Abstract
A measure of deformation energy suitable for fitting deformable
models to image data is described. An object's displacement is
constrained to be globally smooth by penalizing the variation of the
deformation gradient tensor. This homogeneous deformation measure is
invariant to arbitrary rigid body motion of object and viewpoint, given
the correspondence between model and data. It remains quadratic in the
displacement parameters, leading to linear-least-squares fits. The
method was used to reconstruct the nonhomogeneous 3-D motion of the
heart wall from tomographic magnetic resonance images. A finite-element
model of the left ventricle was deformed to fit material points tracked
in biplanar views. Only the in-plane components were available from each
separate image, the through-plane components being reconstructed in the
fit
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