Parametric Level-sets Enhanced To Improve Reconstruction (PaLEnTIR)

In this paper, we consider the restoration and reconstruction of piecewise constant objects in two and three dimensions using PaLEnTIR, a significantly enhanced Parametric level set (PaLS) model relative to the current state-of-the-art. The primary contribution of this paper is a new PaLS formulation which requires only a single level set function to recover a scene with piecewise constant objects possessing multiple unknown contrasts. Our model offers distinct advantages over current approaches to the multi-contrast, multi-object problem, all of which require multiple level sets and explicit estimation of the contrast magnitudes. Given upper and lower bounds on the contrast, our approach is able to recover objects with any distribution of contrasts and eliminates the need to know either the number of contrasts in a given scene or their values. We provide an iterative process for finding these space-varying contrast limits. Relative to most PaLS methods which employ radial basis functions (RBFs), our model makes use of non-isotropic basis functions, thereby expanding the class of shapes that a PaLS model of a given complexity can approximate. Finally, PaLEnTIR improves the conditioning of the Jacobian matrix required as part of the parameter identification process and consequently accelerates the optimization methods by controlling the magnitude of the PaLS expansion coefficients, fixing the centers of the basis functions, and the uniqueness of parametric to image mappings provided by the new parameterization. We demonstrate the performance of the new approach using both 2D and 3D variants of X-ray computed tomography, diffuse optical tomography (DOT), denoising, deconvolution problems. Application to experimental sparse CT data and simulated data with different types of noise are performed to further validate the proposed method.Comment: 31 pages, 56 figure

Model extensions and applications in mathematical imaging.

Mathematical imaging consists of many different applications including image segmentation, image classification, and inpainting. This work deals more specifically with image segmentation: the partition of an image into the background and the objects present in the image. The main focus is the active contours without gradient model by Tony Chan and Luminita Vese which deals with fitting a curve imbedded in the plane image. The fitting of the curve comes from an evolutionary partial differential equation. The dissertation contributes three novel ideas: a linearized version of the active contours without gradient model published in [20]; a new procedure using fourth order fitting terms in place of the second order fitting terms which gives faster segmentation and may be used to provide a good initial condition; a novel way of tracking regions present in bulk data in order to gain an understanding of macroscopic details associated with some physical application. Results include images showing the accuracy of the segmentation for the methods, a discussion of the choice of initial condition, and discussion of feasibility for the data tracking. These results compare to those obtained with the nonlinear model and serve as a proof-of-concept for further investigation. The dissertation ends with a discussion of future research

Quelques extensions des level sets et des graph cuts et leurs applications à la segmentation d'images et de vidéos

Image processing techniques are now widely spread out over a large quantity of domains: like medical imaging, movies post-production, games... Automatic detection and extraction of regions of interest inside an image, a volume or a video is challenging problem since it is a starting point for many applications in image processing. However many techniques were developed during the last years and the state of the art methods suffer from some drawbacks: The Level Sets method only provides a local minimum while the Graph Cuts method comes from Combinatorial Community and could take advantage of the specificity of image processing problems. In this thesis, we propose two extensions of the previously cited methods in order to soften or remove these drawbacks. We first discuss the existing methods and show how they are related to the segmentation problem through an energy formulation. Then we introduce stochastic perturbations to the Level Sets method and we build a more generic framework: the Stochastic Level Sets (SLS). Later we provide a direct application of the SLS to image segmentation that provides a better minimization of energies. Basically, it allows the contours to escape from local minimum. Then we propose a new formulation of an existing algorithm of Graph Cuts in order to introduce some interesting concept for image processing community: like initialization of the algorithm for speed improvement. We also provide a new approach for layer extraction from video sequence that retrieves both visible and hidden layers in it.Les techniques de traitement d'image sont maintenant largement répandues dans une grande quantité de domaines: comme l'imagerie médicale, la post-production de films, les jeux... La détection et l'extraction automatique de régions d'intérêt à l'intérieur d'une image, d'un volume ou d'une vidéo est réel challenge puisqu'il représente un point de départ pour un grand nombre d'applications en traitement d'image. Cependant beaucoup de techniques développées pendant ces dernières années et les méthodes de l'état de l'art souffrent de quelques inconvénients: la méthode des ensembles de niveaux fournit seulement un minimum local tandis que la méthode de coupes de graphe vient de la communauté combinatoire et pourrait tirer profit de la spécificité des problèmes de traitement d'image. Dans cette thèse, nous proposons deux prolongements des méthodes précédemment citées afin de réduire ou enlever ces inconvénients. Nous discutons d'abord les méthodes existantes et montrons comment elles sont liées au problème de segmentation via une formulation énergétique. Nous présentons ensuite des perturbations stochastiques a la méthode des ensembles de niveaux et nous établissons un cadre plus générique: les ensembles de niveaux stochastiques (SLS). Plus tard nous fournissons une application directe du SLS à la segmentation d'image et montrons qu'elle fournit une meilleure minimisation des énergies. Fondamentalement, il permet aux contours de s'échapper des minima locaux. Nous proposons ensuite une nouvelle formulation d'un algorithme existant des coupes de graphe afin d'introduire de nouveaux concepts intéressant pour la communauté de traitement d'image: comme l'initialisation de l'algorithme pour l'amélioration de vitesse. Nous fournissons également une nouvelle approche pour l'extraction de couches d'une vidéo par segmentation du mouvement et qui extrait à la fois les couches visibles et cachées présentes

Graph Theoretic Algorithms Adaptable to Quantum Computing

Computational methods are rapidly emerging as an essential tool for understanding and solving complex engineering problems, which complement the traditional tools of experimentation and theory. When considered in a discrete computational setting, many engineering problems can be reduced to a graph coloring problem. Examples range from systems design, airline scheduling, image segmentation to pattern recognition, where energy cost functions with discrete variables are extremized. However, using discrete variables over continuous variables introduces some complications when defining differential quantities, such as gradients and Hessians involved in scientific computations within solid and fluid mechanics. Consequently, graph techniques are under-utilized in this important domain. However, we have recently witnessed great developments in quantum computing where physical devices can solve discrete optimization problems faster than most well-known classical algorithms. This warrants further investigation into the re-formulation of scientific computation problems into graph-theoretic problems, thus enabling rapid engineering simulations in a soon-to-be quantum computing world. The computational techniques developed in this thesis allow the representation of surface scalars, such as perimeter and area, using discrete variables in a graph. Results from integral geometry, specifically Cauchy-Crofton relations, are used to estimate these scalars via submodular functions. With this framework, several quantities important to engineering applications can be represented in graph-based algorithms. These include the surface energy of cracks for fracture prediction, grain boundary energy to model microstructure evolution, and surface area estimates (of grains and fibers) for generating conformal meshes. Combinatorial optimization problems for these applications are presented first. The last two chapters describe two new graph coloring algorithms implemented on a physical quantum computing device: the D-wave quantum annealer. The first algorithm describes a functional minimization approach to solve differential equations. The second algorithm describes a realization of the Boltzmann machine learning algorithm on a quantum annealer. The latter allows generative and discriminative learning of data, which has vast applications in many fields. Theoretical aspects and the implementation of these problems are outlined with a focus on engineering applications.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/168116/1/sidsriva_1.pd

Aplicação de uma métrica de similaridade não linear em algoritmos de segmentação

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Ciência da Computação, 2015.Um dos principais processos utilizados no campo de processamento digital de imagens é a segmentação, processo no qual a imagem é separada em seus elementos ou partes constituintes. Na literatura, existem diferentes e bem conhecidos métodos usados para segmentação, tais como clusterização, limiarização, segmentação com redes neurais e segmentação por crescimento de regiões . No intuito de melhorar de melhorar o desempenho dos algoritmos de segmentação, um estudo sobre o efeito da aplicação de uma métrica não linear em algoritmos de segmentação foi realizado neste trabalho. Foram selecionados três algoritmos de segmentação (Mumford-Shah, Color Structure Code e Felzenszwalb and Huttenlocher) provenientes do método de crescimento de regiões e nestes se alterou a parte de análise de similaridade utilizando para tal uma métrica não linear. A métrica não linear utilizada, denominada Polinomial Mahalanobis, é uma variação da distância de Mahalanobis utilizada para medir a distância estatística entre distribuições. Uma avaliação qualitativa e uma análise empírica foram realizadas neste trabalho para comparar os resultados obtidos em termos de eficácia. Os resultados desta comparação, apresentados neste estudo, apontam uma melhoria nos resultados de segmentação obtidos pela abordagem proposta. Em termos de eficiência, foram analisados os tempos de execução dos algoritmos com e sem o aprimoramento e os resultados desta análise mostraram um aumento do tempo de execução dos algoritmos com abordagem proposta.Abstract : One of the main procedures used on digital image processing is segmentation,where the image is split into its constituent parts or objects. In the literature,there are different well-known methods used for segmentation, suchas clustering, thresholding, segmentation using neural network and segmentationusing region growing. Aiming to improve the performance of the segmentationalgorithms, a study off the effect of the application of a non-linearmetric on segmentation algorithms was performed in this work. Three segmentationalgorithms were chosen (Mumford-Shah, Color Structure Code,Felzenszwalb and Huttenlocher) originating from region growing techniques,and on those the similarity metric was enhanced with a non-linear metric.The non-linear metric used, known as Polynomial Mahalanobis, is a variationfrom the statistical Mahalanobis distance used for measure the distancebetween distributions. A qualitative evaluation and empirical analysis wasperformed in this work to compare the obtained results in terms of efficacy.The results from these comparison, presented in this study, indicate an improvementon the segmentation result obtained by the proposed approach. Interms of efficiency, the execution time of the algorithms with and without theproposed improvement were analyzed and the result of this analysis showedan increase of the execution time for the algorithms with the proposed approach

Machine Learning and Its Application to Reacting Flows

This open access book introduces and explains machine learning (ML) algorithms and techniques developed for statistical inferences on a complex process or system and their applications to simulations of chemically reacting turbulent flows. These two fields, ML and turbulent combustion, have large body of work and knowledge on their own, and this book brings them together and explain the complexities and challenges involved in applying ML techniques to simulate and study reacting flows. This is important as to the world’s total primary energy supply (TPES), since more than 90% of this supply is through combustion technologies and the non-negligible effects of combustion on environment. Although alternative technologies based on renewable energies are coming up, their shares for the TPES is are less than 5% currently and one needs a complete paradigm shift to replace combustion sources. Whether this is practical or not is entirely a different question, and an answer to this question depends on the respondent. However, a pragmatic analysis suggests that the combustion share to TPES is likely to be more than 70% even by 2070. Hence, it will be prudent to take advantage of ML techniques to improve combustion sciences and technologies so that efficient and “greener” combustion systems that are friendlier to the environment can be designed. The book covers the current state of the art in these two topics and outlines the challenges involved, merits and drawbacks of using ML for turbulent combustion simulations including avenues which can be explored to overcome the challenges. The required mathematical equations and backgrounds are discussed with ample references for readers to find further detail if they wish. This book is unique since there is not any book with similar coverage of topics, ranging from big data analysis and machine learning algorithm to their applications for combustion science and system design for energy generation

Machine Learning and Its Application to Reacting Flows

This open access book introduces and explains machine learning (ML) algorithms and techniques developed for statistical inferences on a complex process or system and their applications to simulations of chemically reacting turbulent flows. These two fields, ML and turbulent combustion, have large body of work and knowledge on their own, and this book brings them together and explain the complexities and challenges involved in applying ML techniques to simulate and study reacting flows. This is important as to the world’s total primary energy supply (TPES), since more than 90% of this supply is through combustion technologies and the non-negligible effects of combustion on environment. Although alternative technologies based on renewable energies are coming up, their shares for the TPES is are less than 5% currently and one needs a complete paradigm shift to replace combustion sources. Whether this is practical or not is entirely a different question, and an answer to this question depends on the respondent. However, a pragmatic analysis suggests that the combustion share to TPES is likely to be more than 70% even by 2070. Hence, it will be prudent to take advantage of ML techniques to improve combustion sciences and technologies so that efficient and “greener” combustion systems that are friendlier to the environment can be designed. The book covers the current state of the art in these two topics and outlines the challenges involved, merits and drawbacks of using ML for turbulent combustion simulations including avenues which can be explored to overcome the challenges. The required mathematical equations and backgrounds are discussed with ample references for readers to find further detail if they wish. This book is unique since there is not any book with similar coverage of topics, ranging from big data analysis and machine learning algorithm to their applications for combustion science and system design for energy generation