Bayesian inference for structured additive regression models for large-scale problems with applications to medical imaging

In der angewandten Statistik können Regressionsmodelle mit hochdimensionalen Koeffizienten auftreten, die sich nicht mit gewöhnlichen Computersystemen schätzen lassen. Dies betrifft unter anderem die Analyse digitaler Bilder unter Berücksichtigung räumlich-zeitlicher Abhängigkeiten, wie sie innerhalb der medizinisch-biologischen Forschung häufig vorkommen. In der vorliegenden Arbeit wird ein Verfahren formuliert, das in der Lage ist, Regressionsmodelle mit hochdimensionalen Koeffizienten und nicht-normalverteilten Zielgrößen unter moderaten Anforderungen an die benötigte Hardware zu schätzen. Hierzu wird zunächst im Rahmen strukturiert additiver Regressionsmodelle aufgezeigt, worin die Limitationen aktueller Inferenzansätze bei der Anwendung auf hochdimensionale Problemstellungen liegen, sowie Möglichkeiten diskutiert, diese zu umgehen. Darauf basierend wird ein Algorithmus formuliert, dessen Stärken und Schwächen anhand von Simulationsstudien analysiert werden. Darüber hinaus findet das Verfahren Anwendung in drei verschiedenen Bereichen der medizinisch-biologischen Bildgebung und zeigt dadurch, dass es ein vielversprechender Kandidat für die Beantwortung hochdimensionaler Fragestellungen ist.In applied statistics regression models with high-dimensional coefficients can occur which cannot be estimated using ordinary computers. Amongst others, this applies to the analysis of digital images taking spatio-temporal dependencies into account as they commonly occur within bio-medical research. In this thesis a procedure is formulated which allows to fit regression models with high-dimensional coefficients and non-normal response values requiring only moderate computational equipment. To this end, limitations of different inference strategies for structured additive regression models are demonstrated when applied to high-dimensional problems and possible solutions are discussed. Based thereon an algorithm is formulated whose strengths and weaknesses are subsequently analyzed using simulation studies. Furthermore, the procedure is applied to three different fields of bio-medical imaging from which can be concluded that the algorithm is a promising candidate for answering high-dimensional problems

Applications of Simple Markov Models to Computer Vision

In this report we advocate the use of computationally simple algorithms for computer vision, operating in parallel. The design of these algorithms is based on physical constraints present in the image and object spaces. In particular, we discuss the design, implementation, and performance of a Markov Random Field based algorithm for low level segmentation. In addition to having a simple and fast implementation, the algorithm is flexible enough to allow intensity information to be fused with motion and edge information from other sources

Simultaneous motion detection and background reconstruction with a conditional mixed-state markov random field

In this work we present a new way of simultaneously solving the problems of motion detection and background image reconstruction. An accurate estimation of the background is only possible if we locate the moving objects. Meanwhile, a correct motion detection is achieved if we have a good available background model. The key of our joint approach is to define a single random process that can take two types of values, instead of defining two different processes, one symbolic (motion detection) and one numeric (background intensity estimation). It thus allows to exploit the (spatio-temporal) interaction between a decision (motion detection) and an estimation (intensity reconstruction) problem. Consequently, the meaning of solving both tasks jointly, is to obtain a single optimal estimate of such a process. The intrinsic interaction and simultaneity between both problems is shown to be better modeled within the so-called mixed-state statistical framework, which is extended here to account for symbolic states and conditional random fields. Experiments on real sequences and comparisons with existing motion detection methods support our proposal. Further implications for video sequence inpainting will be also discussed. © 2011 Springer Science+Business Media, LLC.postprin

Markov Random Field Models: A Bayesian Approach to Computer Vision Problems

The object of our study is the Bayesian approach in solving computer vision problems. We examine in particular: (i) applications of Markov random field (MRF) models to modeling spatial images; (ii) MRF based statistical methods for image restoration, segmentation, texture modeling and integration of different visual cues

Multiscale representations of Markov random fields

Caption title. "December 1992."Includes bibliographical references (leaf [4]).Supported by the Draper Laboratory IR&D Program. DL-H-418524 Supported by the Office of Naval Research. N00014-91-J-1004 Supported by the Army Research Office. DAAL03-92-G-0115 Supported by the Air Force Office of Scientific Research. AFOSR-92-J-0002 F49620-91-C-0047Mark R. Luettgen ... [et al.]

Synthetic aperture radar analysis of floating ice at Terra Nova Bay-an application to ice eddy parameter extraction

In the framework of a study of ice formation in Antarctica, synthetic aperture radar (SAR) image acquisitions were planned over Terra Nova Bay (TNB). Thanks to the European Space Agency (ESA) Third Party Mission program, Cosmo-SkyMed and Radarsat-2 images over TNB were obtained for the period of February 20 to March 20, 2015; in addition, available Sentinel-1 images for the same period were retrieved from the ESA scientific data hub. The first inspection of the images revealed the presence of a prominent eddy, i.e., an ice vortex presumably caused by the wind blowing from the continent. The important parameters of an eddy are its area and lifetime. While the eddy lifetime was easily obtained from the image sequence, the area was measured using a specific processing scheme that consists of nonlinear filtering and Markov random field segmentation. The main goal of our study was to develop a segmentation scheme to detect and measure "objects" in SAR images. In addition, the connection between eddy area and wind field was investigated using parametric and nonparametric correlation functions; statistically significant correlation values were obtained in the analyzed period. After March 15, a powerful katabatic wind completely disrupted the surface eddy