“…Haralick features have received much recent attention due to the advance of machine learning and artificial intelligence algorithms capable of accurately and quickly classifying textures over a wide range of applications, such as biomedical imaging (Cao et al, 2022;Devnath et al, 2022;Feng et al, 2022;Ferro et al, 2023a;Akhter et al, 2023;Ferro et al, 2023b;Criss et al, 2023;Nakata and Siina, 2023;Prinzi et al, 2023), cybersecurity (Lunt, 1993;Chang et al, 2019;Karanja et al, 2020;Baldini et al, 2021), or crowd abnormality (Sivarajasingam et al, 2003;Lloyd et al, 2017;Naik and Gopalakrishna, 2017). However, beyond five-decade-old definitions (Haralick et al, 1973), little progress has been made on the theoretical and analytical understanding of Haralick features, deriving theoretical lower and upper bounds, the dependence of GLCM and Haralick features on image depth, and other related issues.…”