This paper presents a novel approach to feature-based brain image warping, by using a hybrid implicit/explicit framework, which unifies many prior approaches in a common framework. In the first step, we develop links between image warping and the level-set method, and we formulate the fundamental mathematics required for this hybrid implicit/explicit approach. In the second step, we incorporate the large-deformation models into these formulations, leading to a complete and elegant treatment of anatomical structure matching. In this latest approach, exact matching of anatomy is achieved by comparing the target to the warped source structure under the forward mapping and the source to the warped target structure under the backward mapping. Because anatomy is represented nonparametrically, a path is constructed linking the source to the target structure without prior knowledge of their point correspondence. The final point correspondence is constructed based on the linking path with the minimal energy. Intensity-similarity measures can be naturally incorporated in the same framework as landmark constraints by combining them in the gradient descent body forces. We illustrate the approach with two applications: (1) tensor-based morphometry of the corpus callosum in autistic children; and (2) matching cortical surfaces to measure the profile of cortical anatomic variation. In summary, the new mathematical techniques introduced here contribute fundamentally to the mapping of brain structure and its variation and provide a framework that unites feature and intensity-based image registration techniques.