# Documentation

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# imdilate

## Syntax

IM2 = imdilate(IM,SE)
IM2 = imdilate(IM,NHOOD)
IM2 = imdilate(___,PACKOPT)
IM2 = imdilate(___,SHAPE)
gpuarrayIM2 = imdilate(gpuarrayIM,___)

## Description

IM2 = imdilate(IM,SE) dilates the grayscale, binary, or packed binary image IM, returning the dilated image, IM2. The argument SE is a structuring element object, or array of structuring element objects, returned by the strel or offsetstrel function.

If IM is logical, the structuring element must be flat and imdilate performs binary dilation. Otherwise, imdilate performs grayscale dilation. If SE is an array of structuring element objects, imdilate performs multiple dilations of the input image, using each structuring element in succession.

IM2 = imdilate(IM,NHOOD) dilates the image IM, where NHOOD is a matrix of 0's and 1's that specifies the structuring element neighborhood. This is equivalent to the syntax imdilate(IM,strel(NHOOD)). The imdilate function determines the center element of the neighborhood by floor((size(NHOOD)+1)/2).

IM2 = imdilate(___,PACKOPT) specifies whether IM is a packed binary image. PACKOPT can have either of the following values. Default value is enclosed in braces ({}).

Value

Description

'ispacked'

IM is treated as a packed binary image as produced by bwpack. IM must be a 2-D uint32 array and SE must be a flat 2-D structuring element. If the value of PACKOPT is 'ispacked', PADOPT must be 'same'.

{'notpacked'}

IM is treated as a normal array.

IM2 = imdilate(___,SHAPE) specifies the size of the output image. SHAPE can have either of the following values. Default value is enclosed in braces ({}).

Value

Description

{'same'}

Make the output image the same size as the input image. If the value of PACKOPT is 'ispacked', SHAPE must be 'same'.

'full'

Compute the full dilation.

gpuarrayIM2 = imdilate(gpuarrayIM,___) performs the operation on a graphics processing unit (GPU), where gpuarrayIM is a gpuArray that contains a grayscale or binary image. gpuarrayIM2 is a gpuArray of the same class as the input image. Note that the PACKOPT syntax is not supported on a GPU. This syntax requires the Parallel Computing Toolbox™.

Code Generation support: Yes.

MATLAB Function Block support: Yes.

## Class Support

IM can be logical or numeric and must be real and nonsparse. It can have any dimension. If IM is logical, SE must be flat. The output has the same class as the input. If the input is packed binary, then the output is also packed binary.

gpuarrayIM must be a gpuArray of type uint8 or logical. When used with a gpuarray, the structuring element must be flat and two-dimensional. The output has the same class as the input.

## Examples

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Read a binary image into the workspace.

Create a vertical line shaped structuring element.

se = strel('line',11,90);

Dilate the image with a vertical line structuring element and compare the results.

BW2 = imdilate(BW,se);
imshow(BW), title('Original')
figure, imshow(BW2), title('Dilated')

Read grayscale image into the workspace.

Create a nonflat ball-shaped structuring element.

se = offsetstrel('ball',5,5);

Dilate the image.

dilatedI = imdilate(originalI,se);

Display the original image and the dilated image.

figure
imshow(originalI)
figure
imshow(dilatedI)

Create two flat, line-shaped structuring elements, one at 0 degrees and the other at 90 degrees.

se1 = strel('line',3,0)
se2 = strel('line',3,90)
se1 =

strel is a line shaped structuring element with properties:

Neighborhood: [1 1 1]
Dimensionality: 2

se2 =

strel is a line shaped structuring element with properties:

Neighborhood: [3×1 logical]
Dimensionality: 2

Dilate the scalar value 1 with both structuring elements in sequence, using the 'full' option.

composition = imdilate(1,[se1 se2],'full')
composition =

1     1     1
1     1     1
1     1     1

Create a logical 3D volume with two points.

BW = false(100,100,100);
BW(25,25,25) = true;
BW(75,75,75) = true;

Dilate the 3D volume using a spherical structuring element.

se = strel('sphere',25);
dilatedBW = imdilate(BW,se);

Visualize the dilated image volume.

figure
isosurface(dilatedBW)

Create a structuring element.

se = strel('line',11,90);

Dilate the image with a vertical line structuring element and compare the results. Note how the example passes the image to the gpuArray function as it passes it to imdilate.

dilatedBW = imdilate(gpuArray(originalBW),se);
figure, imshow(originalBW), figure, imshow(dilatedBW)

Create a structuring element.

se = strel('disk',5);

Dilate a grayscale image with a rolling ball structuring element.

dilatedI = imdilate(gpuArray(originalI),se);
figure, imshow(originalI), figure, imshow(dilatedI)

## Definitions

The binary dilation of A by B, denoted $A\oplus B$, is defined as the set operation:

$A\oplus B=\left\{z|{\left(\stackrel{^}{B}\right)}_{z}\cap A\ne \varnothing \right\},$

where $\stackrel{^}{B}$ is the reflection of the structuring element B. In other words, it is the set of pixel locations z, where the reflected structuring element overlaps with foreground pixels in A when translated to z. Note that some people use a definition of dilation in which the structuring element is not reflected.

In the general form of gray-scale dilation, the structuring element has a height. The gray-scale dilation of A(x,y) by B(x,y) is defined as:

$\left(A\oplus B\right)\left(x,y\right)=\mathrm{max}\left\{A\left(x-{x}^{\prime },y-{y}^{\prime }\right)+B\left({x}^{\prime },{y}^{\prime }\right)|\left({x}^{\prime },{y}^{\prime }\right)\in {D}_{B}\right\},$

where DB is the domain of the structuring element B and A(x,y) is assumed to be −∞ outside the domain of the image. To create a structuring element with nonzero height values, use the syntax strel(nhood,height), where height gives the height values and nhood corresponds to the structuring element domain, DB.

Most commonly, gray-scale dilation is performed with a flat structuring element (B(x,y) = 0). Gray-scale dilation using such a structuring element is equivalent to a local-maximum operator:

$\left(A\oplus B\right)\left(x,y\right)=\mathrm{max}\left\{A\left(x-{x}^{\prime },y-{y}^{\prime }\right)|\left({x}^{\prime },{y}^{\prime }\right)\in {D}_{B}\right\}.$

All of the strel syntaxes except for strel(nhood,height), strel('arbitrary',nhood,height), and strel('ball', ...) produce flat structuring elements.

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### Code Generation

This function supports the generation of C code using MATLAB® Coder™. Note that if you choose the generic MATLAB Host Computer target platform, the function generates code that uses a precompiled, platform-specific shared library. Use of a shared library preserves performance optimizations but limits the target platforms for which code can be generated. For more information, see Understanding Code Generation with Image Processing Toolbox.

When generating code, note the following:

• The input image, IM, must be 2-D or 3-D.

• The structuring element argument SE must be a single element—arrays of structuring elements are not supported. To obtain the same result as that obtained using an array of structuring elements, call the function sequentially.

• When the target is MATLAB Host Computer, the PACKOPT and SHAPE arguments must be compile-time constants. When the target is any other platform, the PACKOPT syntax is not supported.

### MATLAB Function Block

You can use this function in the MATLAB Function Block in Simulink.

### Algorithms

imdilate automatically takes advantage of the decomposition of a structuring element object (if it exists). Also, when performing binary dilation with a structuring element object that has a decomposition, imdilate automatically uses binary image packing to speed up the dilation.

Dilation using bit packing is described in [3].

## References

[1] Gonzalez, R. C., R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLAB, Gatesmark Publishing, 2009.

[2] Haralick, R. M., and L. G. Shapiro, Computer and Robot Vision, Vol. I, Addison-Wesley, 1992, pp. 158-205.

[3] van den Boomgard, R, and R. van Balen, "Methods for Fast Morphological Image Transforms Using Bitmapped Images," Computer Vision, Graphics, and Image Processing: Graphical Models and Image Processing, Vol. 54, Number 3, pp. 254-258, May 1992.