Modeling Brain Anatomy with 3D Arrangements of Curves

We employ 3D arrangements of curves to represent and analyze biological shapes, in particular, the anatomy of the human brain. The arrangements of curves may vary from fairly sparse - such as a collection of sulcal lines that coarsely approximates the global shape of the brain - to very dense decompositions of the cortical surface into space curves. A space of shapes of such arrangements is constructed equipped with geodesic metrics that can be used in conjunction with curve registration techniques to quantify shape resemblance or dissimilarity, as well as to identify the regions where anatomical differences are most pronounced. The metric is applied to the panellation and labeling of configurations associated with the left and right hemispheres of the brain. Examples are also given of geodesic interpolations between decompositions into space curves of surfaces representing the entire left hemisphere of the brain.