“…In recent decades, different OF estimation methods have been proposed, including gradient-based methods ( Awad, 2016 ; Li et al, 2018 ), slit-based approaches ( Oliveira & Leite, 2008 ), frequency domain-based estimations ( Ciezar & Pochylski, 2022 ; Park & Park, 2005 ), learning-based models ( Cao & Jain, 2018 ; Qu et al, 2018 ), and gray-level variance methods ( Dyre & Sumathi, 2017 ; Bian et al, 2019 ; Turroni et al, 2011 ). Currently, the most popular of these fingerprint image OF estimation approaches is the gradient-based method because of its high resolution, high accuracy, and low computational demand ( Turroni et al, 2011 ; Sharma & Dey, 2019 ; Ratha, Chen & Jain, 1995 ; Gottschlich, Mihailescu & Munk, 2009 ; Bazen & Gerez, 2002 ; Liu & Dai, 2006 ; Kekre & Bharadi, 2009 ; Mei, Sun & Xia, 2009 ; Wieclaw, 2013 ; Wang, Hu & Han, 2007 ; Bazen & Gerez, 2000 ).…”