Interactive Medical Image Registration With Multigrid Methods and Bounded Biharmonic Functions

Interactive image registration is important in some medical applications since automatic image registration is often slow and sometimes error-prone. We consider interactive registration methods that incorporate user-specified local transforms around control handles. The deformation between handles is interpolated by some smooth functions, minimizing some variational energies. Besides smoothness, we expect the impact of a control handle to be local. Therefore we choose bounded biharmonic weight functions to blend local transforms, a cutting-edge technique in computer graphics. However, medical images are usually huge, and this technique takes a lot of time that makes itself impracticable for interactive image registration. To expedite this process, we use a multigrid active set method to solve bounded biharmonic functions (BBF). The multigrid approach is for two scenarios, refining the active set from coarse to fine resolutions, and solving the linear systems constrained by working active sets. We\u27ve implemented both weighted Jacobi method and successive over-relaxation (SOR) in the multigrid solver. Since the problem has box constraints, we cannot directly use regular updates in Jacobi and SOR methods. Instead, we choose a descent step size and clamp the update to satisfy the box constraints. We explore the ways to choose step sizes and discuss their relation to the spectral radii of the iteration matrices. The relaxation factors, which are closely related to step sizes, are estimated by analyzing the eigenvalues of the bilaplacian matrices. We give a proof about the termination of our algorithm and provide some theoretical error bounds. Another minor problem we address is to register big images on GPU with limited memory. We\u27ve implemented an image registration algorithm with virtual image slices on GPU. An image slice is treated similarly to a page in virtual memory. We execute a wavefront of subtasks together to reduce the number of data transfers. Our main contribution is a fast multigrid method for interactive medical image registration that uses bounded biharmonic functions to blend local transforms. We report a novel multigrid approach to refine active set quickly and use clamped updates based on weighted Jacobi and SOR. This multigrid method can be used to efficiently solve other quadratic programs that have active sets distributed over continuous regions

Community landscapes: an integrative approach to determine overlapping network module hierarchy, identify key nodes and predict network dynamics

Background: Network communities help the functional organization and evolution of complex networks. However, the development of a method, which is both fast and accurate, provides modular overlaps and partitions of a heterogeneous network, has proven to be rather difficult. Methodology/Principal Findings: Here we introduce the novel concept of ModuLand, an integrative method family determining overlapping network modules as hills of an influence function-based, centrality-type community landscape, and including several widely used modularization methods as special cases. As various adaptations of the method family, we developed several algorithms, which provide an efficient analysis of weighted and directed networks, and (1) determine pervasively overlapping modules with high resolution; (2) uncover a detailed hierarchical network structure allowing an efficient, zoom-in analysis of large networks; (3) allow the determination of key network nodes and (4) help to predict network dynamics. Conclusions/Significance: The concept opens a wide range of possibilities to develop new approaches and applications including network routing, classification, comparison and prediction.Comment: 25 pages with 6 figures and a Glossary + Supporting Information containing pseudo-codes of all algorithms used, 14 Figures, 5 Tables (with 18 module definitions, 129 different modularization methods, 13 module comparision methods) and 396 references. All algorithms can be downloaded from this web-site: http://www.linkgroup.hu/modules.ph

Parallel Preconditioners for an Ocean Model in Climate Simulations

In this work, we evaluate different solvers and preconditioners for solving the barotropic system of an ocean model to achieve optimal performance on a high-performance computer. In the field of support theory, we derive upper bounds for the condition number of a system that is preconditioned with a block-Jacobi Steiner graph preconditioner. Furthermore, we analyze the application of a high-level approach for programming preconditioners on FPGAs

Probabilistic modeling of texture transition for fast tracking and delineation

In this thesis a probabilistic approach to texture boundary detection for tracking applications is presented. We have developed a novel fast algorithm for Bayesian estimation of texture transition locations from a short sequence of pixels on a scanline that combines the desirable speed of edge-based line search and the sophistication of Bayesian texture analysis given a small set of observations. For the cases where the given observations are too few for reliable Bayesian estimation of probability of texture change we propose an innovative machine learning technique to generate a probabilistic texture transition model. This is achieved by considering a training dataset containing small patches of blending textures. By encompassing in the training set enough examples to accurately model texture transitions of interest we can construct a predictor that can be used for object boundary tracking that can deal with few observations and demanding cases of tracking of arbitrary textured objects against cluttered background. Object outlines are then obtained by combining the texture crossing probabilities across a set of scanlines. We show that a rigid geometric model of the object to be tracked or smoothness constraints in the absence of such a model can be used to coalesce the scanline texture crossing probabilities obtained using the methods mentioned above. We propose a Hidden Markov Model to aggregate robustly the sparse transition probabilities of scanlines sampled along the projected hypothesis model contour. As a result continuous object contours can be extracted using a posteriori maximization of texture transition probabilities. On the other hand, stronger geometric constraints such as available rigid models of the target are directly enforced by robust stochastic optimization. In addition to being fast, the allure of the proposed probabilistic framework is that it accommodates a unique infrastructure for tracking of heterogeneous objects which utilizes the machine learning-based predictor as well as the Bayesian estimator interchangeably in conjunction with robust optimization to extract object contours robustly. We apply the developed methods to tracking of textured and non textured rigid objects as well as deformable body outlines and monocular articulated human motion in challenging conditions. Finally, because it is fast, our method can also serve as an interactive texture segmentation tool

Hardware-accelerated algorithms in visual computing

This thesis presents new parallel algorithms which accelerate computer vision methods by the use of graphics processors (GPUs) and evaluates them with respect to their speed, scalability, and the quality of their results. It covers the fields of homogeneous and anisotropic diffusion processes, diffusion image inpainting, optic flow, and halftoning. In this turn, it compares different solvers for homogeneous diffusion and presents a novel \u27extended\u27 box filter. Moreover, it suggests to use the fast explicit diffusion scheme (FED) as an efficient and flexible solver for nonlinear and in particular for anisotropic parabolic diffusion problems on graphics hardware. For elliptic diffusion-like processes, it recommends to use cascadic FED or Fast Jacobi schemes. The presented optic flow algorithm represents one of the fastest yet very accurate techniques. Finally, it presents a novel halftoning scheme which yields state-of-the-art results for many applications in image processing and computer graphics.Diese Arbeit präsentiert neue parallele Algorithmen zur Beschleunigung von Methoden in der Bildinformatik mittels Grafikprozessoren (GPUs), und evaluiert diese im Hinblick auf Geschwindigkeit, Skalierungsverhalten, und Qualität der Resultate. Sie behandelt dabei die Gebiete der homogenen und anisotropen Diffusionsprozesse, Inpainting (Bildvervollständigung) mittels Diffusion, die Bestimmung des optischen Flusses, sowie Halbtonverfahren. Dabei werden verschiedene Löser für homogene Diffusion verglichen und ein neuer \u27erweiterter\u27 Mittelwertfilter präsentiert. Ferner wird vorgeschlagen, das schnelle explizite Diffusionsschema (FED) als effizienten und flexiblen Löser für parabolische nichtlineare und speziell anisotrope Diffusionsprozesse auf Grafikprozessoren einzusetzen. Für elliptische diffusionsartige Prozesse wird hingegen empfohlen, kaskadierte FED- oder schnelle Jacobi-Verfahren einzusetzen. Der vorgestellte Algorithmus zur Berechnung des optischen Flusses stellt eines der schnellsten und dennoch äußerst genauen Verfahren dar. Schließlich wird ein neues Halbtonverfahren präsentiert, das in vielen Bereichen der Bildverarbeitung und Computergrafik Ergebnisse produziert, die den Stand der Technik repräsentieren

The roles of random boundary conditions in spin systems

Random boundary conditions are one of the simplest realizations of quenched disorder. They have been used as an illustration of various conceptual issues in the theory of disordered spin systems. Here we review some of these result