Implicit Brain Imaging

Guillermo Sapiro
University of Minnesota

We describe how implicit surface representations can be used to solve fundamental problems in brain imaging. This kind of representation is
not only natural following the state-of-the-art segmentation algorithms reported in the literature to extract the different brain
tissues, but it is also, as shown in this paper, the most appropriate one from the computational point of view. Examples are provided for
finding constrained special curves on the cortex, such as sulcal beds, regularizing surface based measures, such as cortical thickness, and
for computing warping fields between surfaces such as the brain cortex. All these result from efficiently solving partial differential
equations and variational problems on surfaces represented in implicit form. The implicit framework avoids the need to construct intermediate mappings between 3D anatomical surfaces and parametric objects such planes or spheres, a complex step that introduces errors and is required by many other cortical processing approaches.

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