Gray level co-occurrence matrix

The co-occurrence matrix is defined by the joint probability density of pixels in two locations. It not only reflects the brightness distribution, but also reflects the location distribution between pixels with the same brightness or close to the brightness, is a second-order statistical feature related to image brightness changes. It is the basis for defining a set of texture features.

The gray-scale co-occurrence matrix of an image reflects the comprehensive information of the gray scale of the image on the direction, adjacent interval, and change amplitude. It is the basis for analyzing the local pattern of the image and their arrangement rules.

If f (x, y) is a two-dimensional digital image with the size of m × n and the gray level of NG, the gray level co-occurrence matrix meeting a certain spatial relationship is

P (I, j) = # {(x1, Y1), (X2, Y2) ε m × n | f (x1, Y1) = I, F (X2, Y2) = J}

Where # (x) indicates the number of elements in set X. Obviously, P is a ng × ng matrix. If the distance between (x1, Y1) and (X2, Y2) is D, if the angle between the two and the X-axis is θ, a gray-scale co-occurrence matrix P (I, j, D, θ) with various spacing and angles can be obtained ).

One effective method for texture feature extraction is the gray-level spatial correlation matrix, that is, the co-occurrence matrix, which is based on [7], because the image is separated (△x, △y) the co-occurrence frequency distribution of two gray pixels at the same time can be expressed using a gray-scale co-occurrence matrix. If the gray level of the image is set to N, the co-occurrence matrix is n × N, which can be expressed as M (△x, △y) (H, k), where (H, k) The mhk value of the element indicates the number of occurrences of the pixel pairs with a gray scale of H and a gray scale of K separated by (△x, △y.
For areas with coarse textures, The mhk value of the gray-scale co-occurrence matrix is concentrated near the main diagonal. For Coarse textures, pixel pairs tend to have the same gray scale. For the fine grain area, the mhk value in the gray-scale co-occurrence matrix is scattered everywhere.

To more intuitively describe texture conditions using a co-occurrence matrix, some parameters that reflect the matrix conditions are derived from the co-occurrence matrix. The following are typical examples:

(1) Energy: it is the sum of squares of the element values in the gray-scale co-occurrence matrix. Therefore, it is also called Energy, which reflects the gray-scale distribution uniformity and coarse texture fineness of the image. If all values in the co-occurrence matrix are equal, the ASM value is small. On the contrary, if some values are large and others are small, the ASM value is large. When elements in the symbiotic matrix are centrally distributed, the ASM value is large. The ASM value is large, indicating a texture pattern with uniform and regular changes.

(2) contrast: where. It reflects the definition of the image and the depth of the texture. The deeper the texture groove, the larger the contrast, the clearer the visual effect. If the contrast is small, the groove is light and the effect is blurred. The gray difference indicates that the greater the contrast, the greater the number of pixels. The larger the element value of the gray-scale common matrix, the larger the con value.

(3) correlation: it measures the similarity of gray-scale co-occurrence matrix elements in the row or column direction. Therefore, the correlation value reflects the local gray-scale correlation in the image. When the matrix element values are even and equal, the correlation value is large. On the contrary, if the matrix element values differ greatly, the correlation value is small. If the image has a horizontal texture, the CoR value of the horizontal direction matrix is greater than the CoR value of the other matrices.

(4) entropy: a measure of the amount of information in an image. Texture Information is also a measure of randomness, when all elements in the symbiosis matrix have the largest randomness and all values in the space symbiosis matrix are almost the same, the entropy is large when the elements in the symbiosis matrix are dispersed. It indicates the degree of uneven or complex texture in the image.

(5) inverse difference: it reflects the homogeneity of the Image Texture and measures the local variation of the image texture. If the value is large, the image texture does not change between different regions, and the local texture is very even.

Other parameters:

Median <mean>

Covariance <variance>

Homogeneous/inverse gaps

Contrast <contrast>

Difference <dissimilarity>

Entropy <entropy>

Second degree <angular second moment>

auto-correlation