473 research outputs found

    Network Flow Algorithms for Discrete Tomography

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    Tomography is a powerful technique to obtain images of the interior of an object in a nondestructive way. First, a series of projection images (e.g., X-ray images) is acquired and subsequently a reconstruction of the interior is computed from the available project data. The algorithms that are used to compute such reconstructions are known as tomographic reconstruction algorithms. Discrete tomography is concerned with the tomographic reconstruction of images that are known to contain only a few different gray levels. By using this knowledge in the reconstruction algorithm it is often possible to reduce the number of projections required to compute an accurate reconstruction, compared to algorithms that do not use prior knowledge. This thesis deals with new reconstruction algorithms for discrete tomography. In particular, the first five chapters are about reconstruction algorithms based on network flow methods. These algorithms make use of an elegant correspondence between certain types of tomography problems and network flow problems from the field of Operations Research. Chapter 6 deals with a problem that occurs in the application of discrete tomography to the reconstruction of nanocrystals from projections obtained by electron microscopy.The research for this thesis has been financially supported by the Netherlands Organisation for Scientific Research (NWO), project 613.000.112.UBL - phd migration 201

    Acta Cybernetica : Volume 21. Number 1.

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    Programmation mathématique en tomographie discrète

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    La tomographie est un ensemble de techniques visant à reconstruirel intérieur d un objet sans toucher l objet lui même comme dans le casd un scanner. Les principes théoriques de la tomographie ont été énoncéspar Radon en 1917. On peut assimiler l objet à reconstruire à une image,matrice, etc.Le problème de reconstruction tomographique consiste à estimer l objet àpartir d un ensemble de projections obtenues par mesures expérimentalesautour de l objet à reconstruire. La tomographie discrète étudie le cas où lenombre de projections est limité et l objet est défini de façon discrète. Leschamps d applications de la tomographie discrète sont nombreux et variés.Citons par exemple les applications de type non destructif comme l imageriemédicale. Il existe d autres applications de la tomographie discrète, commeles problèmes d emplois du temps.La tomographie discrète peut être considérée comme un problème d optimisationcombinatoire car le domaine de reconstruction est discret et le nombrede projections est fini. La programmation mathématique en nombres entiersconstitue un outil pour traiter les problèmes d optimisation combinatoire.L objectif de cette thèse est d étudier et d utiliser les techniques d optimisationcombinatoire pour résoudre les problèmes de tomographie.The tomographic imaging problem deals with reconstructing an objectfrom a data called a projections and collected by illuminating the objectfrom many different directions. A projection means the information derivedfrom the transmitted energies, when an object is illuminated from a particularangle. The solution to the problem of how to reconstruct an object fromits projections dates to 1917 by Radon. The tomographic reconstructingis applicable in many interesting contexts such as nondestructive testing,image processing, electron microscopy, data security, industrial tomographyand material sciences.Discete tomography (DT) deals with the reconstruction of discret objectfrom limited number of projections. The projections are the sums along fewangles of the object to be reconstruct. One of the main problems in DTis the reconstruction of binary matrices from two projections. In general,the reconstruction of binary matrices from a small number of projections isundetermined and the number of solutions can be very large. Moreover, theprojections data and the prior knowledge about the object to reconstructare not sufficient to determine a unique solution. So DT is usually reducedto an optimization problem to select the best solution in a certain sense.In this thesis, we deal with the tomographic reconstruction of binaryand colored images. In particular, research objectives are to derive thecombinatorial optimization techniques in discrete tomography problems.PARIS-CNAM (751032301) / SudocSudocFranceF

    Discrete Tomography by Convex-Concave Regularization using Linear and Quadratic Optimization

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    Discrete tomography concerns the reconstruction of objects that are made up from a few different materials, each of which comprising a homogeneous density distribution. Under the assumption that these densities are a priori known new algorithms can be developed which typically need less projection data to reveal appealing reconstruction results

    Development of tomographic reconstruction methods in materials science with focus on advanced scanning methods

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    Conditioning of and Algorithms for Image Reconstruction from Irregular Frequency Domain Samples.

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    The problem of reconstructing an image from irregular samples of its 2-D DTFT arises in synthetic aperture radar (SAR), magnetic resonance imaging (MRI), computed tomography (CT), limited angle tomography, and 2-D filter design. The problem of determining a configuration of a limited number of 2-D DTFT samples also arises in magnetic resonance spectroscopic imaging (MRSI) and 3-D MRI. This work first focuses on the selection of the measurement data. Since there is no 2-D Lagrange interpolation formula, sufficient conditions for the uniqueness and conditioning of the reconstruction problem are both not apparent. Kronecker substitutions, such as the Good-Thomas FFT, the helical scan FFT, and the 45-degree rotated support, unwrap the 2-D problem into a 1-D problem, resulting in uniqueness and insights into the problem conditioning. The variance of distances between the adjacent unwrapped 1-D DTFT samples was developed as a sensitivity measure to quickly and accurately estimate of the condition number of the system matrix. A well-conditioned configuration of DTFT samples, restricted to radial lines in CT or spirals in MRI, is found by simulated annealing with the variance sensitivity measure as the objective function. The preconditioned conjugate gradient method reconstructs the 1-D solution that is then rewrapped to a 2-D image. In unrestricted cases, 2-D DTFT configurations like a regular hexagonal pattern can be unwrapped to uniformly-spaced and perfectly conditioned 1-D configurations and quickly solved using an inverse 1-D DFT. The next focus is on developing fast reconstruction algorithms. A non-iterative DFT-based method of reconstructing an image is presented, by first masking the 2-D DTFT samples with the frequency response of a filter that is zeroed at the unknown 2-D DFT locations, and then quickly deconvolving the filtered image using three 2-D DFTs. The masking filter needs to be precomputed only once per DTFT configuration. A divide-and-conquer image reconstruction method is also presented using subband decomposition and Gabor filters to solve smaller subband problems, leading to a quick unaliased low-resolution image or later to be recombined into the full solution. All methods are applied to actual CT data resulting in faster reconstructions than POCS and FBP with equivalent errors.Ph.D.Electrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/77912/1/leebc_1.pd

    A geometric projection-space reconstruction algorithm

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    Cover title.Includes bibliographical references.Supported by the National Science Foundation. ECS-87-00903 Supported by the U.S. Army Research Office. DAAL03-86-K-1071 [i.e. DAAL03-86-K-0171] Partially supported by a U.S. Army Research Office fellowship.Jerry L. Prince, Alan S. Willsky

    The 9th Conference of PhD Students in Computer Science

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    Analysis of 3D human gait reconstructed with a depth camera and mirrors

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    L'évaluation de la démarche humaine est l'une des composantes essentielles dans les soins de santé. Les systèmes à base de marqueurs avec plusieurs caméras sont largement utilisés pour faire cette analyse. Cependant, ces systèmes nécessitent généralement des équipements spécifiques à prix élevé et/ou des moyens de calcul intensif. Afin de réduire le coût de ces dispositifs, nous nous concentrons sur un système d'analyse de la marche qui utilise une seule caméra de profondeur. Le principe de notre travail est similaire aux systèmes multi-caméras, mais l'ensemble de caméras est remplacé par un seul capteur de profondeur et des miroirs. Chaque miroir dans notre configuration joue le rôle d'une caméra qui capture la scène sous un point de vue différent. Puisque nous n'utilisons qu'une seule caméra, il est ainsi possible d'éviter l'étape de synchronisation et également de réduire le coût de l'appareillage. Notre thèse peut être divisée en deux sections: reconstruction 3D et analyse de la marche. Le résultat de la première section est utilisé comme entrée de la seconde. Notre système pour la reconstruction 3D est constitué d'une caméra de profondeur et deux miroirs. Deux types de capteurs de profondeur, qui se distinguent sur la base du mécanisme d'estimation de profondeur, ont été utilisés dans nos travaux. Avec la technique de lumière structurée (SL) intégrée dans le capteur Kinect 1, nous effectuons la reconstruction 3D à partir des principes de l'optique géométrique. Pour augmenter le niveau des détails du modèle reconstruit en 3D, la Kinect 2 qui estime la profondeur par temps de vol (ToF), est ensuite utilisée pour l'acquisition d'images. Cependant, en raison de réflections multiples sur les miroirs, il se produit une distorsion de la profondeur dans notre système. Nous proposons donc une approche simple pour réduire cette distorsion avant d'appliquer les techniques d'optique géométrique pour reconstruire un nuage de points de l'objet 3D. Pour l'analyse de la démarche, nous proposons diverses alternatives centrées sur la normalité de la marche et la mesure de sa symétrie. Cela devrait être utile lors de traitements cliniques pour évaluer, par exemple, la récupération du patient après une intervention chirurgicale. Ces méthodes se composent d'approches avec ou sans modèle qui ont des inconvénients et avantages différents. Dans cette thèse, nous présentons 3 méthodes qui traitent directement les nuages de points reconstruits dans la section précédente. La première utilise la corrélation croisée des demi-corps gauche et droit pour évaluer la symétrie de la démarche, tandis que les deux autres methodes utilisent des autoencodeurs issus de l'apprentissage profond pour mesurer la normalité de la démarche.The problem of assessing human gaits has received a great attention in the literature since gait analysis is one of key components in healthcare. Marker-based and multi-camera systems are widely employed to deal with this problem. However, such systems usually require specific equipments with high price and/or high computational cost. In order to reduce the cost of devices, we focus on a system of gait analysis which employs only one depth sensor. The principle of our work is similar to multi-camera systems, but the collection of cameras is replaced by one depth sensor and mirrors. Each mirror in our setup plays the role of a camera which captures the scene at a different viewpoint. Since we use only one camera, the step of synchronization can thus be avoided and the cost of devices is also reduced. Our studies can be separated into two categories: 3D reconstruction and gait analysis. The result of the former category is used as the input of the latter one. Our system for 3D reconstruction is built with a depth camera and two mirrors. Two types of depth sensor, which are distinguished based on the scheme of depth estimation, have been employed in our works. With the structured light (SL) technique integrated into the Kinect 1, we perform the 3D reconstruction based on geometrical optics. In order to increase the level of details of the 3D reconstructed model, the Kinect 2 with time-of-flight (ToF) depth measurement is used for image acquisition instead of the previous generation. However, due to multiple reflections on the mirrors, depth distortion occurs in our setup. We thus propose a simple approach for reducing such distortion before applying geometrical optics to reconstruct a point cloud of the 3D object. For the task of gait analysis, we propose various alternative approaches focusing on the problem of gait normality/symmetry measurement. They are expected to be useful for clinical treatments such as monitoring patient's recovery after surgery. These methods consist of model-free and model-based approaches that have different cons and pros. In this dissertation, we present 3 methods that directly process point clouds reconstructed from the previous work. The first one uses cross-correlation of left and right half-bodies to assess gait symmetry while the other ones employ deep auto-encoders to measure gait normality
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