Large deformation diffeomorphic metric curve mapping

摘要

We present a matching criterion for curves and integrate it into the large deformation diffeomorphic metric mapping (LDDMM) scheme for computing an optimal transformation between two curves embedded in Euclidean space R-d. Curves are first represented as vector-valued measures, which incorporate both location and the first order geometric structure of the curves. Then, a Hilbert space structure is imposed on the measures to build the norm for quantifying the closeness between two curves. We describe a discretized version of this, in which discrete sequences of points along the curve are represented by vector-valued functionals. This gives a convenient and practical way to define a matching functional for curves. We derive and implement the curve matching in the large deformation framework and demonstrate mapping results of curves in R-2 and R-3. Behaviors of the curve mapping are discussed using 2D curves. The applications to shape classification is shown and experiments with 3D curves extracted from brain cortical surfaces are presented.