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

Accurate image registration is a necessary prerequisite for many diagnostic and therapy planning procedures
where complementary information from different images has to be combined. The design of robust and reliable
non-parametric registration schemes is currently a very active research area. Modern approaches combine
the pure registration scheme with other image processing routines such that both ingredients may benefit from
each other. One of the new approaches is the combination of segmentation and registration ("segistration").
Here, the segmentation part guides the registration to its desired configuration, whereas on the other hand
the registration leads to an automatic segmentation. By joining these image processing methods it is possible
to overcome some of the pitfalls of the individual methods. Here, we focus on the benefits for the registration task.
In the current work, we present a novel unified framework for non-parametric registration combined with energy-based
segmentation through active contours. In the literature, one may find various ways to combine these image
processing routines. Here, we present the most promising approaches within the general framework. It is based
on a single variational formulation of both the registration and the segmentation part. The performance tests
are carried out for magnetic resonance (MR) images of the brain, and they demonstrate the potential of the
proposed methods.

A unified framework for joint registration and segmentation

In vielen praktischen Problemstellungen ist der Anwender nur in wenigen ausgezeichneten Bildbereichen an einer hochgenauen Registrierung interessiert. Dieser Umstand wird in der vorliegenden Arbeit konsequent umgesetzt. Es wird eine Multiresolutionsstrategie vorgestellt, die es dem Anwender erstmalig erlaubt, auf ausgewahlte Bildbereiche zu fokussieren. Das Verfahren ist in einen variationellen Kontext eingebettet und bietet einen deutlichen Geschwindigkeitsvorteil gegenuber herkommlichen Methoden. Neben der Herleitung wird die Wirkungsweise des Verfahrens beispielhaft illustriert und die Qualitat der Ergebnisse diskutiert. Es zeigt sich, dass dieser neue Ansatz den problemangepassten Einsatz variationeller Methoden in zeitkritischen Anwendungen erlaubt.

Registrierung im Fokus

In non-parametric image registration it is often not possible to work with the original resolution of the images due to high processing times and lack of memory. However, for some medical applications the information contained in the original resolution is crucial in certain regions of the image while being negligible in others. To adapt to this problem we will present an approach using tensor grids, which provide a sparser image representation and thereby allow the use of the highest image resolution locally. Applying the presented scheme to a lung ventilation estimation shows that one may considerably save on time and memory while preserving the registration quality in the regions of interest.

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Image Registration Using Tensor Grids for Lung Ventilation Studies

Image fusion or registration is central to many challenges in medical imaging today and has a vast range of applications. The purpose of this paper is to give an introduction to intensity based non-linear registration and fusion problems from a variational point of view. 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. A generic registration or fusion method depends on an appropriate chosen distance measure, a regularization, and some additional constraints. The idea of constraints is to incorporate higher level information about the expected deformation. We examine the most common constraints and show again that they may be conveniently phrased in a variational setting. As a consequence, all of discussed modules allow for fast implementations and may be combined in any favorable order. We discuss individual methods for various applications, including the registration of magnetic resonance images of a female breast subject to some volume preserving constraints.

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Image fusion and registration – a variational approach

Registration of medical images is an active field of current research. The problem is to find a transformation which aligns two given images. The resulting displacement field may be described as a linear combination of pre-selected basis functions (parametric approach), or, as in our case, it may be computed as a minimizer of a functional (non-parametric or variational approach). This functional combines a similarity measure and a smoothness term. The first one puts the comparison of the images into quantifiable terms whereas the latter one regularizes the displacement field. The minimizing task is tackled by computing the Gâteaux derivative of the functional resulting in a set of nonlinear partial differential equations for the displacement field. These equations are linearized by means of a fixed–point iteration scheme and discretized by a standard finite difference approach. A conventional variational method results in a globally smooth displacement field. However, a variety of clinical applications involve topology changes between the two images as for instance brain shift or tumor appearance or resection. For such applications a generalization of the standard method is needed which allows for localized discontinuities in the displacement field. The variational image registration approach presented here assumes a segmentation of the images into corresponding subdomains. At the interfaces between neighbouring subdomains the influence of the smoothness term can be suppressed by introducing a spatially dependent weighting function. By choosing it appropriately this allows for opening or closing of a gap between image regions. We demonstrate the capability of this new registration method by means of a one-dimensional synthetic example and a two-dimensional MR head image. However, our method can be applied to images of arbitrary dimensionality.

Bernd Fischer

Papers

A unified framework for joint registration and segmentation

Registrierung im Fokus

Image Registration Using Tensor Grids for Lung Ventilation Studies

Image fusion and registration – a variational approach

Variational Image Registration Allowing for Discontinuities in the Displacement Field