Jan Modersitzki

Numerical methods for image registration

1. Introduction 2. The Human Neuroscanning Project 3. The mathematical setting I PARAMETRIC IMAGE REGISTRATION 4. Landmark based registration 5. Principal axes based registration 6. Optimal linear registration 7. Summarizing parametric image registration II NON-PARAMETRIC IMAGE REGISTRATION 8. Non-parametric image registration 9. Elastic registration 10. Fluid registration 11. Diffusion registration 12. Curvature registration 13. Concluding remarks

Visual field representations and locations of visual areas V1/2/3 in human visual cortex

The position, surface area and visual field representation of human visual areas V1, V2 and V3 were measured using fMRI in 7 subjects (14 hemispheres). Cortical visual field maps of the central 12 deg were measured using rotating wedge and expanding ring stimuli. The boundaries between areas were identified using an automated procedure to fit an atlas of the expected visual field map to the data. All position and surface area measurements were made along the boundary between white matter and gray matter. The representation of the central 2 deg of visual field in areas V1, V2, V3 and hV4 spans about 2100 mm2 and is centered on the lateral-ventral aspect of the occipital lobes at Talairach coordinates -29, -78, -11 and 25, -80, -9. The mean area between the 2-deg and 12-deg eccentricities for the primary visual areas was: V1: 1470 mm2; V2: 1115 mm2; and V3: 819 mm2. The sizes of areas V1, V2 and V3 varied by about a factor of 2.5 across individuals; the sizes of V1 and V2 are significantly correlated within individuals, but there is a very low correlation between V1 and V3. These in vivo measurements of normal human retinotopic visual areas can be used as a reference for comparison to unusual cases involving developmental plasticity, recovery from injury, identifying homology with animal models, or analyzing the computational resources available within the visual pathways.

Curvature Based Image Registration

A fully automated, non-rigid image registration algorithm is presented. The deformation field is found by minimizing a suitable measure subject to a curvature based constraint. It is a well-known fact that non-rigid image registration techniques may converge poorly if the initial position is not sufficiently near to the solution. A common approach to address this problem is to perform a time consuming rigid pre-registration step. In this paper we show that the new curvature registration not only produces accurate and smooth solutions but also allows for an automatic rigid alignment. Thus, in contrast to other popular registration schemes, the new method no longer requires a pre-registration step. Furthermore, we present an implementation of the new scheme based on the numerical solution of the underlying Euler-Lagrange equations. The real discrete cosine transform is the backbone of our implementation and leads to a stable and fast O(N log N) algorithm, where N denotes the number of voxels. Finally, we report on some numerical test runs.

Intensity Gradient Based Registration and Fusion of Multi-modal Images

OBJECTIVES A particular problem in image registration arises for multi-modal images taken from different imaging devices and/or modalities. Starting in 1995, mutual information has shown to be a very successful distance measure for multi-modal image registration. Therefore, mutual information is considered to be the state-of-the-art approach to multi-modal image registration. However, mutual information has also a number of well-known drawbacks. Its main disadvantage is that it is known to be highly non-convex and has typically many local maxima. METHODS This observation motivates us to seek a different image similarity measure which is better suited for optimization but as well capable to handle multi-modal images. RESULTS In this work, we investigate an alternative distance measure which is based on normalized gradients. CONCLUSIONS As we show, the alternative approach is deterministic, much simpler, easier to interpret, fast and straightforward to implement, faster to compute, and also much more suitable to numerical optimization.

Ill-posed medicine?an introduction to image registration

Image registration is the process of aligning two or more images of the same scene taken at different times, from different viewpoints and/or by different sensors. Image registration is a crucial step in imaging problems where the valuable information is contained in more than one image. Here, spatial alignment is required to properly integrate useful information from the separate images. It is the goal of this paper to give an overview on modern techniques in this area. It turns out that the registration problem is an inverse problem which does require a sound regularization and the use of proper models. Also, the numerics have to be done with great care. We will comment on these issues and supplement it by real life examples.

Numerical methods for volume preserving image registration

Image registration is one of todays challenging image processing problems, particularly in medical imaging. Since the problem is ill posed, one may like to add additional information about distortions. This applies, for example, to the registration of time series of contrast-enhanced images, where variations of substructures are not related to patient motion but to contrast uptake. Here, one may only be interested in registrations which do not alter the volume of any substructure. In this paper, we discuss image registration techniques with a focus on volume preserving constraints. These constraints can reduce the non-uniqueness of the registration problem significantly. Our implementation is based on a constrained optimization formulation. Upon discretization, we obtain a large, discrete, highly nonlinear optimization problem and the necessary conditions for the solution form a discretized nonlinear partial differential equation. To solve the problem we use a variant of the sequential quadratic programming method. Finally, we present results on synthetic as well as on real-life data.

A Multilevel Method for Image Registration

In this paper we introduce a new framework for image registration. Our formulation is based on consistent discretization of the optimization problem coupled with a multigrid solution of the linear system which evolves in a Gauss--Newton iteration. We show that our discretization is

Fast inversion of matrices arising in image processing

h

Intensity gradient based registration and fusion of multi-modal images

-elliptic independent of parameter choice, and therefore a simple multigrid implementation can be used. To overcome potential large nonlinearities and to further speed up computation, we use a multilevel continuation technique. We demonstrate the efficiency of our method on a realistic highly nonlinear registration problem.

Image Registration of Sectioned Brains

In recent years, new nonlinear partial differential equation (PDE) based approaches have become popular for solving image processing problems. Although the outcome of these methods is often very promising, their actual realization is in general computationally intensive. Therefore, accurate and efficient schemes are needed. The aim of this paper is twofold. First, we will show that the three dimensional alignment problem of a histological data set of the human brain may be phrased in terms of a nonlinear PDE. Second, we will devise a fast direct solution technique for the associated structured large systems of linear equations. In addition, the potential of the derived method is demonstrated on real-life data.