“…Following the pioneering work by Bookstein, Grenander and Bajscy [4], [8], [22], the past several years have seen an explosion in the use of template matching methods in computer vision and medical imaging [3], [14], [24], [25], [30], [33], [36]- [40], [51], [53]- [56]. These methods have enabled the systematic measurement and comparison of anatomical shapes and structures in biomedical imagery leading to better understanding of neurodevelopmental, neuropsychiatric and neurological disorders in recent years [5], [6], [11], [13], [17], [20], [42]- [48], [50], [52], [59]. The mathematical theory of Grenander's deformable template models, when applied to these problems, involves smooth invertible maps (diffeomorphisms), as presented in this context in [55], [56], [14], [41], [36] and [33].…”