纹理特征四：NGTDM--邻域灰度差矩阵

纹理特征四：NGTDM–邻域灰度差矩阵

1. NGTDM 的解释与计算

NGTDM(Neighbourhood gray-tone difference matrix，邻域灰度差矩阵）。
定义： 假设$i=f(k,l)$是坐标为$(k,l)$上的像素值。那么点$(k,l)$的周围的平均灰度值 A i ‾ \overline{A_i} Ai​​的计算公式如下：
A i ‾ = A ‾ ( k , l ) = 1 W − 1 [ ∑ m = − d d ∑ n = − d d f ( k + m , l + n ) ] , ( m , n ) ≠ ( 0 , 0 ) \overline{A_i}=\overline{A}(k,l)=\frac{1}{W-1}[\sum_{m=-d}^d\sum_{n=-d}^{d}f(k+m,l+n)], (m,n)\neq(0,0) Ai​​=A(k,l)=W−11​[m=−d∑d​n=−d∑d​f(k+m,l+n)],(m,n)​=(0,0)
此处$d$用来定义邻域尺寸， W = ( 2 d + 1 ) 2 W=(2d+1)^2 W=(2d+1)2。
然后计算得出在NGTDM中第$i$个元素值为：
s ( i ) = ∑ ∣ i − A i ‾ ∣ , ⋅ ⋅ ⋅ ⋅ ⋅ i ∈ N i ( N i ≠ 0 ) s(i)=\sum|i-\overline{A_i}|, ·····i \in N_i (N_i \neq0) s(i)=∑∣i−Ai​​∣,⋅⋅⋅⋅⋅i∈Ni​(Ni​​=0) = 0 , ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ o t h e r w i s e =0,···············otherwise

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