Nonlinear Registration Via Displacement Fields

This article presents a brief review on nonlinear registration techniques based on a variational formulation. The main advantages of this setting are its great modeling potential and its modular setting. This enables easy changes and adaptations for fine-tuning for particular applications. Furthermore, this setting also enables the integration of additional information. This can be formulated in terms of either soft or hard constraints, such as privileged handling of anatomical landmarks, local rigidity of structures, and emphasis on volume preservation or limitations of volume changes. The latter is of particular interest for one-to-one displacement fields (also known as diffeomorphic registration).

The setting is supported by a rigorous mathematical theory and can be translated into fast and stable implementations. Although the focus of this article is not on the practical realization, important concepts such as multiscale and multilevel representations and reduction of ambiguities of results based on proper regularization are also briefly discussed.