# Dilation

Dilation[image,ker]

gives the morphological dilation of image with respect to the structuring element ker.

Dilation[image,r]

gives the dilation with respect to a range-r square.

Dilation[data,]

applies dilation to an array of data.

# Details and Options • Dilation is also known as Minkowski addition.
• Dilation works with arbitrary 2D and 3D images, operating separately on each channel, as well as data arrays of any rank.
• The structuring element ker is a matrix containing s and s.
• Dilation[image,r] is equivalent to Dilation[image,BoxMatrix[r]].
• The structuring element is automatically padded with zeros to have odd dimensions. »
• Dilation takes a Padding option that specifies the values to assume for pixels outside the image.
• By default, Padding0 is used for images, corresponding to pixel value 0 for all channels.

# Examples

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## Basic Examples(3)

Dilation of a binary image:

Dilation of a grayscale image:

Dilation of a 3D shape:

## Scope(13)

### Data(7)

Dilation of a 2D binary array:

Dilation of a binary image:

Dilation of a numeric array:

Dilation of a numeric vector:

Dilation of a grayscale image:

Dilation of a color image:

Dilation on a symbolic array of data:

### Parameters(6)

Dilate horizontally:

Dilate vertically:

Dilate with radius , equivalent to BoxMatrix[r]:

Dilate with a diagonal structuring element:

Structuring elements with even dimensions are right-padded with zeros:

Dilate a 3D volume using a 3D kernel:

## Options(2)

By default, the smallest possible number is used for padding when applying dilation to arrays:

By default, Padding->0 is used for images:

## Applications(2)

Dilation increases the amount of white space in the image, therefore removing smaller, dark features:

Compute external morphological gradient as a difference between dilated and original image:

## Properties & Relations(2)

Binary dilation is extensive if the center of the structuring element is 1:

Extensivity means that all elements of f are included in the Dilation[f,ker]:

Dilation with a box structuring element is the same as MaxFilter:

## Possible Issues(1)

Image dilation with a kernel of all zeros will result in a zero image:

Array dilation with an all-zero kernel will result in an array of :