Equations for 3D Haralick Texture Feature

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     large size of the co-occurrence matrix.
 
     large size of the co-occurrence matrix.
  
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    --<math>p_x(i)/p_y(i)</math>: ''i''th entry in the marginal-probability distribution matrix obtained by summing the rows/columns of <math>p(i,j)</math>.
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  --<math>p_x(i)/p_y(i)</math>: ''i''th entry in the marginal-probability distribution matrix obtained by summing the rows/columns of <math>p(i,j)</math>.
  
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    --<math>N_g</math>: Number of distinct gray levels in the image.
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  --<math>N_g</math>: Number of distinct gray levels in the image.
  
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     --<math>p_{x+y}(k)</math>: <math> p_{x+y}(k) = \sum_i x</math>:
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  --<math>p_{x+y}(k):</math> <math> p_{x+y}(k) = \sum_{i=0}^{N_g} \sum_{j=0,i+j=k}^{N_g} p(i,j), k=2,3,...,2N_g </math>
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  --<math>p_{x-y}(k):</math> <math> p_{x-y}(k) = \sum_{i=0}^{N_g} \sum_{j=0,|i-j|=k}^{N_g} p(i,j), k=0,1,...,N_g-1 </math>

Revision as of 02:33, 27 April 2009

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):  p_{x+y}(k) = \sum_{i=0}^{N_g} \sum_{j=0,i+j=k}^{N_g} p(i,j), k=2,3,...,2N_g 

  --px − y(k):  p_{x-y}(k) = \sum_{i=0}^{N_g} \sum_{j=0,|i-j|=k}^{N_g} p(i,j), k=0,1,...,N_g-1
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