Dilation

✖
`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, Padding0 is used for images, corresponding to pixel value 0 for all channels.

Examples

open allclose all

Basic Examples (3)Summary of the most common use cases

Dilation of a binary image:

In[1]:=1

✖

https://wolfram.com/xid/0j439g3u-0c1z44

Out[1]=1

Dilation of a grayscale image:

In[1]:=1

✖

https://wolfram.com/xid/0j439g3u-xggcoy

Out[1]=1

Dilation of a 3D shape:

In[1]:=1

✖

https://wolfram.com/xid/0j439g3u-cemqva

Out[1]=1

Scope (13)Survey of the scope of standard use cases

Data (7)

Dilation of a 2D binary array:

In[1]:=1

✖

https://wolfram.com/xid/0j439g3u-0o41u8

Dilation of a binary image:

In[1]:=1

✖

https://wolfram.com/xid/0j439g3u-cjhv08

Out[1]=1

Dilation of a numeric array:

In[1]:=1

✖

https://wolfram.com/xid/0j439g3u-dx28gs

Dilation of a numeric vector:

In[1]:=1

✖

https://wolfram.com/xid/0j439g3u-om08hy

In[2]:=2

✖

https://wolfram.com/xid/0j439g3u-6i5x1p

Out[2]=2

Dilation of a grayscale image:

In[1]:=1

✖

https://wolfram.com/xid/0j439g3u-daz3f6

Out[1]=1

Dilation of a color image:

In[1]:=1

✖

https://wolfram.com/xid/0j439g3u-9nvbmk

Out[1]=1

Dilation on a symbolic array of data:

In[1]:=1

✖

https://wolfram.com/xid/0j439g3u-ioqpw6

Out[1]=1

Parameters (6)

Dilate horizontally:

In[1]:=1

✖

https://wolfram.com/xid/0j439g3u-clylnb

Out[1]=1

Dilate vertically:

In[1]:=1

✖

https://wolfram.com/xid/0j439g3u-peee

Out[1]=1

Dilate with radius , equivalent to BoxMatrix[r]:

In[1]:=1

✖

https://wolfram.com/xid/0j439g3u-sdyn1w

Out[1]=1

Dilate with a diagonal structuring element:

In[1]:=1

✖

https://wolfram.com/xid/0j439g3u-brpwj8

Out[1]=1

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

In[1]:=1

✖

https://wolfram.com/xid/0j439g3u-mxexwk

Out[1]=1

Dilate a 3D volume using a 3D kernel:

In[1]:=1

✖

https://wolfram.com/xid/0j439g3u-yrg1gy

Out[1]=1

Options (2)Common values & functionality for each option

Padding (2)

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

In[1]:=1

✖

https://wolfram.com/xid/0j439g3u-wifq5d

Out[1]=1

Specify a custom padding:

In[2]:=2

✖

https://wolfram.com/xid/0j439g3u-1lxavm

Out[2]=2

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

In[1]:=1

✖

https://wolfram.com/xid/0j439g3u-m3hb9l

In[2]:=2

✖

https://wolfram.com/xid/0j439g3u-rzmg3t

Out[2]=2

Specify a custom padding:

In[3]:=3

✖

https://wolfram.com/xid/0j439g3u-vm3kbp

Out[3]=3

Applications (2)Sample problems that can be solved with this function

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

In[1]:=1

✖

https://wolfram.com/xid/0j439g3u-fp261r

Out[1]=1

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

In[1]:=1

✖

https://wolfram.com/xid/0j439g3u-fd8j67

Out[1]=1

Properties & Relations (2)Properties of the function, and connections to other functions

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

In[1]:=1

✖

https://wolfram.com/xid/0j439g3u-d7vgl7

In[2]:=2

✖

https://wolfram.com/xid/0j439g3u-5tg1pq

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

In[3]:=3

✖

https://wolfram.com/xid/0j439g3u-pqq2qk

Out[3]=3

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

In[1]:=1

✖

https://wolfram.com/xid/0j439g3u-jm6ubz

Out[1]=1

Possible Issues (1)Common pitfalls and unexpected behavior

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

In[1]:=1

✖

https://wolfram.com/xid/0j439g3u-4tis0c

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

In[2]:=2

✖

https://wolfram.com/xid/0j439g3u-8g6rxg

Out[2]=2

Top