3D deformable image matching using multiscale minimization of global energy functions

This paper presents a hierarchical framework to perform deformable matching of three dimensional (3D) images. 3D shape deformations are parameterized at different scales, using a decomposition of the continuous deformation vector field over a sequence of nested subspaces, generated from a single scaling function. The parameterization of the field enables to enforce smoothness and differentiability constraints without performing explicit regularization. A global energy function, depending on the reference image and the transformed one, is minimized via a coarse-to-fine algorithm over this multiscale decomposition. Contrary to standard multigrid approaches, no reduction of image data is applied. The continuous field of deformation is always sampled at the same resolution, ensuring that the same energy function is handled at each scale and that the energy decreases at each step of the minimization.