Stefan Henn

A New Approach to Fast Elastic Alignment with Applications to Human Brain

A technique is presented for elastic alignment applicable to human brains. The transformation which minimizes the distance measure D(u) between template and reference is determined, thereby simultaneously satisfying smoothness constraints derived from an elastic potential known from the theory of kontinuum mechanics. The resulting partial differential equations, with up to 3·220 unknowns are directly solved for each voxel, that is, without interpolation, by an adapted full multigrid-method (FMG) providing a perfect alignment. For further increases of resolution, the full advantages of the FMG are maintained, that is, parallelization and linear effort with O(N), N being the number of grid-points.

Iterative Multigrid Regularization Techniques for Image Matching

In this paper, we consider the problem of matching images, i.e., to find a deformation u, which transforms a digital image into another such that the images have nearly equal gray values in every image element. The difference of the two images is measured by their L2-difference, which should be minimized. This yields a nonlinear ill conditioned inverse problem for u, so the numerical solution is quite difficult. A Tikhonov regularization method is considered to rule out discontinuous and irregular solutions to the minimization problem. An important problem is a proper choice of the regularization parameter

A multigrid approach for minimizing a nonlinear functional for digital image matching

\alpha

A Multigrid Method for a Fourth-Order Diffusion Equation with Application to Image Processing

. For the practical choice of

Computational methods for nonlinear image registration

\alpha,

A Full Curvature Based Algorithm for Image Registration

we use iterative regularization methods based on multigrid techniques. To obtain a suitable initial guess, we use an approach similar to the full multigrid (FMG) developed by Brandt [Math. Comp., 31 (1977), pp. 333--390]. The algorithms have optimal complexity: the amount of work is proportional to the number of picture elements. Finally, we present some experimental results for synthetic and real images.

A LEVENBERG-MARQUARDT SCHEME FOR NONLINEAR IMAGE REGISTRATION ∗

Abstract In this paper, we consider a multigrid application in digital image processing. Here, the problem is to find a map, which transforms an image T into another image R such that the grey level of the different images are nearly equal in every picture-element. This problem arises in the investigation of human brains. The complete inverse problem is ill posed in the sense of Hadamard and nonlinear, so the numerical solution is quite difficult. We solve the inverse problem by a Landweber iteration. In each minimization step an approximate solution for the linearized problem is computed with a multigrid method as an inner iteration. Finally, we present some experimental results for synthetic and real images.

Elastische Anpassung in der digitalen Bildverarbeitung auf mehreren Auflösungsstufen mit Hilfe von Mehrgitterverfahren

In this paper we are concerned with the efficient solution of the elliptic system

Multimodal Image Registration Using a Variational Approach

(\alpha L +\nobreak I) u =\nobreak f

Image Registration Based on Multiscale Energy Information

, where