Co-occurrence matrix

A co-occurrence matrix or co-occurrence distribution is a matrix that is defined over an image to be the distribution of co-occurring pixel values (grayscale values, or colors) at a given offset. A co-occurrence matrix or co-occurrence distribution is a matrix that is defined over an image to be the distribution of co-occurring pixel values (grayscale values, or colors) at a given offset. For an image with p {displaystyle p} different pixel values, the p × p {displaystyle p imes p} co-occurrence matrix C is defined over an n × m {displaystyle n imes m} image I, parameterized by an offset ( Δ x , Δ y ) {displaystyle (Delta x,Delta y)} , as: where: i {displaystyle i} and j {displaystyle j} are the pixel values; x {displaystyle x} and y {displaystyle y} are the spatial positions in the image I; the offsets ( Δ x , Δ y ) {displaystyle (Delta x,Delta y)} define the spatial relation for which this matrix is calculated; and I ( x , y ) {displaystyle I(x,y)} indicates the pixel value at pixel ( x , y ) {displaystyle (x,y)} . The 'value' of the image originally referred to the grayscale value of the specified pixel, but could be anything, from a binary on/off value to 32-bit color and beyond. (Note that 32-bit color will yield a 232 × 232 co-occurrence matrix!) Co-occurrence matrices can also be parameterized in terms of a distance, d {displaystyle d} , and an angle, θ {displaystyle heta } , instead of an offset ( Δ x , Δ y ) {displaystyle (Delta x,Delta y)} . Any matrix or pair of matrices can be used to generate a co-occurrence matrix, though their most common application has been in measuring texture in images, so the typical definition, as above, assumes that the matrix is an image. It is also possible to define the matrix across two different images. Such a matrix can then be used for color mapping.