ImageCooccurrence

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`ImageCooccurrence`

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ImageCooccurrence[image,n]

gives the n×n co-occurrence matrix for image.

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ImageCooccurrence[image,n,ker]

computes a co-occurrence matrix for arbitrary spatial relationships specified by a kernel ker.

Details and Options

ImageCooccurrence[image,n] returns an n×n matrix m whose elements m_ij represent the probability of all occurrences of a pixel with intensity i to the left or bottom of a pixel with intensity j, assuming all pixels to lie in one of n successive bins.
With ImageCooccurrence[image,n,ker], the co-occurrence matrix can be computed for arbitrary spatial relationships specified by a matrix ker.
The default two-dimensional kernel used by ImageCooccurrence is .
ImageCooccurrence[{image₁,image₂},…] computes the co-occurrence matrix across two images. The images must have the same dimensions.
ImageCooccurrence supports a Masking option. The default setting is Masking->All, constructing the co-occurrence matrix based on all of the image pixels.

Examples

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Basic Examples (2)Summary of the most common use cases

A co-occurrence matrix:

In[1]:=1

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https://wolfram.com/xid/0hyu2oefqhhzvwq8-w86wz9

Out[1]=1

3D profile of a co-occurrence matrix:

In[1]:=1

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https://wolfram.com/xid/0hyu2oefqhhzvwq8-182azz

Out[1]=1

Scope (4)Survey of the scope of standard use cases

Graylevel co-occurrence matrix, computed for a color image:

In[1]:=1

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https://wolfram.com/xid/0hyu2oefqhhzvwq8-642qcz

Out[1]=1

Joint histogram of two color channels of the same image:

In[1]:=1

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https://wolfram.com/xid/0hyu2oefqhhzvwq8-eb8gso

Out[1]=1

Specify a horizontally symmetric kernel:

In[1]:=1

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https://wolfram.com/xid/0hyu2oefqhhzvwq8-fh3v8u

Out[1]=1

Specify a diagonal kernel that matches the pattern of the image:

In[1]:=1

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https://wolfram.com/xid/0hyu2oefqhhzvwq8-uwfhd

Out[1]=1

Options (1)Common values & functionality for each option

Masking (1)

Use a binary mask to specify the region of interest:

In[1]:=1

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https://wolfram.com/xid/0hyu2oefqhhzvwq8-dilexn

Out[1]=1

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

Define a function that computes the Haralick texture contrast measure:

In[1]:=1

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https://wolfram.com/xid/0hyu2oefqhhzvwq8-860u67

Contrast of a checkerboard image and a flat image:

In[2]:=2

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https://wolfram.com/xid/0hyu2oefqhhzvwq8-32i90x

Out[2]=2

Haralick texture correlation measure for grayscale images:

In[1]:=1

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https://wolfram.com/xid/0hyu2oefqhhzvwq8-ntrsr3

Compute the horizontal correlation:

In[2]:=2

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https://wolfram.com/xid/0hyu2oefqhhzvwq8-1cehmx

Out[2]=2

Vertical correlation:

In[3]:=3

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https://wolfram.com/xid/0hyu2oefqhhzvwq8-sygydq

Out[3]=3

Properties & Relations (4)Properties of the function, and connections to other functions

Co-occurrence matrix of a random image:

In[1]:=1

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https://wolfram.com/xid/0hyu2oefqhhzvwq8-9dsh14

Out[1]=1

The total of all elements of the co-occurrence matrix is 1:

In[1]:=1

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https://wolfram.com/xid/0hyu2oefqhhzvwq8-vja2oh

Out[1]=1

Co-occurrence matrix of a checkerboard image:

In[1]:=1

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https://wolfram.com/xid/0hyu2oefqhhzvwq8-57nkt7

Co-occurrence matrix of a striped image using a horizontal kernel:

In[1]:=1

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https://wolfram.com/xid/0hyu2oefqhhzvwq8-kwujl3

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