This work describes a non-rigid registration method for open 2D manifold embedded in 3D Euclidian space. The
method is based on difference of distance maps and grid based warps interpolated by splines constrained in such
a way that the deformation field is diffeomorphic. We then create a dense surface to surface correspondence using
angle weighted normals and ray tracing. The implementation using a derivation of the inverse compositional
algorithm for optimization of computational speed is described. The results are evaluated as a shape model
showing the principal modes of variation.
We evaluate a novel method for fully automated rigid registration of 2D manifolds in 3D space based on distance
maps, the Gibbs sampler and Iterated Conditional Modes (ICM). The method is tested against the ICP considered
as the gold standard for automated rigid registration. Furthermore, the influence of different norms and sampling
point densities is evaluated. The performance of the two methods has been evaluated on data consisting of 178
scanned ear impressions taken from the right ear. To quantify the difference of the two methods we calculate
the registration cost and the mean point to point distance. T-test for common mean are used to determine
the performance of the two methods (supported by a Wilcoxon signed rank test). The performance influence of
sampling density, sampling quantity, and norms is analyzed using a similar method.
Image registration is an important task in most medical imaging applications. Numerous algorithms have been
proposed and some are widely used. However, due to the vast amount of data collected by eg. a computed
tomography (CT) scanner, most registration algorithms are very slow and memory consuming. This is a huge
problem especially in atlas building, where potentially hundreds of registrations are performed. This paper
describes an approach for accelerated image registration. A grid-based warp function proposed by Cootes and
Twining, parameterized by the displacement of the grid-nodes, is used. Using a coarse-to-fine approach, the
composition of small diffeomorphic warps, results in a final diffeomorphic warp. Normally the registration is
done using a standard gradient-based optimizer, but to obtain a fast algorithm the optimization is formulated in
the inverse compositional framework proposed by Baker and Matthews. By switching the roles of the target and
the input volume, the Jacobian and the Hessian can be pre-calculated resulting in a very efficient optimization
algorithm. By exploiting the local nature of the grid-based warp, the storage requirements of the Jacobian and
the Hessian can be minimized. Furthermore, it is shown that additional constraints on the registration, such
as the location of markers, are easily embedded in the optimization. The method is applied on volumes built
from CT-scans of pig-carcasses, and results show a two-fold increase in speed using the inverse compositional
approach versus the traditional gradient-based method.
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