Deformable templates using large deformation kinematics
Christensen, G.E.; Rabbitt, R.D.; Miller, M.I.
Image Processing, IEEE Transactions on
Volume 5, Issue 10, Oct 1996 Page(s):1435 - 1447
Digital Object Identifier 10.1109/83.536892
Summary:A general automatic approach is presented for accommodating local
shape variation when mapping a two-dimensional (2-D) or
three-dimensional (3-D) template image into alignment with a
topologically similar target image. Local shape variability is
accommodated by applying a vector-field transformation to the underlying
material coordinate system of the template while constraining the
transformation to be smooth (globally positive definite Jacobian).
Smoothness is guaranteed without specifically penalizing large-magnitude
deformations of small subvolumes by constraining the transformation on
the basis of a Stokesian limit of the fluid-dynamical Navier-Stokes
equations. This differs fundamentally from quadratic penalty methods,
such as those based on linearized elasticity or thin-plate splines, in
that stress restraining the motion relaxes over time allowing
large-magnitude deformations. Kinematic nonlinearities are inherently
necessary to maintain continuity of structures during large-magnitude
deformations, and are included in all results. After initial global
registration, final mappings are obtained by numerically solving a set
of nonlinear partial differential equations associated with the
constrained optimization problem. Automatic regridding is performed by
propagating templates as the nonlinear transformations evaluated on a
finite lattice become singular. Application of the method to
intersubject registration of neuroanatomical structures illustrates the
ability to account for local anatomical variability
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