Image registration is an important enabling technology in medical image analysis. The current emphasis is on development and validation of application-specific non-rigid techniques, but there is already a plethora of techniques and terminology in use. In this paper we discuss the current state of the art of non-rigid registration to put on-going research in context and to highlight current and future clinical applications that might benefit from this technology. The philosophy and motivation underlying non-rigid registration is discussed and a guide to common terminology is presented. The core components of registration systems are described and outstanding issues of validity and validation are confronted.

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Non-rigid image registration: theory and practice

Computerized Image Registration approaches can offer automatic and accurate image alignments without extensive user involvement and provide tools for visualizing combined images. The aim of this survey is to present a review of publications related to Medical Image Registration. This paper paints a comprehensive picture of image registration methods and their applications. This paper is an introduction for those new to the ﬁeld, an overview for those working in the ﬁeld and a reference for those searching for literature on a speciﬁc application. Methods are classiﬁed according to the diﬀerent aspects of Medical Image Registration.

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Survey of Medical Image Registration

Medical image analysis

In this paper, we extend a previously reported intensity-based nonrigid registration algorithm by using a novel regularization term to constrain the deformation. Global motion is modeled by a rigid transformation while local motion is described by a free-form deformation based on B-splines. An information theoretic measure, normalized mutual information, is used as an intensity-based image similarity measure. Registration is performed by searching for the deformation that minimizes a cost function consisting of a weighted combination of the image similarity measure and a regularization term. The novel regularization term is a local volume-preservation (incompressibility) constraint, which is motivated by the assumption that soft tissue is incompressible for small deformations and short time periods. The incompressibility constraint is implemented by penalizing deviations of the Jacobian determinant of the deformation from unity. We apply the nonrigid registration algorithm with and without the incompressibility constraint to precontrast and postcontrast magnetic resonance (MR) breast images from 17 patients. Without using a constraint, the volume of contrast-enhancing lesions decreases by 1%-78% (mean 26%). Image improvement (motion artifact reduction) obtained using the new constraint is compared with that obtained using a smoothness constraint based on the bending energy of the coordinate grid by blinded visual assessment of maximum intensity projections of subtraction images. For both constraints, volume preservation improves, and motion artifact correction worsens, as the weight of the constraint penalty term increases. For a given volume change of the contrast-enhancing lesions (2% of the original volume), the incompressibility constraint reduces motion artifacts better than or equal to the smoothness constraint in 13 out of 17 cases (better in 9, equal in 4, worse in 4). The preliminary results suggest that incorporation of the incompressibility regularization term improves intensity-based free-form nonrigid registration of contrast-enhanced MR breast images by greatly reducing the problem of shrinkage of contrast-enhancing structures while simultaneously allowing motion artifacts to be substantially reduced.

Volume-preserving nonrigid registration of MR breast images using free-form deformation with an incompressibility constraint

A methodology for estimating the force distribution that occurs along a needle shaft during insertion is described. An experimental system for measuring planar tissue phantom deformation during needle insertions has been developed and is presented. A two-dimensional linear elastostatic material model, discretised using the finite element method, is used to derive contact force information that is not directly measurable. This approach provides a method for quantifying the needle forces and soft tissue deformations that occur during general needle trajectories in multiple dimensions. The needle force distribution is used for graphical and haptic real-time simulations of needle insertion. Since the force displacement relationship is required only along the needle, a condensation technique is shown to achieve very fast interactive simulations. Stiffness matrix changes corresponding to changes in boundary conditions and material coordinate frames are performed using low-rank matrix updates.

Needle insertion modeling and simulation

The accuracy of image-guided neurosurgery generally suffers from brain deformations due to intraoperative changes. These deformations cause significant changes of the anatomical geometry (organ shape and spatial interorgan relations), thus making intraoperative navigation based on preoperative images error prone. In order to improve the navigation accuracy, the authors developed a biomechanical model of the human head based on the finite element method, which can be employed for the correction of preoperative images to cope with the deformations occurring during surgical interventions. At the current stage of development, the two-dimensional (2-D) implementation of the model comprises two different materials, though the theory holds for the three-dimensional (3-D) case and is capable of dealing with an arbitrary number of different materials. For the correction of a preoperative image, a set of homologous landmarks must be specified which determine correspondences. These correspondences can be easily integrated into the model and are maintained throughout the computation of the deformation of the preoperative image. The necessary material parameter values have been determined through a comprehensive literature study. The authors' approach has been tested for the case of synthetic images and yields physically plausible deformation results. Additionally, they carried out registration experiments with a preoperative MR image of the human head and a corresponding postoperative image simulating an intraoperative image. The authors found that their approach yields good prediction results, even in the case when correspondences are given in a relatively small area of the image only.

Biomechanical modeling of the human head for physically based, nonrigid image registration

Coupling of fluid and elastic models for biomechanical simulations of brain deformations using FEM.

The accuracy of image-guided neurosurgery generally suffers from brain deformations due to intraoperative changes, e.g., brain shift or tumor resection. In order to improve the accuracy, we developed a biomechanical model of the human head which can be employed for the correction of preoperative images. By now, the model comprises two different materials. The correction of the preoperative image is driven by a set of given landmark correspondences. Our approach has been tested using synthetic images and yields physically plausible results. Additionally, we carried out registration experiments with a preoperative MR image and a corresponding postoperative image simulating an intra-operative image. We found, that our approach yields good prediction results, even in the case when correspondences are given in a small area of the image only.

Nonrigid matching of tomographic images based on a biomechanical model of the human head

In order to improve the accuracy of image-guided neurosurgery, different biomechanical models have been developed to correct preoperative images w.r.t. intraoperative changes like brain shift or tumor resection. All existing biomechanical models simulate different anatomical structures by using either appropriate boundary conditions or by spatially varying material parameter values, while assuming the same physical model for all anatomical structures. In general, this leads to physically implausible results, especially in the case of adjacent elastic and fluid structures. Therefore, we propose a new approach which allows to couple different physical models. In our case, we simulate rigid, elastic, and fluid regions by using the appropriate physical description for each material, namely either the Navier equation or the Stokes equation. To solve the resulting differential equations, we derive a linear matrix system for each region by applying the finite element method (FEM). Thereafter, the linear matrix systems are linked together, ending up with one overall linear matrix system. Our approach has been tested using synthetic as well as tomographic images. It turns out from experiments, that the integrated treatment of rigid, elastic, and fluid regions significantly improves the prediction results in comparison to a pure linear elastic model.© (2000) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Biomechanically based simulation of brain deformations for intraoperative image correction: coupling of elastic and fluid models

The accuracy of image-guided neurosurgery generally suffers from brain deformations due to intraoperative changes, e.g. brain shift or tumor resection. In order to improve the accuracy, we developed a biomechanical model of the human head which can be employed for the correction of preoperative images. By now, the model comprises two different materials while the correction of the preoperative image is driven by a set of given landmark correspondences. Our approach has been tested on synthetic images and yields physically plausible results. Additionally, we carried out registration experiments with a preoperative MR image and a corresponding postoperative image simulating an intraoperative image. We found, that our approach yields good prediction results, even in the case when correspondences are given in a small area of the image only.

Alexander Hagemann

Papers

Biomechanical modeling of the human head for physically based, nonrigid image registration

Coupling of fluid and elastic models for biomechanical simulations of brain deformations using FEM.

Nonrigid matching of tomographic images based on a biomechanical model of the human head

Biomechanically based simulation of brain deformations for intraoperative image correction: coupling of elastic and fluid models

A Biomechanical Model of the Human Head for Elastic Registration of MR-Images