Table 3 The calculation formulas of second-order texture features

Angular second moment

\(Asm = \sum\limits_{i = 0}^{L - 1} {\sum\limits_{j = 0}^{L - 1} {[p(i,j)]^{2} } }\)

Contrast

\(Con = \sum\limits_{i = 0}^{L - 1} {\sum\limits_{j = 0}^{L - 1} {p(i,j)(i - j)^{2} } }\)

Entropy

\(Ent = - \sum\limits_{i = 0}^{L - 1} {\sum\limits_{j = 0}^{L - 1} {p(i,j)\log p(i,j)} }\)

Inverse differential moment

\(Idm = \sum\limits_{i = 0}^{L - 1} {\sum\limits_{j = 0}^{L - 1} {\frac{p(i,j)}{{1 + (i - j)^{2} }}} }\)

Correlation

\(Cor = \frac{1}{{\sigma_{x} \sigma_{y} }}\sum\limits_{i = 0}^{L - 1} {\sum\limits_{j = 0}^{L - 1} {[p(i,j)ij]} - \mu_{x} \mu_{y} }\) where \(\mu_{x} = \sum\limits_{i = 0}^{L - 1} {\sum\limits_{j = 0}^{L - 1} {ip(i,j)} }\), \(\mu_{y} = \sum\limits_{i = 0}^{L - 1} {\sum\limits_{j = 0}^{L - 1} {jp(i,j)} }\) \(\sigma_{x} = \sum\limits_{i = 0}^{L - 1} {\sum\limits_{j = 0}^{L - 1} {(i - \mu_{x} )^{2} p(i,j)} }\),\(\sigma_{y} = \sum\limits_{i = 0}^{L - 1} {\sum\limits_{j = 0}^{L - 1} {(j - \mu_{y} )^{2} p(i,j)} }\)