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Table 3 Extraction of twenty-two GLCM features

From: A probabilistic segmentation and entropy-rank correlation-based feature selection approach for the recognition of fruit diseases

Feature name Equation
Auto correlation \(\widetilde {\phi ^{R}}=\sum _{k}\sum _{l}(k\times l)P(k,l)\)
Contrast \(\widetilde {\phi ^{C}}=\sum _{k=1}^{\phi ^{\Gamma }}\sum _{l=1}^{\phi ^{\Gamma }}|k-l|^{2}P(k,l) \)
Correlation 1 \(\widetilde {\phi ^{R_{1}}}=\sum _{k=0}^{\phi ^{\Gamma }-1}\sum _{l=0}^{\phi ^{\Gamma }-1}(k\times l)P(k,l)-\phi ^{\mu _{x}}\phi ^{\mu _{y}} \)
Correlation 2 \(\widetilde {\phi ^{R_{2}}}=\frac {\sum _{k=0}^{\phi ^{\Gamma }-1}\sum _{l=0}^{\phi ^{\Gamma }-1}(k-\phi ^{\mu _{k}})(l-\phi ^{\mu _{l}})P(k,l)}{\sigma }\)
Cluster prominence \(\widetilde {\phi ^{\mathbb {P}}}=\sum _{k=0}^{\phi ^{\Gamma }-1}\sum _{l=0}^{\phi ^{\Gamma }-1}\{k+l-\phi ^{\mu _{x}}-\phi ^{\mu _{y}}\}^{4}P(k,l)\)
Cluster shade \(\widetilde {\phi ^{S}}=\sum _{k=0}^{\phi ^{\Gamma }-1}\sum _{l=0}^{\phi ^{\Gamma }-1}\{k+l-\phi ^{\mu _{x}}\phi ^{\mu _{y}}\}^{3}P(k,l)\)
Dissimilarity \(\widetilde {\phi ^{D}}=\sum _{k}\sum _{l}P(k,l)|k-l|\)
Energy \(\widetilde {\phi ^{\mathbb {E}}}=\sum _{k}\sum _{l} P(k,l)^{2}\)
Entropy \(\widetilde {\phi ^{H}}=\sum _{k}\sum _{l} P(k,l)logP(k,l)\)
Homogeneity 1 \(\widetilde {\phi ^{\alpha _{1}}}=\frac {\sum _{k}^{\phi ^{\Gamma }-1}\sum _{l}^{\phi ^{\Gamma }-1}P(k,l)}{1+|k-l|}\)
Homogeneity 2 \(\widetilde {\phi ^{\alpha _{2}}}=\frac {\sum _{k}^{\phi ^{\Gamma }-1}\sum _{l}^{\phi ^{\Gamma }-1}P(k,l)}{1+(k-l)^{2}}\)
Maximum probability \(\widetilde {\phi ^{P}}=max_{k,l}\ P(k,l)\)
Sum of squares (variance) \(\widetilde {\phi ^{\sum {\hat \sigma ^{2}}}}=\sum _{k=0}^{\phi ^{\Gamma }-1}\sum _{l=0}^{\phi ^{\Gamma }-1} (k-\phi ^{\mu })^{2} P(k,l)\)
Sum average \(\widetilde {\phi ^{\sum \mathbb {A}}}=\sum _{k=2}^{2\phi ^{\Gamma }-2}k P_{x+y}(k)\)
Sum entropy \( \widetilde {\phi ^{\sum {H}}}=-\sum _{k=2}^{2\phi ^{\Gamma }-2}P_{x+y}(k)log(P_{k+l}(k))\)
Sum variance \(\widetilde {\phi ^{\sum \sigma ^{2}}}= \sum _{k=2}^{2\phi ^{\Gamma }-2}(k-\widetilde {\phi ^{H}})P_{x+y}(k) \)
Difference variance \(\widetilde {\phi ^{\bar {\sigma ^{2}}}}=\sigma ^{2}(P_{x-y})\)
Difference entropy \(\widetilde {\phi ^{\breve {H}}} = -\sum _{k=0}^{\phi ^{\Gamma }-1}P_{k-l}(k)log\{P_{k-l}(k)\}\)
Information measure of correlation 1 \(\widetilde {\phi ^{MR_{1}}}=\frac {\widetilde {\phi ^{H}}-H_{xy1}}{max(H_{x},H_{y})} \)
Information measure of correlation 2 \(\widetilde {\phi ^{MR_{2}}}=\sqrt {(1-exp\left [-2.0\left (H_{xy2}-\widetilde {\phi ^{H}}\right)\right ]}\)
Inverse difference normalized \(\widetilde {\phi ^{D^{-1}}}=\sum _{k} \sum _{l}\frac {P(k,l)}{1+\frac {|k-l|}{\phi ^{\Gamma }}}\)
Inverse difference moment normalized \(\widetilde {\phi ^{DM^{-1}}}=\sum _{k} \sum _{l}\frac {P(k,l)}{1+\frac {(k-l)^{2}}{\phi ^{\Gamma }}}\)