“…A Riemannian metric on such a space provides means to define distances between shapes, to interpolate between shapes by computing shortest geodesic paths, and to explore the space by constructing the geodesic curve starting from a point into a given direction. Shape spaces have proven useful for applications in areas such as computer graphics (Kilian et al, 2007;Heeren et al, 2012;Wang et al, 2018) and vision (Heeren et al, 2018;Xie et al, 2014), medical imaging (Kurtek et al, 2011b;Samir et al, 2014;Kurtek et al, 2016;Bharath et al, 2018), computational biology (Laga et al, 2014), and computational anatomy (Miller et al, 2006;Pennec, 2009;Kurtek et al, 2011a). For an introduction to the topic, we refer to the textbook of Younes (2010).…”