creates a nonflat structuring element with the additive offset specified in the matrix `offset`.```

### Input Arguments

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Radius of the ball-shaped structuring element in the x-y plane, specified as a nonnegative integer.

Data Types: `double`

Maximum offset height, specified as a real scalar.

Data Types: `double`

Number of nonflat line-shaped structuring elements used to approximate the shape, specified as a nonnegative integer.

Value of nBehavior
`n > 0``offsetstrel` uses a sequence of `n` nonflat, line-shaped structuring elements to approximate the shape. `n` must be an even number.
`n = 0``offsetstrel` does not use any approximation. The structuring element members comprise all pixels whose centers are no greater than `r` away from the origin. The corresponding height values are determined from the formula of the ellipsoid specified by `r` and `h`.

Data Types: `double`

Values to be added to each pixel location in the neighborhood when performing the morphological operation, specified as a numeric matrix. Values that are `-Inf` are not considered in the computation.

Data Types: `double`

## Properties

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Structuring element neighborhood with offsets, specified as a numeric matrix.

Data Types: `logical`

Dimensions of structuring element, specified as a nonnegative scalar.

Data Types: `double`

## Object Functions

 `decompose` Return sequence of decomposed structuring elements `reflect` Reflect structuring element `translate` Translate structuring element

## Examples

expand all

Create a ball-shaped structuring element.

`SE = offsetstrel('ball',5, 6)`
```SE = offsetstrel is a ball shaped offset structuring element with properties: Offset: [11x11 double] Dimensionality: 2 ```

View the structuring element.

`SE.Offset`
```ans = Columns 1 through 7 -Inf -Inf 0 0.7498 1.4996 2.2494 1.4996 -Inf 0.7498 1.4996 2.2494 2.9992 2.9992 2.9992 0 1.4996 2.2494 2.9992 3.7491 3.7491 3.7491 0.7498 2.2494 2.9992 3.7491 4.4989 4.4989 4.4989 1.4996 2.9992 3.7491 4.4989 5.2487 5.2487 5.2487 2.2494 2.9992 3.7491 4.4989 5.2487 5.9985 5.2487 1.4996 2.9992 3.7491 4.4989 5.2487 5.2487 5.2487 0.7498 2.2494 2.9992 3.7491 4.4989 4.4989 4.4989 0 1.4996 2.2494 2.9992 3.7491 3.7491 3.7491 -Inf 0.7498 1.4996 2.2494 2.9992 2.9992 2.9992 Columns 8 through 11 0.7498 0 -Inf -Inf 2.2494 1.4996 0.7498 -Inf 2.9992 2.2494 1.4996 0 3.7491 2.9992 2.2494 0.7498 4.4989 3.7491 2.9992 1.4996 4.4989 3.7491 2.9992 2.2494 4.4989 3.7491 2.9992 1.4996 3.7491 2.9992 2.2494 0.7498 2.9992 2.2494 1.4996 0 2.2494 1.4996 0.7498 -Inf ```