Co-occurrence matrix

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Definition

If there are two matrices A and B, with same size and both with n grey-levels, then the co-occurrence matrix of A and B is a [n*n] matrix. Let the co-occurrence matrix be C, then the value in C[i][j] equals the number of appearance of this situation: A has a i value in a position while B has a j value in the same position.

Following is Matlab Codes for calculating a co-occurrence matrix mentioned above:

function M=getCoMatrix(M1,M2)
GREY_LEVEL_NUM=2;
ROW_NUM=size(M1);
ROW_NUM=ROW_NUM(1);
M=zeros(GREY_LEVEL_NUM:GREY_LEVEL_NUM);

for i=1:ROW_NUM,
for j=1:ROW_NUM,
X=M1(i, j)+1;
Y=M2(i, j)+1;
M(X, Y)=M(X, Y)+1;
end
end

Application to
A co-occurrence matrix, also referred to as a co-occurrence distribution, is defined over an image to be the distribution of co-occurring values at a given offset. Mathematically, a co-occurrence matrix C is defined over an n x m image I, parameterized by an offset (Δx,Δy), as:
[C(i,j)=\sum_^n\sum_^m\begin 1, & \mboxI(p,q)=i\mboxI(p+\Delta\ x,q+\Delta\ y)=j \\ 0, & \mbox\end]
Whether considering the intensity values of the image or various dimensions of color, the co-occurrence matrix can measure the texture of the image. Because co-occurrence matrices are typically large and sparse, various metrics of the matrix are often taken to get a more useful set of features. However, there has been some success using the raw values of the co-occurrence matrix to discriminate between image textures.

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