Implicit Brain Imaging
Guillermo Sapiro
University of Minnesota
Mathematics
We describe how implicit surface representations can be used to address fundamental problems in brain imaging. Such representations arise naturally from state-of-the-art segmentation algorithms used to extract different brain tissues and, as shown in this work, are particularly well suited from a computational perspective.
Examples include the identification of constrained special curves on the cortex, such as sulcal beds; the regularization of surface-based measures, such as cortical thickness; and the computation of warping fields between cortical surfaces. These applications rely on the efficient solution of partial differential equations and variational problems defined on surfaces represented in implicit form.
The implicit framework eliminates the need to construct intermediate mappings between three-dimensional anatomical surfaces and parametric objects such as planes or spheres. This step, required in many alternative cortical processing approaches, is complex and may introduce additional sources of error.
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