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

B-splines are a well-known approach for non-rigid image registration. Though successfully applied to various medical applications they exhibit a high computational complexity mainly because of the lack of dedicated optimization methods. In this work we focus on a Levenberg-Marquardt type optimization routine. As a similarity measure we use least-squares functionals such as the sum of squared differences, the cross-correlation and the local correlation measure, respectively. The latter is used for multi-modality registration tasks. The proposed registration algorithm consists of three main parts. In each iteration step one has to (a) build a linear system of equations, (b) solve this system and compute an update, (c) determine the step length for the following iteration step. Appropriate stopping criteria ensure the termination of the registration task. A standard approach for (c) and several modifications are investigated. Using a quadratic model we are able to avoid additional execution of (b) during the step length adaption. Several solvers (Cholesky, CG, pre-conditioning) for (b) have been evaluated. Also, modifications on the most time consuming task (a) are investigated, leading to a speed-up by a factor up to 30. Finally, the algorithm is embedded in a multi-scale framework (both on image and on parameter level) providing additional regularization, an increased capture range and speed-up. Convergence tests have been successfully applied for a priori known transformations. Feasibility of the proposed approach is also shown for clinical applications including PET-CT registrations (19 data sets) and MR mammography.

B-spline registration of 3D images with Levenberg-Marquardt optimization

Image registration is central to many challenges in medical imaging today and has a vast range of applications. The purpose of this note is to provide a toolbox for intensity based non-rigid registration problems. To do so, we review some of the most promising non-linear registration strategies currently used in medical imaging and show that all these techniques may be phrased in terms of a variational problem and allow for a unified treatment.

FLIRT: A Flexible Image Registration Toolbox

We present a unified approach for the construction of polynomial wavelets. Our main tool is orthogonal polynomials. With the help of their properties we devise schemes for the construction of time localized polynomial bases on bounded and unbounded subsets of the real line. Several examples illustrate the new approach.

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Wavelets based on orthogonal polynomials

On parameter choice and iterative convergence for stabilised discretisations of advection-diffusion problems

The hypothalamus-pituitary-adrenal (HPA) system is closely related to stress and the restoration of homeostasis. This system is stimulated in the second half of the night, decreases its activity in the daytime, and reaches the homeostatic level during the late evening. In this paper, we derive and discuss a novel model for the HPA system. It is based on three simple rules that constitute a principle of homeostasis and include only the most substantive physiological elements. In contrast to other models, its main components include, apart from the conventional negative feedback ingredient, a positive feedback loop. To validate the model, we present a parameter estimation procedure that enables one to adapt the model to clinical observations. Using this methodology, we are able to show that the novel model is capable of simulating clinical trials. Furthermore, the stationary state of the system is investigated. We show that, under mild conditions, the system always has a well-defined set-point, which reflects the clinical situation to be modeled. Finally, the computed parameters may be interpreted from a physiological point of view, thereby leading to insights about diseases like depression, obesity, or diabetes.

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Bernd Fischer

Papers

B-spline registration of 3D images with Levenberg-Marquardt optimization

FLIRT: A Flexible Image Registration Toolbox

Wavelets based on orthogonal polynomials

On parameter choice and iterative convergence for stabilised discretisations of advection-diffusion problems

Modeling the hypothalamus–pituitary–adrenal system: homeostasis by interacting positive and negative feedback