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Non-Linear Image Registration on PC-Clusters Using Parallel FFT Techniques
Abstract
Reliable image registration is a key problem within the three-dimensional reconstruction of data obtained by two-dimensional image stacks. Here, a parallel implementation of the so-called elastic matching algorithm approach is presented. This algorithm is based on a fixpointtype iteration, where in each step a linear system of equations has to be solved. To compute the solution of the linear systems fast fourier techniques are used. The algorithm as well as some numerical examples are presented.
... If we want to preserve and visualize histologic details like the lamination pattern of the cerebral cortex images of a minimal size of 512×512 pixels must be registered. Therefore, Modersitzki (1999, 2001) have developed a fast solver based on the inverse Fast Fourier Transform that was also implemented in parallel on a high performance cluster (Böhme et al., 2002). ...
Image registration is a fundamental task in today’s medical imaging. In particular for histological serial sectioning, where a three-dimensional object is cut into thin sections for a further microscopic analysis, registration leads to a three-dimensional reconstruction of the sections. This reconstruction enables an exploration of the digitized data in any direction, not only in the cutting direction. We describe cutting and reconstruction procedures. For the reconstruction, we use linear as well as nonlinear registration schemes. Moreover, we present some results for a whole brain of a Sprague Dawley rat.
... If we want to preserve and visualize histologic details like the lamination pattern of the cerebral cortex images of a minimal size of 512×512 pixels must be registered. Therefore, Modersitzki (1999, 2001) have developed a fast solver based on the inverse Fast Fourier Transform that was also implemented in parallel on a high performance cluster (Böhme et al., 2002). ...
The physical (microtomy), optical (microscopy), and radiologic (tomography) sectioning of biological objects and their digitization lead to stacks of images. Due to the sectioning process and disturbances, movement of objects during imaging for example, adjacent images of the image stack are not optimally aligned to each other. Such mismatches have to be corrected automatically by suitable registration methods.
Here, a whole brain of a Sprague Dawley rat was serially sectioned and stained followed by digitizing the 20 μm thin histologic sections. We describe how to prepare the images for subsequent automatic intensity based registration. Different registration schemes are presented and their results compared to each other from an anatomical and mathematical perspective. In the first part we concentrate on rigid and affine linear methods and deal only with linear mismatches of the images. Digitized images of stained histologic sections often exhibit inhomogenities of the gray level distribution coming from staining and/or sectioning variations. Therefore, a method is developed that is robust with respect to inhomogenities and artifacts. Furthermore we combined this approach by minimizing a suitable distance measure for shear and rotation mismatches of foreground objects after applying the principal axes transform. As a consequence of our investigations, we must emphasize that the combination of a robust principal axes based registration in combination with optimizing translation, rotation and shearing errors gives rise to the best reconstruction results from the mathematical and anatomical view point.
Because the sectioning process introduces nonlinear deformations to the relative thin histologic sections as well, an elastic registration has to be applied to correct these deformations.
In the second part of the study a detailed description of the advances of an elastic registration after affine linear registration of the rat brain is given. We found quantitative evidence that affine linear registration is a suitable starting point for the alignment of histologic sections but elastic registration must be performed to improve significantly the registration result. A strategy is presented that enables to register elastically the affine linear preregistered~ rat brain sections and the first one hundred images of serial histologic sections through both occipital lobes of a human brain (6112 images). Additionally, we will describe how a parallel implementation of the elastic registration was realized. Finally, the computed force fields have been applied here for the first time to the morphometrized data of cells determined automatically by an image analytic framework.
In this article, we present a parallel algorithm for intensity-based elastic image registration. This algorithm integrates several components: parallel octrees, multigrid preconditioning, a Gauss-Newton-Krylov solver, and grid continuation. We use a non-parametric deformation model based on trilinear finite element shape functions defined on octree meshes. Our C++ based implementation uses the Message Passing Interface (MPI) standard and is built on top of the Dendro and PETSc libraries. We demonstrate the performance of our method on synthetic and medical images. We demonstrate the scalability of our implementation on up to 4096 processors on the Sun Constellation Linux Cluster "Ranger" at the Texas Advanced Computing Center (TACC).
Das Ziel des Human Neuroscanning Projects ist die dreidimensionale Rekonstruktion der neuronalen Verteilung in einem menschlichen Gehirn auf der Basis hochaufgelöster histologischer Schnittbilder. Eine Zuordnung der aus den Schnitten abgeleiteten Daten zu ihren originaren Positionen erfordert eine nicht-lineare Registrierung der Schnitte.
Wir stellen ein auf globaler Bildinformation basierendes Verfahren zur Minimierung der mittleren Grauwertdistanz vor. Die Deformation wird, um die physikalischen Eigenschaften des Gewebes zu modellieren, als im physikalischen Sinne elastisch angenommen (elastische Deformation). Ein auf FFT-Techniken basierendes, schnelles Verfahren zur Berechnung der Deformation und dessen parallele Umsetzung wird präsentiert.
This thesis treats different methods and theoretical aspects of the calculus of variations and their applications in image processing, especially those in which gradient flows for the minimization of the variational problems are used. The focus lies on geometrical methods for image registration, as well as numerical methods for computing the solution for an implicit variant of Willmore flow (level set method). The problem of image registration aims at finding a suitable correspondence map by means of a deformation of one image domain to the other, such that significant structures are overlaid correctly. In practical applications, these images are often aquired by different sensors and hence yield different image modalities.
Image registration plays an important role in the clinical evaluation of medical data as for example from computed tomography or magnetic resonance imaging, as well as diagnosis and surgery planning. The proposed method aims at an alignment of geometrical descriptors instead of merely comparing image intensities. In particular, the approach is morphological (contrast invariant).
Registration methods are in general ill-posed inverse problems, hence regularization methods are necessary. In order to ensure a robust and stable minimization process, three complementary regularization strategies are incorporated and linked to each other, namely multiscale methods, Tikhonov-regularization and regularized gradient flows. The latter are based on the definition of a regularizing metric, that is used to define the representation of the regularized gradient of the energy functional. Furthermore, a nonlinear polyconvex and hyperelastic energy functional that takes the role of the Tikhonov-regularization functional allows to devise an existence proof of the geometric registration approach.
The theoretical justification of the multiscale approach is given by the study of the variational convergence of the regularized functionals by means of Gamma-convergence. In order to further stabilize the registration process, a new Mumford-Shah-based method to align significant edges is proposed. It aims the simultaneous process of registration, segmentation (feature detection) and image restoration, since these processes typically interdepend on each other.
Here, two different approaches are proposed, numerically incorporated and compared: a phase-field approach, that is based on the Ambrosio-Tortorelli approximation of the Mumford-Shah functional and a corresponding level set approach. The minimization of the Willmore functional via a semi-implicit numerical scheme is
applied to the recontruction of destroyed regions of surfaces that are given by a level set representation. The introduction of an implicit narrow band method allows a significant acceleration of the geometrical evolution.
The first component of this work is a parallel algorithm for constructing non-uniform octree meshes for finite element computations. Prior to octree meshing, the linear octree data structure must be constructed and a constraint known as "2:1 balancing" must be enforced; parallel algorithms for these two subproblems are also presented. The second component of this work is a parallel matrix-free geometric multigrid algorithm for solving elliptic partial differential equations (PDEs) using these octree meshes. The last component of this work is a parallel multiscale Gauss Newton optimization algorithm for solving the elastic image registration problem. The registration problem is discretized using finite elements on octree meshes and the parallel geometric multigrid algorithm is used as a preconditioner in the Conjugate Gradient (CG) algorithm to solve the linear system of equations formed in each Gauss Newton iteration. Several ideas were used to reduce the overhead for constructing the octree meshes. These include (a) a way to lower communication costs by reducing the number of synchronizations and reducing the communication message size, (b) a way to reduce the number of searches required to build element-to-vertex mappings, and (c) a compression scheme to reduce the memory footprint of the entire data structure. To our knowledge, the multigrid algorithm presented in this work is the only matrix-free multiplicative geometric multigrid implementation for solving finite element equations on octree meshes using thousands of processors. The proposed registration algorithm is also unique; it is a combination of many different ideas: adaptivity, parallelism, fast optimization algorithms, and fast linear solvers. All the algorithms were implemented in C++ using the Message Passing Interface (MPI) standard and were built on top of the PETSc library from Argonne National Laboratory. The multigrid implementation has been released as an open source software: Dendro. Several numerical experiments were performed to test the performance of the algorithms. These experiments were performed on a variety of NSF TeraGrid platforms. Our largest run was a highly-nonuniform, 8-billion-unknown, elasticity calculation on 32,000 processors. Ph.D. Committee Chair: Vuduc, Richard; Committee Member: Biros, George; Committee Member: Davatzikos, Christos; Committee Member: Tannenbaum, Allen; Committee Member: Zhou, Hao Min
Serial histologic sections of a whole human brain may have extensions of up to 130 x 130 mm within the coronal plane around the temporal lobe. To date, however, technology has not provided a bright field microscope that is able to shift the object holder continuously in the x- and y-direction over such distances and still possess the same optical capabilities as comparable devices. We developed a new light microscope to continuously quantify such sections. We also developed the computing environment for controlling the device and for analyzing the data produced. In principle, we are now able to quantify each neuron of a human brain. The data ultimately will provide the most detailed structural information about the human brain ascertained thus far. Such detailed information of the spatial distribution of neurons is essential to develop realistic models for simulation of large-scale neuronal networks and to investigate the significance of neuronal arrangements with respect to neuronal signal processing in the CNS. After preprocessing of the data produced by the new microscope, we are able to detect lamination patterns in the spatial distribution of gravity centers of cells. Furthermore, morphological features like size of the projection area and mean staining intensity are visualized as a particle process. The particle process presents the sizes and staining intensity of perikaryons and allows a distinction of gray matter and white matter. These results provide evidence that the system works correctly and can be applied to a systematic analysis of a larger sequence of serial histologic sections. The objective of this study is to introduce the very large section analyzing microscope (VLSAM) and to present the initial data produced by the system. Moreover, we will discuss workload and future developments of the parallel image analysis system that are associated with the microscope.
Prior knowledge on the space of possible images is given in the form of a function or template in some domain. The set of all possible true images is assumed to be formed by a composition of that function with continuous mappings of the domain into itself. A prior Gaussian distribution is given on the set of continuous mappings. The observed image is assumed to be a degradation of the true image with additive noise. Given the observed image, a posterior distribution is then obtained and has the form of a nonlinear perturbation of the Gaussian measure on the space of mappings. We present simulations of the posterior distribution that lead to structural reconstructions of the true image in the sense that it enables us to determine landmarks and other characteristic features of the image, as well as to spot pathologies in it. Moreover, we show that the reconstruction algorithm is relatively robust when the images are degraded by noise that is not necessarily additive.
The Myrinet local area network employs the same technology used
for packet communication and switching within massively parallel
processors. In realizing this distributed MPP network, we developed
specialized communication channels, cut-through switches, host
interfaces, and software. To our knowledge, Myrinet demonstrates the
highest performance per unit cost of any current LAN
Part 1 Introduction: heterogeneous network computing trends in distributed computing PVM overview other packages. Part 2 The PVM system. Part 3 Using PVM: how to obtain the PVM software setup to use PVM setup summary starting PVM common startup problems running PVM programs PVM console details host file options. Part 4 Basic programming techniques: common parallel programming paradigms workload allocation porting existing applications to PVM. Part 5 PVM user interface: process control information dynamic configuration signalling setting and getting options message passing dynamic process groups. Part 6 Program examples: fork-join dot product failure matrix multiply one-dimensional heat equation. Part 7 How PVM works: components messages PVM daemon libpvm library protocols message routing task environment console program resource limitations multiprocessor systems. Part 8 Advanced topics: XPVM porting PVM to new architectures. Part 9 Troubleshooting: geting PVM installed getting PVM running compiling applications running applications debugging and tracing debugging the system. Appendices: history of PVM versions PVM 3 routines.
In recent years, new nonlinear partial differential equation (PDE) based approaches have become popular for solving image
processing problems. Although the outcome of these methods is often very promising, their actual realization is in general
computationally intensive. Therefore, accurate and efficient schemes are needed. The aim of this paper is twofold. First,
we will show that the three dimensional alignment problem of a histological data set of the human brain may be phrased in
terms of a nonlinear PDE. Second, we will devise a fast direct solution technique for the associated structured large systems
of linear equations. In addition, the potential of the derived method is demonstrated on real-life data.
The registration of image volumes has been described in several publications for different imaging modalities, such as MRI, PET, SPECT and CT. However, for the 3-D alignment of histology and MRI investigations concerning the influence of local nonlinear distortions are required. A non-iterative and noninteractive least-squares 3-D affine transformation with trilinear interpolation in conjunction with a correlation-based 3-D searching algorithm was developed in order to estimate the influence of local deformations and the number of reference points with respect to the best transformation parameters. The application of the implemented software is demonstrated with data from human brains, which were visualized using magnetic resonance imaging and subsequently in histological sections. The procedures are presented with a discussion of quantitative error analysis for assessing the usefulness of the transformation under real conditions, e.g., the projections of the surface reconstructions in three orthogonal directions revealed a misalignment of 1.9, 2.9 and 3.1%, respectively.
This paper presents both worst case and average case analysis of roundoff errors occuring in the floating point computation of fast Fourier transform (FFT) with precomputed twiddle factors and shows the strong influence of precomputation errors on the numerical stability of FFT. Numerical tests confirm the theoretical results.
The classical principal-axes transformation (PAT) has been used in numerous publications for three-dimensional (3-D) reconstructions by sequential alignment of histological sections. However, the PAT can determine at most 1/2n(n + 1) parameters (scaling-rotation) in n dimensions. Distortions (shearing) of histological sections can be described by an affine transformation with n2 parameters. An analytical model is devised for calculating rotational and scaling errors which can be determined by relating the transformation parameters of the PAT to the exact solution of a singular value decomposition (SVD) of the perturbation matrix. The results show that form and deformation of the form are intertwined and that these results can be transferred to real data. The model is important for assessing the quality that can be expected with the PAT for 3-D reconstructions if no multimodality reference is available (rigid transformation) and reveals the misalignment in terms of rotational and scaling errors resulting from the PAT as derived in a previously published paper.
Thesis (D. Sc.)--Washington University, 1994. Dept. of Electrical Engineering. Vita. Includes bibliographical references.
We present the concept of non-rigid matching based on demons, by
reference to Maxwell's demons. We contrast this concept with the more
conventional viewpoint of attraction. We show that demons and attractive
points are clearly distinct for large deformations, but also that they
become similar for small displacements, encompassing techniques close to
optical flow. We describe a general iterative matching method based on
demons, and derive from it three different non-rigid matching
algorithms, one using all the image intensities, one using only
contours, and one for already segmented images. At last, we present
results with synthesized and real deformations, with applications to
Computer Vision and Medical Image Processing
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