Medical image registration is an important task in medical image processing. It refers to the process of aligning data sets, possibly from different modalities (e.g., magnetic resonance and computed tomography), different time points (e.g., follow-up scans), and/or different subjects (in case of population studies). A large number of methods for image registration are described in the literature. Unfortunately, there is not one method that works for all applications. We have therefore developed elastix, a publicly available computer program for intensity-based medical image registration. The software consists of a collection of algorithms that are commonly used to solve medical image registration problems. The modular design of elastix allows the user to quickly configure, test, and compare different registration methods for a specific application. The command-line interface enables automated processing of large numbers of data sets, by means of scripting. The usage of elastix for comparing different registration methods is illustrated with three example experiments, in which individual components of the registration method are varied.

elastix : A Toolbox for Intensity-Based Medical Image Registration

Large linear systems of saddle point type arise in a wide variety of applications throughout computational science and engineering. Due to their indefiniteness and often poor spectral properties, such linear systems represent a significant challenge for solver developers. In recent years there has been a surge of interest in saddle point problems, and numerous solution techniques have been proposed for this type of system. The aim of this paper is to present and discuss a large selection of solution methods for linear systems in saddle point form, with an emphasis on iterative methods for large and sparse problems.

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Numerical solution of saddle point problems

Deformable image registration is a fundamental task in medical image processing. Among its most important applications, one may cite: 1) multi-modality fusion, where information acquired by different imaging devices or protocols is fused to facilitate diagnosis and treatment planning; 2) longitudinal studies, where temporal structural or anatomical changes are investigated; and 3) population modeling and statistical atlases used to study normal anatomical variability. In this paper, we attempt to give an overview of deformable registration methods, putting emphasis on the most recent advances in the domain. Additional emphasis has been given to techniques applied to medical images. In order to study image registration methods in depth, their main components are identified and studied independently. The most recent techniques are presented in a systematic fashion. The contribution of this paper is to provide an extensive account of registration techniques in a systematic manner.

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Deformable Medical Image Registration: A Survey

http://www.mathcs.emory.edu/%7Ebenzi/Web_papers/survey.pdf

Preconditioning techniques for large linear systems: a survey

Barycentric interpolation is a variant of Lagrange polynomial interpolation that is fast and stable. It deserves to be known as the standard method of polynomial interpolation.

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Barycentric Lagrange Interpolation

One of the challenging tasks in today image processing is image registration. Image registration is inevitable whenever images taken for example at different times or from different perspectives need to be compared or to be integrated. Typically, the location of corresponding points in the different views of one object or even of different objects is distorted. For example, motion or different properties of the underlying optical systems (MR, CT) are responsible for the distortion. Thus, a basic problem is to find a meaningful spatial transformation of a given image, such that the transformed image becomes similar to a given second one. Typically, the transformation is computed by minimizing a suitable similarity measure. For many applications it is also desirable to guide the registration by additional information, like the locations of outstanding points. In this note, be present a general variational based approach for image registration which allows the choice of a user supplied similarity measure and a user supplied regularizer as well as the integration of external knowledge, like, for example, the location of outstanding points.

Combining landmark and intensity driven registrations

Objectives: In this paper, we propose a novel registration technique, which combines the concepts of landmark and automatic, non-rigid intensity-based approaches. A general framework, which might be used for many different registration problems is presented. The novel approach enables the incorporation of different distance measures as well as different smoothers. Methods: The proposed scheme minimizes a regularized distance measure subject to some interpolation constraints. The desired deformation is computed iteratively using an Euler-scheme for the first variation of the chosen objective functional. Results: A fast and robust numerical scheme for the computation of the wanted minimizer is developed, implemented, and applied to various registration tasks. This includes the registration of pre- and postintervention images of the human eye. Conclusions: A novel framework for a parameter-free, non-rigid registration scheme which allows for the additional incorporation of user-defined landmarks is proposed. It enhances the reliability of conventional approaches considerably and thereby their acceptability by practitioners in a clinical environment.

Intensity-based image registration with a guaranteed one-to-one point match.

We present a super-fast and parameter-free algorithm for non-rigid elastic registration of images of a serially sectioned whole rat brain. The purpose is to produce a three-dimensional high-resolution reconstruction. The registration is modelled as a minimization problem of a functional consisting of a distance measure and a regularizer based on the elastic potential of the displacement field. The minimization of the functional leads to a system of non-linear partial differential equations, the so-called Navier-Lame equations (NLE). Discretization of the NLE and a fixed point type iteration method lead to a linear system of equations, which has to be solved at each iteration step. We not only present a super-fast solution technique for this system, but also come up with sound strategies for accelerating the outer iteration. This does include a multi-scale approach based on a Gaussian pyramid as well as a clever estimation of the material constants for the elastic potential. The results of the registration process were controlled by an expert who was able to recognize histological details like laminations which was not possible before. Therefore, it is essential to apply elastic registration to this kind of imaging problem. Finally, the visually pleasing results were quantified by a distance measure leading to an improvement of about 79% after just 35 iteration steps.

Superfast elastic registration of histologic images of a whole rat brain for 3D reconstruction

We consider the problem of generating the recursion coefficients of orthogonal polynomials for a given weight function. The weight function is assumed to be the weighted sum of weight functions, each supported on its own interval. Some of these intervals may coincide, overlap or are contiguous. We discuss three algorithms. Two of them are based on modified moments, whereas the other is based on an explicit expression for the desired coefficients. Several examples, illustrating the numerical performance of the various methods, are presented.

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On generating polynomials which are orthogonal over several intervals

In this paper we present a novel 3-D free-form non-rigid registration algorithm which combines the mutual information similarity measure with a particular curvature based regularizer, which has been demonstrated to produce very satisfactory results in conjunction with the sum of squared differences distance measure. The method is evaluated for inter-subject MR brain image registration using simulated deformations and compared with a scheme that applies the same similarity measure but with a viscous fluid regularizer.

Bernd Fischer

Papers

Combining landmark and intensity driven registrations

Intensity-based image registration with a guaranteed one-to-one point match.

Superfast elastic registration of histologic images of a whole rat brain for 3D reconstruction

On generating polynomials which are orthogonal over several intervals

Free-form registration using mutual information and curvature regularization