The theoretical foundations of computational anatomy have similarities with continuum mechanics. In particular, they fall in the general framework of the Euler-Poincare Variational Priciple, which has many applications in fluid mechanics, like, for example, the analysis of waves is shallow water, colled solitons.

Computational anatomy and the way it addresses the analysis of shape has its own equations, which are not related to any physical phenomenon. They form a novel framework which is called shape mechanics. However, because the theories are structurally similar, standard notions of classical mechanics find their counterpart in computational anatomy. For example, it is possible to define least energy shape evolution, which corresponds to motion under no external forces in mechanics, and to demonstrate properties like the conservation of energy for such a system. Also valid is the conservation of momentum, which has important consequences in the characterization and description of motion. In computational anatomy, the fact that a shape can be described by the momentum of the least energy path linking it to a target shape can be used to characterize it, and serves as the basis of statistical shape analysis.