A new proposed GLCM texture feature: modified Rényi Deng entropy

This study introduces a novel gray-level co-occurrence matrix (GLCM) feature called modified Rényi–Deng entropy, denoted as \(E_{RD}^{\alpha } \left( {T_{f} } \right)\). The practical application involves the utilizations of a digital elevation model raster dataset and diagnosing melanoma dataset. \(E_{RD}^{\alpha } \left( {T_{f} } \right)\)’s performance was compared with other GLCM texture features (including entropy, angular second moment, energy, dissimilarity, contrast, homogeneity, variance, and correlation) at various scale parameters (\(\alpha =0, \alpha \to 1\), \(\alpha =2\) and \(\alpha =3\)) through Pearson correlation analysis. Visualization of all features was achieved using ArcGIS. The results demonstrate significant associations between all GLCM texture features, except for correlation, and the parametric measures of \(E_{RD}^{\alpha } \left( {T_{f} } \right)\). Notably, entropy shows the strongest correlations with \(E_{RD}^{\alpha } \left( {T_{0} } \right)\) measures, while dissimilarity and homogeneity are most closely associated with \(E_{RD}^{0} \left( {T_{1} } \right)\), \(E_{RD}^{ \to 1} \left( {T_{1} } \right)\) and \(E_{RD}^{2} \left( {T_{1} } \right)\). Entropy and \(E_{RD}^{ \to 1} \left( {T_{0} } \right)\) exhibit identical distribution patterns, given that Rényi–Deng entropy converges to Deng entropy when α → 1, and Deng entropy transitions to Shannon entropy when α → 1 and \(f=0\). Angular second moment and energy also display high correlations with \(E_{RD}^{\alpha } \left( {T_{f} } \right)\) measures, indicating that angular second moment and energy increase as \(E_{RD}^{\alpha } \left( {T_{f} } \right)\) measures decrease. In conclusion, the modified Rényi–Deng entropy effectively characterizes grid-based textural features, with the exception of correlation. Therefore, it can be employed as a GLCM texture feature by utilizing alfa scale parameters ranging from 0 to infinity.