This paper describes the variational formulation of template matching problems of computational anatomy (CA); introduces the EPDiff evolution equation in the context of an analogy between CA and fluid dynamics; discusses the singular solutions for the EPDiff equation and explains why these singular solutions exist (singular momentum map). Then it draws the consequences of EPDiff for outline matching problem in CA and gives numerical examples. "I shall speak of things . . . so singular in their oddity as in some manner to instruct, or at least entertain, without wearying." - Lorenzo da Ponte