This chapter introduces the fluid registration scheme of Christensen and relates this to the elastic registration. Though the fluid approach is more related to a flow approach rather than to an optimization approach, the analogy becomes visible using iterative Tychonov regularization. The chapter summarizes basic conservation laws like conservation of mass and conservation of linear momentum. Assuming a Stokes fluid, the underlying partial differential equation for the fluid registration is derived. It is shown that these equations can be solved numerically, and a fluid registration algorithm is presented together with various comments and remarks concerning implementation details. Various examples and a discussion of the fluid registration are given.
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