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Fast Curvature Based Registration of
Abstract
We introduce a new non-linear registration model based on a curvature type regularizer. We show that ane linear transformations belong to the kernel of this regularizer. Consequently, an additional global registration is superuous. Furthermore, we present an implementation of the new scheme based on the numerical solution of the underlying Euler-Lagrange equations. The real DCT is the backbone of our implementation and leads to a stable and fast O(n log n) algorithm, where n denotes the number of voxels. We demonstrate the advantages of the new technique for synthetic data sets. Moreover, rst convincing results for the registration of MR-mammography images are presented.
... A popular approach is the variational-based methods, where the deformation field is obtained by minimizing an energy functional that encodes the similarity between images, and a regularization term that enforces certain properties of the deformation field to exclude suboptimal solutions [15]. Various regularizations, such as diffusion, elastic [15], and curvature [5] have been proposed to obtain smooth deformation. When dealing with non-smooth sliding motion, special regularizers have been proposed. ...
In this paper, we propose a new approach to deformable image registration that captures sliding motions. The large deformation diffeomorphic metric mapping (LDDMM) registration method faces challenges in representing sliding motion since it per construction generates smooth warps. To address this issue, we extend LDDMM by incorporating both zeroth- and first-order momenta with a non-differentiable kernel. This allows to represent both discontinuous deformation at switching boundaries and diffeomorphic deformation in homogeneous regions. We provide a mathematical analysis of the proposed deformation model from the viewpoint of discontinuous systems. To evaluate our approach, we conduct experiments on both artificial images and the publicly available DIR-Lab 4DCT dataset. Results show the effectiveness of our approach in capturing plausible sliding motion.
... 5. Now, what is necessary to remove local registration errors is the determination of the complete remaining displacement vector field. Therefore, a curvature-based non-linear registration described by a 4th order partial differential equation (PDE) is accomplished [5]. The coupled system of PDEs for the displacement fields is solved using successive approximation and discrete Fourier transform (DFT). ...
In this short note we briefly introduce a newly developed image processing chain for a 3D reconstruction of serially sectioned tissue specimens. Provided a stack of digitised transmitted light microscope colour images of cervical tissue specimens, the procedure finally results in a 3D quantification and visualisation of the tumour invasion front of the respective cervical tumour within the specimen achieving, to our knowledge, the most detailed three-dimensional reconstruction of the invasion of a solid tumour so far.
Brain image registration aims at reducing anatomical variability across subjects to create a common space for group analysis. Multi-modal approaches intend to minimize cortex shape variations along with internal structures, such as fiber bundles. These approaches require prior identification of the structures, which remains a challenging task in the absence of a complete reference atlas. We propose an extension of the Diffeomorphic Demons image registration to jointly register images and fiber bundles. In this thesis we analyze differents representations of the fiber bundles such as ordered points, clouds of points, Currents and Measures. Different distances are analyzed and implemented into the registration algorithm. To simplify white matter representation we also analyze, use and extend existing clustering algorithms. By extending the image registration to include geometric fiber bundles descriptors we hope to improve future analyses regarding both, grey and white matter. We demonstrate the efficacy of our algorithm by registering simultaneously T1 images and fiber bundles and compare results with a multi-modal T1+Fractional Anisotropy (FA) and a tensor-based registration algorithms and obtain superior performance with our approach. We provide preliminary evidence that our implementation improves the sensitivity of activation detection in fMRI group studies.
The convergence of the multiplicative multisplitting-type method for solving the linear complementarity problem with an H-matrix is discussed using classical and new results from the theory of splitting. This directly results in a sufficient condition for guaranteeing the convergence of the multiplicative multisplitting method. Moreover, the multiplicative multisplitting method is applied to the H-compatible splitting and the multiplicative Schwarz method, separately. Finally, we establish the monotone convergence of the multiplicative multisplitting method under appropriate conditions.
Die 3D-Charakterisierung des Invasionsmusters beim Plattenepithelkarzinom des Geb?rmutterhalses anhand histologischer Serienschnitte ist eine aktuelle klini-sche Fragestellung, die h?chste Anforderungen besonders an Bildverarbeitung und-analyse stellt. Die Arbeit ist Teil eines Projektes und hat die weitere Auf-kl?rung der Tumorinvasion am Beispiel des Plattenepithelkarzinoms des Geb?r-mutterhalses (Cervix Uteri) zum Ziel. Bei der Ausbreitung von Tumoren spielen viele Einzelfaktoren eine Rolle, deren Zusammenspiel sich in Variationen mor-phologisch charakterisierbarer Invasionsmuster niederschl?gt, obwohl der dersel-be Tumortyp vorliegt (hier: Plattenepithelkarzinom). Die Variationsbreite reicht dabei von einer glatten Tumor-Wirt-Grenz ?che bis hin zu di us aufgesplitter-ten Mustern, die unterschiedliche prognostische Relevanz besitzen [1]. Wichtige Einschr?nkung dieser Studien ist, da? alle morphologischen Einteilungen nur anhand einzelner histologischer Schnitte erfolgt sind. Zur genauen Analyse von Gewebevolumina mit Submillimeteraufl?sung wer-den histologische Serienschnitte als Referenzmethode angesehen. Daher wurde für unsere Fragestellung prinzipiell auf diese Technik zurückgegri en. Allerdings mu? eine Vielzahl von Artefakten (Verzerrungen, Risse, Falten, Schwankungen der HE-F?rbung) in Kauf genommen werden. Diese k?nnen bei routinem??igen Untersuchungen vom Pathologen gut toleriert werden. Für eine automatische Rekonstruktion mit Registrierung und Segmentierung resultieren daraus aber er-hebliche Anforderungen. Daher wird in der vorliegenden Arbeit ein mehrstu ges
The paper deals with the registration of pre-operative 3DCT- data to tracked intra-operative 2D-US-slices in the context of
liver surgery. To bring such a method to clinical practice, it has to be fast and robust. In order to meet these demanding
criteria, we propose two strategies. Instead of applying a time-consuming compounding process to obtain a 3D-US image, we
use the 2D-slices directly and thereby drastically reduce the complexity and enhance the robustness of the scheme. Naturally,
the surgeon does not need the same high resolution for the whole liver. We make use of this fact by applying a focusing technique
to regions of special interest. With this, we reduce the overall amount of data to register significantly without sacrificing
the accuracy in the ROIs. In contrast to other attempts, the high resolution result in the ROI is combined in a natural way
with a global deformation field to obtain a smooth registration of the whole liver. Overall we arrive at a method with a favorable
timing. The proposed algorithm was applied to four different patient data-sets and evaluated with respect to the reached vessel-overlap
on validation slices. The obtained results are very convincing and will help to bring non-linear registration techniques to
the operation theater.
Variational registration models are non-rigid and deformable imaging techniques for accurate registration of two images. As with other models for inverse problems using the Tikhonov regularization, they must have a suitably chosen regularization term as well as a data fitting term. One distinct feature of registration models is that their fitting term is always highly nonlinear and this nonlinearity restricts the class of numerical methods that are applicable. This paper first reviews the current state-of-the-art numerical methods for such models and observes that the nonlinear fitting term is mostly ‘avoided’ in developing fast multigrid methods. It then proposes a unified approach for designing fixed point type smoothers for multigrid methods. The diffusion registration model (second-order equations) and a curvature model (fourth-order equations) are used to illustrate our robust methodology. Analysis of the proposed smoothers and comparisons to other methods are given. As expected of a multigrid method, being many orders of magnitude faster than the unilevel gradient descent approach, the proposed numerical approach delivers fast and accurate results for a range of synthetic and real test images.
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