Ill-posed medicine—an introduction to image registration

Fischer, Bernd; Modersitzki, Jan

doi:10.1088/0266-5611/24/3/034008

Cited by 159 publications

(99 citation statements)

References 80 publications

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“…[22]), i.e. finding the alignment of the geometries of two consecutive time frames, so to have a displacement field that maps the points on the surface of the lumen at a given time frame to the surface in the subsequent one.…”

Section: Mathematical and Numerical Formulationmentioning

confidence: 99%

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Applications of variational data assimilation in computational hemodynamics

D’Elia

Mirabella

Passerini

et al. 2012

MS&A

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The development of new technologies for acquiring measures and images in order to investigate cardiovascular diseases raises new challenges in scientific computing. These data can be in fact merged with the numerical simulations for improving the accuracy and reliability of the computational tools. Assimilation of measured data and numerical models is well established in meteorology, whilst it is relatively new in computational hemodynamics. Different approaches are possible for the mathematical setting of this problem. Among them, we follow here a variational formulation, based on the minimization of the mismatch between data and numerical results by acting on a suitable set of control variables. Several modeling and methodological problems related to this strategy are open, such as the analysis of the impact of the noise affecting the data, and the design of effective numerical solvers. In this chapter we present three examples where a mathematically sound (variational) assimilation of data can significantly improve the reliability of the numerical models. Accuracy and reliability of computational models are increasingly important features in view of the progressive adoption of numerical tools in the design of new therapies and, more in general, in the decision making process of medical doctors.

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Section: Mathematical and Numerical Formulationmentioning

confidence: 99%

“…Here we resort to an algorithm relying upon a minimization procedure [22]. The registration is performed over 3D surfaces representing the vessel at the different time frames.…”

Section: Assimilation Of Segmented Vascular Surfacesmentioning

confidence: 99%

Applications of variational data assimilation in computational hemodynamics

D’Elia

Mirabella

Passerini

et al. 2012

MS&A

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show abstract

“…The data term attempts to align the input image with the target image by maximizing a similarity measure between those, for instance mutual information, normalized gradients, cross correlation or least squares [34]. Registration is an illposed problem and the regularization terms are required to ensure a sufficiently smooth deformation field by penalizing spatially large and strongly varying deformations [18]. The minimization of (1) produces as output a deformation field maximizing the similarity measure of choice.…”

Section: A Mathematical Framework and Problem Formulationmentioning

confidence: 99%

Segmentation-Driven Image Registration-Application to 4D DCE-MRI Recordings of the Moving Kidneys

Hodneland

Hanson

Lundervold

et al. 2014

IEEE Trans. on Image Process.

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Abstract-Dynamic contrast enhanced magnetic resonance imaging (DCE-MRI) of the kidneys requires proper motion correction and segmentation to enable an estimation of glomerular filtration rate through pharmacokinetic modeling. Traditionally, co-registration, segmentation, and pharmacokinetic modeling have been applied sequentially as separate processing steps. In this paper, a combined 4D model for simultaneous registration and segmentation of the whole kidney is presented. To demonstrate the model in numerical experiments, we used normalized gradients as data term in the registration and a Mahalanobis distance from the time courses of the segmented regions to a training set for supervised segmentation. By applying this framework to an input consisting of 4D image time series, we conduct simultaneous motion correction and two-region segmentation into kidney and background. The potential of the new approach is demonstrated on real DCE-MRI data from ten healthy volunteers.

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“…Here, we focus on the special case where P, Q are diffusion regularization expressions [7,8,9,5,4,3,10,11].…”

Section: Theorem 1 Let D ∈ N and R T And W Are D-dimensional Reamentioning

confidence: 99%

A General PDE-Framework for Registration of Contrast Enhanced Images

Ebrahimi

Martel

2009

Medical Image Computing and Computer-Assisted Intervention – MICCAI 2009

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Abstract. This paper presents a general PDE-framework for registration of contrast enhanced images. The approach directly applies the idea of separating the contrast enhancement term from the images in the regularization terms. In our formulation, we stay consistent with existing non-parametric image registration techniques, however, we carry an additional contrast enhancement term throughout. A mathematically rigorous approach is pursued which can exploit various forms of regularization. In this paper, our experiments are built based on diffusion regularization for both contrast enhancement and the deformation field.

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Ill-posed medicine—an introduction to image registration

Cited by 159 publications

References 80 publications

Applications of variational data assimilation in computational hemodynamics

Applications of variational data assimilation in computational hemodynamics

Segmentation-Driven Image Registration-Application to 4D DCE-MRI Recordings of the Moving Kidneys

A General PDE-Framework for Registration of Contrast Enhanced Images

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