Table 1 Selected gray-level co-occurrence matrix (GLCM) texture measures and their abbreviations and equations
GLCM feature | Abbreviation | Formula |
|---|---|---|
Sum average | SA | \(\mathop \sum \limits_{{k = 0}}^{{2(N - 1)}} k~P_{{x + y}} (k)\) |
Entropy | Ent | \({-}\mathop \sum \limits_{{i = 0}}^{{N{-}1}} \mathop \sum \limits_{{j = 0}}^{{N{-}1}} P_{d} (i,~j)\log ~(P_{d} (i,~j))\) |
Difference entropy | DE | \({-}\mathop \sum \limits_{{k = 0}}^{{N{-}1}} P_{{x{-}y}} (k)\log (P_{{x{-}y}} (k))\) |
Sum entropy | SE | \({-}\mathop \sum \limits_{{k = 0}}^{{2\left( {N{-}1} \right)}} P_{{x + y}} (k)\log (P_{{x + y}} (k))\) |
Variance | Var | \(\mathop \sum \limits_{{i = 0}}^{{N{-}1}} \mathop \sum \limits_{{j = 0}}^{{N{-}1}} (i{-}\mu )^{2} P_{d} (i,j)\) |
Difference variance | DV | \(\mathop \sum \limits_{{k = 0}}^{{N{-}1}} \left( {k~{-}\mathop \sum \limits_{{k = 0}}^{{N{-}1}} k~P_{{x{-}y}} (k)} \right)^{2} P_{{x{-}y}} (k)\) |
Sum variance | SV | \({-}\mathop \sum \limits_{{k = 0}}^{{2(N{-}1)}} \left( {k~{-}\mathop \sum \limits_{{k = 0}}^{{2(N{-}1)}} k~P_{{x + y}} (k)} \right)^{2} P_{{x + y}} (k)\) |
Angular second moment (uniformity) | ASM | \(\mathop \sum \limits_{{i = 0}}^{{N{-}1}} \mathop \sum \limits_{{j = 0}}^{{N{-}1}} P_{d} (i,~j)^{2}\) |
Inverse difference moment | IDM | \(\mathop \sum \limits_{{i = 0}}^{{N{-}1}} \mathop \sum \limits_{{j = 0}}^{{N{-}1}} \frac{1}{{1 + (i~{-}~j)^{2} }}P_{d} (i,~j)\) |
Contrast | Con | \(\mathop \sum \limits_{{k = 0}}^{{N{-}1}} k^{2} P_{x-y} (k)\) |
Correlation | Cor | \(\mathop \sum \limits_{{i = 0}}^{{N{-}1}} \mathop \sum \limits_{{j = 0}}^{{N{-}1}} P_{d} (i,~j)\frac{{(i~{-}~~\mu _{x} )(j~{-}~\mu _{y} )}}{{\sigma _{x} \sigma _{y} }}\) |
Information measure of correlation-1 | MOC-1 | \(\frac{{HXY~{-}~HXY1}}{{\max (HX,~HY)}}\) |
Information measure of correlation-2 | MOC-2 | \([1{-}\exp\{{-}2(HXY2{-}HXY)\}]^{{1/2}}\) |