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ImageCooccurrence[image,n]

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

ImageCooccurrence[image,n,ker]

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

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Options  
Masking  
Applications  
Properties & Relations  
See Also
Related Guides
History
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ImageCooccurrence

ImageCooccurrence[image,n]

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

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 mij 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)

A co-occurrence matrix:

Wolfram Language code: MatrixPlot[ImageCooccurrence[[image], 32]]

3D profile of a co-occurrence matrix:

Wolfram Language code: ListPlot3D[ ImageCooccurrence[[image], 32], Mesh -> False, Boxed -> False, Axes -> None, ColorFunction -> "DarkBands"]

Scope  (4)

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

Wolfram Language code: MatrixPlot[ImageCooccurrence[[image], 16]]

Joint histogram of two color channels of the same image:

Wolfram Language code: MatrixPlot[ImageCooccurrence[{[image], [image]}, 16, {{1}}]]

Specify a horizontally symmetric kernel:

Wolfram Language code: MatrixPlot[ImageCooccurrence[[image], 32, {{1, 0, 1}}]]

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

Wolfram Language code: MatrixPlot[ImageCooccurrence[[image], 32, (⁠| | | | | - | - | - | | 1 | 0 | 0 | | 0 | 0 | 0 | | 0 | 0 | 0 |⁠)]]

Options  (1)

Masking  (1)

Use a binary mask to specify the region of interest:

Wolfram Language code: MatrixPlot[ImageCooccurrence[[image], 16, Masking -> [image]]]

Applications  (2)

Define a function that computes the Haralick texture contrast measure:

Wolfram Language code: contrast[image_] := Total[Table[(i - j) ^ 2, {i, 256}, {j, 256}] * ImageCooccurrence[image, 256] / 255 ^ 2, 2];

Contrast of a checkerboard image and a flat image:

Wolfram Language code: {contrast[[image]], contrast[[image]]}

Haralick texture correlation measure for grayscale images:

Wolfram Language code: correlation[image_, ker_] := Module[{miux, mt, m, miuy, stdx, stdy, cm = ImageCooccurrence[image, 256, ker], in = Range[256]}, {m, mt} = Total /@ {cm, Transpose[cm]}; {miuy, miux} = {m.in, mt.in}; {stdy, stdx} = {((in - miuy) ^ 2).m, ((in - miux) ^ 2).mt}; (Total[KroneckerProduct[in, in] * cm, 2] - miux * miuy) / Sqrt[stdx * stdy]]

Compute the horizontal correlation:

Wolfram Language code: correlation[[image], {{0, 0, 1}}]

Vertical correlation:

Wolfram Language code: correlation[[image], {{0}, {0}, {1}}]

Properties & Relations  (4)

Co-occurrence matrix of a random image:

Wolfram Language code: ImageCooccurrence[Image[RandomReal[1, {200, 200}]], 16]// MatrixPlot

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

Wolfram Language code: Total@Flatten[ImageCooccurrence[[image], 100]]

Co-occurrence matrix of a checkerboard image:

Wolfram Language code: ImageCooccurrence[[image], 5] // MatrixForm

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

Wolfram Language code: ImageCooccurrence[[image], 5, {{0, 0, 1}}]//MatrixForm
Wolfram Research (2010), ImageCooccurrence, Wolfram Language function, https://reference.wolfram.com/language/ref/ImageCooccurrence.html.

Text

Wolfram Research (2010), ImageCooccurrence, Wolfram Language function, https://reference.wolfram.com/language/ref/ImageCooccurrence.html.

CMS

Wolfram Language. 2010. "ImageCooccurrence." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ImageCooccurrence.html.

APA

Wolfram Language. (2010). ImageCooccurrence. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ImageCooccurrence.html

BibTeX

@misc{reference.wolfram_2026_imagecooccurrence, author="Wolfram Research", title="{ImageCooccurrence}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/ImageCooccurrence.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_imagecooccurrence, organization={Wolfram Research}, title={ImageCooccurrence}, year={2010}, url={https://reference.wolfram.com/language/ref/ImageCooccurrence.html}, note=[Accessed: 12-June-2026]}