Tomographie A Partir D Un Nombre Limite De Projections Regularisation Par Des Champs Markoviens

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Bayesian Approach to Inverse Problems

Many scientific, medical or engineering problems raise the issue of recovering some physical quantities from indirect measurements; for instance, detecting or quantifying flaws or cracks within a material from acoustic or electromagnetic measurements at its surface is an essential problem of non-destructive evaluation. The concept of inverse problems precisely originates from the idea of inverting the laws of physics to recover a quantity of interest from measurable data. Unfortunately, most inverse problems are ill-posed, which means that precise and stable solutions are not easy to devise. Regularization is the key concept to solve inverse problems. The goal of this book is to deal with inverse problems and regularized solutions using the Bayesian statistical tools, with a particular view to signal and image estimation. The first three chapters bring the theoretical notions that make it possible to cast inverse problems within a mathematical framework. The next three chapters address the fundamental inverse problem of deconvolution in a comprehensive manner. Chapters 7 and 8 deal with advanced statistical questions linked to image estimation. In the last five chapters, the main tools introduced in the previous chapters are put into a practical context in important applicative areas, such as astronomy or medical imaging.
Discrete Tomography

Author: Gabor T. Herman
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
Goals of the Book Overthelast thirty yearsthere has been arevolutionindiagnostic radiology as a result oftheemergenceofcomputerized tomography (CT), which is the process of obtaining the density distribution within the human body from multiple x-ray projections. Since an enormous variety of possible density values may occur in the body, a large number of projections are necessary to ensure the accurate reconstruction oftheir distribution. There are other situations in which we desire to reconstruct an object from its projections, but in which we know that the object to be recon structed has only a small number of possible values. For example, a large fraction of objects scanned in industrial CT (for the purpose of nonde structive testing or reverse engineering) are made of a single material and so the ideal reconstruction should contain only two values: zero for air and the value associated with the material composing the object. Similar as sumptions may even be made for some specific medical applications; for example, in angiography ofthe heart chambers the value is either zero (in dicating the absence of dye) or the value associated with the dye in the chamber. Another example arises in the electron microscopy of biological macromolecules, where we may assume that the object to be reconstructed is composed of ice, protein, and RNA. One can also apply electron mi croscopy to determine the presenceor absence ofatoms in crystallinestruc tures, which is again a two-valued situation.
Computer Vision - ECCV 2004

Welcome to the proceedings of the 8th European Conference on Computer - sion! Following a very successful ECCV 2002, the response to our call for papers was almost equally strong – 555 papers were submitted. We accepted 41 papers for oral and 149 papers for poster presentation. Several innovations were introduced into the review process. First, the n- ber of program committee members was increased to reduce their review load. We managed to assign to program committee members no more than 12 papers. Second, we adopted a paper ranking system. Program committee members were asked to rank all the papers assigned to them, even those that were reviewed by additional reviewers. Third, we allowed authors to respond to the reviews consolidated in a discussion involving the area chair and the reviewers. Fourth, thereports,thereviews,andtheresponsesweremadeavailabletotheauthorsas well as to the program committee members. Our aim was to provide the authors with maximal feedback and to let the program committee members know how authors reacted to their reviews and how their reviews were or were not re?ected in the ?nal decision. Finally, we reduced the length of reviewed papers from 15 to 12 pages. ThepreparationofECCV2004wentsmoothlythankstothee?ortsofthe- ganizing committee, the area chairs, the program committee, and the reviewers. We are indebted to Anders Heyden, Mads Nielsen, and Henrik J. Nielsen for passing on ECCV traditions and to Dominique Asselineau from ENST/TSI who kindly provided his GestRFIA conference software. We thank Jan-Olof Eklundh and Andrew Zisserman for encouraging us to organize ECCV 2004 in Prague.