Gray value matrix

The co-occurrence matrix (engl. Gray level co-occurrence matrix (GLCM) or co-occurrence matrix ) is an important tool in the digital image processing .

The gray value matrix is ​​used for the recognition of textures . In the case of an image with a high-contrast surface structure, the lower left and upper right corners are heavily occupied, while an image with large monotonous areas has a strong main diagonal.

The matrix of the gray combinations is:, where describes the frequency of the gray combinations and the relation between the pixels and . ${\displaystyle {W_{S,\rho }}({g_{1}}{g_{2}})={\begin{bmatrix}{a_{{g_{1}},{g_{2}}}}\end{bmatrix}}}$ ${\displaystyle a_{{g_{1}},{g_{2}}}}$ ${\displaystyle ({g_{1}},{g_{2}})={\begin{bmatrix}s({x_{1}},{y_{1}}),s({x_{2}},{y_{2}})\end{bmatrix}}}$ ${\displaystyle \rho }$ ${\displaystyle ({x_{1}},{y_{1}})}$ ${\displaystyle ({x_{2}},{y_{2}})}$

In addition can be adapted to the elements with the boundary between the gray value of the approximate length and recognize. ${\displaystyle ({g_{1}},{g_{2}})}$ ${\displaystyle {g_{1}}\not ={g_{2}}}$ ${\displaystyle {g_{1}}}$ ${\displaystyle {g_{2}}}$

example

Starting image for the example, in greatly enlarged form. Getting lighter from 0 to 3.

The example is a picture with some monotonous areas and therefore also has a large main diagonal.

Picture with ${\displaystyle S}$

${\displaystyle G=[0,1,2,3]:{\begin{bmatrix}0&1&0&1&2&3\\0&0&1&2&2&2\\0&0&1&1&1&2\\0&1&2&2&3&3\\0&2&2&3&3&3\\2&2&2&3&3&3\\\end{bmatrix}}}$

And relation with ${\displaystyle \rho }$ ${\displaystyle \rho (x,y)=(x+1,y)}$

results in the gray value matrix

${\displaystyle {W_{S,\rho }}({g_{1}},{g_{2}})={\begin{bmatrix}(0,0)&(0,1)&(0,2)&(0,3)\\(1,0)&(1,1)&(1,2)&(1,3)\\(2,0)&(2,1)&(2,2)&(2,3)\\(3,0)&(3,1)&(3,2)&(3,3)\\\end{bmatrix}}}$

It follows:

${\displaystyle {W_{S,\rho }}({g_{1}},{g_{2}})={\begin{bmatrix}2&5&1&0\\1&2&4&0\\0&0&6&4\\0&0&0&5\\\end{bmatrix}}}$

For example, to get the entry , count how often the right neighbor of a one is a two. This occurs at the points [ ; ; ; ], so exactly four times. ${\displaystyle W(1,2)=4}$ ${\displaystyle G}$ ${\displaystyle G(0,3)}$ ${\displaystyle G(1,2)}$ ${\displaystyle G(2,4)}$ ${\displaystyle G(3,1)}$

literature

• Peter Haberäcker: Digital image processing , Hanser Verlag, ISBN 978-3446163393