graycomatrix

Create gray-level co-occurrence matrix from image

Syntax

glcms = graycomatrix(I)

glcms = graycomatrix(I,Name,Value,...)

[glcms,SI] = graycomatrix(___)

Description

glcms = graycomatrix(I) creates a gray-level co-occurrence matrix (GLCM) from image I. Another name for a gray-level co-occurrence matrix is a gray-level spatial dependence matrix. Also, the word co-occurrence is frequently used in the literature without a hyphen, cooccurrence.

graycomatrix creates the GLCM by calculating how often a pixel with gray-level (grayscale intensity) value i occurs horizontally adjacent to a pixel with the value j. (You can specify other pixel spatial relationships using the 'Offsets' parameter.) Each element (i,j) in glcm specifies the number of times that the pixel with value i occurred horizontally adjacent to a pixel with value j.

glcms = graycomatrix(I,Name,Value,...) returns one or more gray-level co-occurrence matrices, depending on the values of the optional name/value pairs. Parameter names can be abbreviated, and case does not matter.

[glcms,SI] = graycomatrix(___) returns the scaled image, SI, used to calculate the gray-level co-occurrence matrix. The values in SI are between 1 and NumLevels.

Examples

Create Gray-Level Co-occurrence Matrix for Grayscale Image

Read a grayscale image into the workspace.

I = imread('circuit.tif');
imshow(I)

Calculate the gray-level co-occurrence matrix (GLCM) for the grayscale image. By default, graycomatrix calculates the GLCM based on horizontal proximity of the pixels: [0 1]. That is the pixel next to the pixel of interest on the same row. This example specifies a different offset: two rows apart on the same column.

glcm = graycomatrix(I,'Offset',[2 0])

glcm = 8×8

       14205        2107         126           0           0           0           0           0
        2242       14052        3555         400           0           0           0           0
         191        3579        7341        1505          37           0           0           0
           0         683        1446        7184        1368           0           0           0
           0           7         116        1502       10256        1124           0           0
           0           0           0           2        1153        1435           0           0
           0           0           0           0           0           0           0           0
           0           0           0           0           0           0           0           0

Create Gray-Level Co-occurrence Matrix Returning Scaled Image

Create a simple 3-by-6 sample array.

I = [ 1 1 5 6 8 8; 2 3 5 7 0 2; 0 2 3 5 6 7]

I = 3×6

     1     1     5     6     8     8
     2     3     5     7     0     2
     0     2     3     5     6     7

Calculate the gray-level co-occurrence matrix (GLCM) and return the scaled image used in the calculation. By specifying empty brackets for the GrayLimits parameter, the example uses the minimum and maximum grayscale values in the input image as limits.

[glcm,SI] = graycomatrix(I,'NumLevels',9,'GrayLimits',[])

glcm = 9×9

     0     0     2     0     0     0     0     0     0
     0     1     0     0     0     1     0     0     0
     0     0     0     2     0     0     0     0     0
     0     0     0     0     0     2     0     0     0
     0     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     2     1     0
     0     0     0     0     0     0     0     1     1
     1     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     0     1

SI = 3×6

     2     2     6     7     9     9
     3     4     6     8     1     3
     1     3     4     6     7     8

Calculate GLCMs using Four Different Offsets

Read a grayscale image into the workspace.

I = imread('cell.tif');
imshow(I)

Define four offsets.

offsets = [0 1; -1 1;-1 0;-1 -1];

Calculate the GLCMs, returning the scaled image as well. Display the scaled image, performing an additional rescaling of data values to the range [0, 1].

[glcms,SI] = graycomatrix(I,'Offset',offsets);
imshow(rescale(SI))

Note how the function returns an array of four GLCMs.

whos

  Name           Size              Bytes  Class     Attributes

  I            159x191             30369  uint8               
  SI           159x191            242952  double              
  glcms          8x8x4              2048  double              
  offsets        4x2                  64  double              

Calculate Symmetric GLCM for Grayscale Image

Read a grayscale image into the workspace.

I = imread('circuit.tif');
imshow(I)

Calculate the GLCM using the Symmetric option, returning the scaled image as well. The GLCM created when you set Symmetric to true is symmetric across its diagonal, and is equivalent to the GLCM described by Haralick (1973).

[glcm,SI] = graycomatrix(I,'Offset',[2 0],'Symmetric',true);
glcm

glcm = 8×8

       28410        4349         317           0           0           0           0           0
        4349       28104        7134        1083           7           0           0           0
         317        7134       14682        2951         153           0           0           0
           0        1083        2951       14368        2870           2           0           0
           0           7         153        2870       20512        2277           0           0
           0           0           0           2        2277        2870           0           0
           0           0           0           0           0           0           0           0
           0           0           0           0           0           0           0           0

Display the scaled image, performing an additional rescaling of data values to the range [0, 1].

imshow(rescale(SI))

Input Arguments

I — Input image

2-D, real, nonsparse, numeric or logical array

Input image, specified as a 2-D, real, nonsparse, numeric or logical array.

Example:

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example:

'GrayLimits' — Range used scaling input image into gray levels

range specified by class (default) | two-element vector [low high]

Range used scaling input image into gray levels, specified as a two-element vector [low high]. If N is the number of gray levels (see parameter 'NumLevels') to use for scaling, the range [low high] is divided into N equal width bins and values in a bin get mapped to a single gray level. Grayscale values less than or equal to low are scaled to 1. Grayscale values greater than or equal to high are scaled to 'NumLevels'. If'GrayLimits' is set to [], graycomatrix uses the minimum and maximum grayscale values in I as limits, [min(I(:)) max(I(:))], for example, [0 1] for class double and [-32768 32767] for class int16.

Example:

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical

'NumLevels' — Number of gray levels

8 for numeric, 2 for binary (default) | integer

Number of gray levels, specified as an integer. For example, if NumLevels is 8, graycomatrix scales the values in I so they are integers between 1 and 8. The number of gray-levels determines the size of the gray-level co-occurrence matrix (glcm).

Example:

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical

'Offset' — Distance between the pixel of interest and its neighbor

[0 1] (default) | p-by-2 array of integers

Distance between the pixel of interest and its neighbor, specified as a p-by-2 array of integers. Each row in the array is a two-element vector, [row_offset, col_offset], that specifies the relationship, or offset, of a pair of pixels. row_offset is the number of rows between the pixel-of-interest and its neighbor. col_offset is the number of columns between the pixel-of-interest and its neighbor. Because the offset is often expressed as an angle, the following table lists the offset values that specify common angles, given the pixel distance D.

Angle	Offset
0	[0 D]
45	[-D D]
90	[-D 0]
135	[-D -D]

The figure illustrates the array: offset = [0 1; -1 1; -1 0; -1 -1]

Example:

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical

'Symmetric' — Consider ordering of values

false (default) | true

Consider ordering of values, specified as the Boolean value true or false. For example, when 'Symmetric' is set to true, graycomatrix counts both 1,2 and 2,1 pairings when calculating the number of times the value 1 is adjacent to the value 2. When 'Symmetric' is set to false, graycomatrix only counts 1,2 or 2,1, depending on the value of 'offset'.

Example:

Data Types: logical

Output Arguments

glcms — Gray-level co-occurrence matrix (or matrices)

double array

Gray-level co-occurrence matrix (or matrices), returned as an NumLevels-by-NumLevels-by-P array of class double, where P is the number of offsets in Offset.

SI — Scaled image used in calculation of GLCM

double matrix

Scaled image used in calculation of GLCM, returned as a double matrix the same size as the input image.

Algorithms

graycomatrix calculates the GLCM from a scaled version of the image. By default, if I is a binary image, graycomatrix scales the image to two gray-levels. If I is an intensity image, graycomatrix scales the image to eight gray-levels. You can specify the number of gray-levels graycomatrix uses to scale the image by using the 'NumLevels' parameter, and the way that graycomatrix scales the values using the 'GrayLimits' parameter .

The following figure shows how graycomatrix calculates several values in the GLCM of the 4-by-5 image I. Element (1,1) in the GLCM contains the value 1 because there is only one instance in the image where two, horizontally adjacent pixels have the values 1 and 1. Element (1,2) in the GLCM contains the value 2 because there are two instances in the image where two, horizontally adjacent pixels have the values 1 and 2. graycomatrix continues this processing to fill in all the values in the GLCM.

graycomatrix ignores pixel pairs if either of the pixels contains a NaN, replaces positive Infs with the value NumLevels, and replaces negative Infs with the value 1. graycomatrix ignores border pixels, if the corresponding neighbor pixel falls outside the image boundaries.

The GLCM created when 'Symmetric' is set to true is symmetric across its diagonal, and is equivalent to the GLCM described by Haralick (1973). The GLCM produced by the following syntax, with 'Symmetric' set to true

 graycomatrix(I, 'offset', [0 1], 'Symmetric', true)

is equivalent to the sum of the two GLCMs produced by the following statements where'Symmetric' is set to false.

graycomatrix(I, 'offset', [0 1], 'Symmetric', false) 
graycomatrix(I, 'offset', [0 -1], 'Symmetric', false)

References

[1] Haralick, R.M., K. Shanmugan, and I. Dinstein, "Textural Features for Image Classification", IEEE Transactions on Systems, Man, and Cybernetics, Vol. SMC-3, 1973, pp. 610-621.

[2] Haralick, R.M., and L.G. Shapiro. Computer and Robot Vision: Vol. 1, Addison-Wesley, 1992, p. 459.