Equations for 3D Haralick Texture Feature

Notation

  --p(i,j): (i,j)th entry in a normalized gray-tone spatial dependence matrix, p(i,j) = P(i,j) / R
    * P(i,j) is the co-occurrence matrix and R is the sum of values in it, thus P(i,j) can be  considered as the joint distribution 
    of i and j, which are gray levels of the original image. The value of entry p(i,j) is supposed to be very small due to the 
    large size of the co-occurrence matrix.

  --px(i) / py(i): ith entry in the marginal-probability distribution matrix obtained by summing the rows/columns of p(i,j).

  --Ng: Number of distinct gray levels in the image.

  --px + y(k): 
    px + y(i) is the probability of co-occurrence matrix coordinates summing to x+y

  --px − y(k): 

For more information about the Textural features, please refer to [1].

Reference

• [1] R. Haralick, K. Shanmugam, and I. Dinstein, "Textural features for image classification," IEEE Transactions on Systems, Man, and Cybernetics, SMC-3, 610-621, 1973.

Textural Features

• 1) Angular Second Moment:
• 2) Contrast:
• 3) Correlation:, where u_x,u_y,σ_x,σ_y are the means and std.deviations of p_x and p_y, the partial probability density functions
• 4) Sum of the Squares of Variance:
• 5) Inverse Difference Moment:
• 6) Sum Average:
• 7) Sum Variance:
• 8) Sum Entropy:
• 9) Entropy:
• 10) Difference Variance:
• 11) Difference Entropy:
• 12) Information Measures of Correlation 1:
• 13) Information Measures of Correlation 2: f₁₃ = (1 − exp( − 2.0 | HXY2 − HXY | ))^{1 / 2}, with ,

,