Sophisticated methods for constructing gray/white cortical manifolds from MRI
data have emerged in recent years. The reconstructed manifolds are triangulated
graphs that permit the computation of principal maximal and minimal curvature at
each point on the manifold via the fitting of the shape operator at each vertex
of the graph. We describe how dynamic programming can be used to track gyral and
sulcal principal curves corresponding to the locus path between two points with
maximal and minimal curvature respectively; a third path which is the shortest
distance between any two points irrespective of the curvature is deemed as the
geodesic. These curves are used to identify and extract cortical sub-manifolds
permitting the construction of local coordinate systems on the sub-manifold. We
can then quantify regional cortical metrics via distribution maps as a function
of these localized cortical coordinates.
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