“…The optimization based deformable registration methods can be divided into two categories (Oliveira and Tavares, 2014; Sotiras et al, 2013): intensity-based (Johnson and Christensen, 2002; Klein et al, 2010; Myronenko and Song, 2010; Tang et al, 2018, 2019; Vercauteren et al, 2009) and feature-based (Auzias et al, 2011; Avants et al, 2008; Ou et al, 2011; Shen and Davatzikos, 2002; Wu et al, 2014, 2010). The deformable registration is often based on linear (rigid/affine) registration (Fan et al, 2016a,b 2017), where the linear registration intends to globally align the two images and the deformation registration is used to correct the local deformations. But unlike linear registration, deformable registration is an often ill-posed high-dimensional optimization problem.…”