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

Due to the long imaging times in SPECT, patient motion is inevitable and constitutes a serious problem for any
reconstruction algorithm. The measured inconsistent projection data leads to reconstruction artefacts which can
significantly affect the diagnostic accuracy of SPECT, if not corrected. Among the most promising attempts
for addressing this cause of artefacts, is the so-called data-driven motion correction methodology. To use this
approach it is necessary to automatically detect patient motion and to subdivide the acquired data in projection
sets accordingly. In this note, we propose three different schemes for automatically detecting patient motion. All
methods were tested on 3D academic examples with different rigid motions, motion times, and camera systems.
On the whole, every method was tested with approximately 400 to 600 test cases. One of the proposed new
methods does show promising results.

Automatic detection of abrupt patient motion in SPECT data acquisition

Registration of images is a crucial part of many medical imaging tasks. The problem is to find a transformation which aligns two given images. The resulting displacement fields may be for example described as a linear combination of pre-selected basis functions (parametric approach), or, as in our case, they may be computed as the solution of an associated partial differential equation (non-parametric approach). Here, the underlying functional consists of a 
smoothness term ensuring that the transformation is anatomically 
meaningful and a distance term describing the similarity between the two images. To be successful, the registration scheme has to be tuned for the problem under consideration. One way of incorporating user 
knowledge is the employment of weighting masks into the distance 
measure, and thereby enhancing or hiding dedicated image parts. In 
general, these masks are based on a given segmentation of both images. We present a method which generates a weighting mask for the second image, given the mask for the first image. The scheme is based on active contours and makes use of a gradient vector flow method. 
As an example application, we consider the registration of abdominal 
computer tomography (CT) images used for radiation therapy. The reference image is acquired well ahead of time and is used for setting up the radiation plan. The second image is taken just before the treatment and its processing is time-critical. We show that the proposed automatic mask generation scheme yields similar results as compared to the approach based on a pre-segmentation of both images. Hence for time-critical applications, as intra-surgery registration, we are able to significantly speed up the computation by avoiding a 
pre-segmentation of the second image.

Weighted medical image registration with automatic mask generation

In navigated liver surgery it is an important task to align intra-operative data to pre-operative planning data.
This work describes a method to register pre-operative 3D-CT-data to tracked intra-operative 2D US-slices.
Instead of reconstructing a 3D-volume out of the two-dimensional US-slice sequence we directly apply the registration
scheme to the 2D-slices. The advantage of this approach is manyfold. We circumvent the time consuming
compounding process, we use only known information, and the complexity of the scheme reduces drastically. As
the liver is a non-rigid organ, we apply non-linear techniques to take care of deformations occurring during the
intervention. During the surgery, computing time is a crucial issue. As the complexity of the scheme is proportional
to the number of acquired slices, we devise a scheme which starts out by selecting a few "key-slices" to
be used in the non-linear registration scheme. This step is followed by multi-level/multi-scale strategies and fast
optimization techniques. In this abstract we briefly describe the new method and show first convincing results.

Fast intra-operative non-linear registration of 3D-CT to tracked, selected 2D-ultrasound slices

Background: Phase-contrast MRI (PC MRI) can be used to assess blood flow dynamics noninvasively inside the human body. The acquired images can be reconstructed into flow vector fields. Traditionally, streamlines can be computed based on the vector fields to visualize flow patterns and particle trajectories. Objectives: The traditional methods may give a false impression of precision, as they do not consider the measurement uncertainty in the PC MRI images. In our prior work, we incorporated the uncertainty of the measurement into the computation of particle trajectories. Methods: As a major part of the contribution, a novel numerical scheme for solving the anisotropic Fast Marching problem is presented. A computing time comparison to state-of-the-art methods is conducted on artificial tensor fields. A visual comparison of healthy to pathological blood flow patterns is given. Results: The comparison shows that the novel anisotropic Fast Marching solver outperforms previous schemes in terms of computing time. The visual comparison of flow patterns directly visualizes large deviations of pathological flow from healthy flow. Conclusions: The novel anisotropic Fast Marching solver efficiently resolves even strongly anisotropic path costs. The visualization method enables the user to assess the uncertainty of particle trajectories derived from PC MRI images.

A Novel Anisotropic Fast Marching Method and its Application to Blood Flow Computation in Phase-contrast MRI

Parameterfreie Algorithmen im Bereich der nichtlinearen Registrierung von Schnittbilddaten weisen relativ lange Laufzeiten auf. Werden hochaufgeloste Datensatze registriert, so ergibt sich die Forderung nach effizienten und stabilen Verfahren. Hochaufgeloste Schnittbilddaten werden bei der mikroskopischen Analyse zellularer Strukturen erzeugt, um funktionelle Bilddaten von Zellverteilungen zu korrelieren. Die Bilddaten sind sehr umfangreich und weisen haufig Artefakte auf. Die Registrierung wird als Minimierungsproblem eines Funktionais aus Distanzmas und Regularisierer formuliert. Die Minimierung fuhrt zu einem System nichtlinearer partieller Differentialgleichungen, das direkt und effizient gelost wird. Nach der Registrierung konnen histologische Details erkannt und neuroanatomische Strukturen korrekt zugeordnet werden, was ohne Registrierung unmoglich ist.

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Bernd Fischer

Papers

Automatic detection of abrupt patient motion in SPECT data acquisition

Weighted medical image registration with automatic mask generation

Fast intra-operative non-linear registration of 3D-CT to tracked, selected 2D-ultrasound slices

A Novel Anisotropic Fast Marching Method and its Application to Blood Flow Computation in Phase-contrast MRI

Vollständige Rekonstruktion eines Rattenhirns aus hochaufgelösten Bildern von histologischen Serienschnitten