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 α T f . The practical application involves the utilizations of a digital elevation model raster dataset and diagnosing melanoma dataset. E RD α T f ’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 ( α = 0 , α → 1 , α = 2 and α = 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 α T f . Notably, entropy shows the strongest correlations with E RD α T 0 measures, while dissimilarity and homogeneity are most closely associated with E RD 0 T 1 , E RD → 1 T 1 and E RD 2 T 1 . Entropy and E RD → 1 T 0 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 α T f measures, indicating that angular second moment and energy increase as E RD α T f 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.