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Table 2 The calculation formulas of first-order gray features

From: Intelligent localization and quantitative evaluation of anterior talofibular ligament injury using magnetic resonance imaging of ankle

Characteristic parameters

Calculation formulas

Mean value

\(\mu = \sum\limits_{i = 0}^{L - 1} {iH(i)}\)

Variance

\(\sigma^{2} = \sum\limits_{i = 0}^{L - 1} {(\mu - i)^{2} H(i)}\)

Skewness

\(H_{s} = \frac{1}{{\sigma^{3} }}\sum\limits_{i = 0}^{L - 1} {(\mu - i)^{3} H(i)}\)

Kurtosis

\(H_{k} = \frac{1}{{\sigma^{4} }}\sum\limits_{i = 0}^{L - 1} {(\mu - i)^{4} H(i) - 3}\)

Energy

\(H_{e} = \sum\limits_{i = 0}^{L - 1} {H(i)^{2} }\)

Entropy

\(H_{t} = - \sum\limits_{i = 0}^{L - 1} {H(i)\log_{2} (H(i))}\)

Proportion of high signal pixels

\(P = \frac{1}{N}\sum\limits_{i = L/2}^{L - 1} {n_{i} }\)

Grayscale corresponding to the right peak

\(Gs = g(\max \{ n_{r} \} , \, r = 50, \ldots ,L - 1)\)