Combinatorial Solutions for Shape Optimization in Computer Vision

This thesis aims at solving so-called shape optimization problems, i.e. problems where the shape of some real-world entity is sought, by applying combinatorial algorithms. I present several advances in this field, all of them based on energy minimization. The addressed problems will become more intricate in the course of the thesis, starting from problems that are solved globally, then turning to problems where so far no global solutions are known. The first two chapters treat segmentation problems where the considered grouping criterion is directly derived from the image data. That is, the respective data terms do not involve any parameters to estimate. These problems will be solved globally. The first of these chapters treats the problem of unsupervised image segmentation where apart from the image there is no other user input. Here I will focus on a contour-based method and show how to integrate curvature regularity into a ratio-based optimization framework. The arising optimization problem is reduced to optimizing over the cycles in a product graph. This problem can be solved globally in polynomial, effectively linear time. As a consequence, the method does not depend on initialization and translational invariance is achieved. This is joint work with Daniel Cremers and Simon Masnou. I will then proceed to the integration of shape knowledge into the framework, while keeping translational invariance. This problem is again reduced to cycle-finding in a product graph. Being based on the alignment of shape points, the method actually uses a more sophisticated shape measure than most local approaches and still provides global optima. It readily extends to tracking problems and allows to solve some of them in real-time. I will present an extension to highly deformable shape models which can be included in the global optimization framework. This method simultaneously allows to decompose a shape into a set of deformable parts, based only on the input images. This is joint work with Daniel Cremers. In the second part segmentation is combined with so-called correspondence problems, i.e. the underlying grouping criterion is now based on correspondences that have to be inferred simultaneously. That is, in addition to inferring the shapes of objects, one now also tries to put into correspondence the points in several images. The arising problems become more intricate and are no longer optimized globally. This part is divided into two chapters. The first chapter treats the topic of real-time motion segmentation where objects are identified based on the observations that the respective points in the video will move coherently. Rather than pre-estimating motion, a single energy functional is minimized via alternating optimization. The main novelty lies in the real-time capability, which is achieved by exploiting a fast combinatorial segmentation algorithm. The results are furthermore improved by employing a probabilistic data term. This is joint work with Daniel Cremers. The final chapter presents a method for high resolution motion layer decomposition and was developed in combination with Daniel Cremers and Thomas Pock. Layer decomposition methods support the notion of a scene model, which allows to model occlusion and enforce temporal consistency. The contributions are twofold: from a practical point of view the proposed method allows to recover fine-detailed layer images by minimizing a single energy. This is achieved by integrating a super-resolution method into the layer decomposition framework. From a theoretical viewpoint the proposed method introduces layer-based regularity terms as well as a graph cut-based scheme to solve for the layer domains. The latter is combined with powerful continuous convex optimization techniques into an alternating minimization scheme. Lastly I want to mention that a significant part of this thesis is devoted to the recent trend of exploiting parallel architectures, in particular graphics cards: many combinatorial algorithms are easily parallelized. In Chapter 3 we will see a case where the standard algorithm is hard to parallelize, but easy for the respective problem instances

Minimum energy path planning for ad hoc networks

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.Includes bibliographical references (p. 85-86).We introduce the problem of finding a path for a mobile node traveling from a source to a destination while communicating with at least one node from a set of stationary nodes in such a way that minimizes the transmission energy used in communication. We characterize this problem and introduce two algorithms. The first is a recursive algorithm useful for problems with one communication node. We show the limitations of this algorithm and how it can find suboptimal paths. The second algorithm, the discretized graph algorithm, can be applied to problems with more communication nodes. We find parameters that allow energy efficient paths to be found in suitable time. We demonstrate the applicability of the minimum energy path planning problem and how the discretized graph algorithm can be used in a more general context through an example.by Danjie Chen.M.Eng

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

Latent Representation and Sampling in Network: Application in Text Mining and Biology.

In classical machine learning, hand-designed features are used for learning a mapping from raw data. However, human involvement in feature design makes the process expensive. Representation learning aims to learn abstract features directly from data without direct human involvement. Raw data can be of various forms. Network is one form of data that encodes relational structure in many real-world domains. Therefore, learning abstract features for network units is an important task. In this dissertation, we propose models for incorporating temporal information given as a collection of networks from subsequent time-stamps. The primary objective of our models is to learn a better abstract feature representation of nodes and edges in an evolving network. We show that the temporal information in the abstract feature improves the performance of link prediction task substantially. Besides applying to the network data, we also employ our models to incorporate extra-sentential information in the text domain for learning better representation of sentences. We build a context network of sentences to capture extra-sentential information. This information in abstract feature representation of sentences improves various text-mining tasks substantially over a set of baseline methods. A problem with the abstract features that we learn is that they lack interpretability. In real-life applications on network data, for some tasks, it is crucial to learn interpretable features in the form of graphical structures. For this we need to mine important graphical structures along with their frequency statistics from the input dataset. However, exact algorithms for these tasks are computationally expensive, so scalable algorithms are of urgent need. To overcome this challenge, we provide efficient sampling algorithms for mining higher-order structures from network(s). We show that our sampling-based algorithms are scalable. They are also superior to a set of baseline algorithms in terms of retrieving important graphical sub-structures, and collecting their frequency statistics. Finally, we show that we can use these frequent subgraph statistics and structures as features in various real-life applications. We show one application in biology and another in security. In both cases, we show that the structures and their statistics significantly improve the performance of knowledge discovery tasks in these domains

Early Vision Optimization: Parametric Models, Parallelization and Curvature

Early vision is the process occurring before any semantic interpretation of an image takes place. Motion estimation, object segmentation and detection are all parts of early vision, but recognition is not. Many of these tasks are formulated as optimization problems and one of the key factors for the success of recent methods is that they seek to compute globally optimal solutions. This thesis is concerned with improving the efficiency and extending the applicability of the current state of the art. This is achieved by introducing new methods of computing solutions to image segmentation and other problems of early vision. The first part studies parametric problems where model parameters are estimated in addition to an image segmentation. For a small number of parameters these problems can still be solved optimally. In the second part the focus is shifted toward curvature regularization, i.e. when the commonly used length and area regularization is replaced by curvature in two and three dimensions. These problems can be discretized over a mesh and special attention is given to the mesh geometry. Specifically, hexagonal meshes are compared to square ones and a method for generating adaptive methods is introduced and evaluated. The framework is then extended to curvature regularization of surfaces. Thirdly, fast methods for finding minimal graph cuts and solving related problems on modern parallel hardware are developed and extensively evaluated. Finally, the thesis is concluded with two applications to early vision problems: heart segmentation and image registration

Design and integrity of deterministic system architectures.

Architectures represented by system construction 'building block' components and interrelationships provide the structural form. This thesis addresses processes, procedures and methods that support system design synthesis and specifically the determination of the integrity of candidate architectural structures. Particular emphasis is given to the structural representation of system architectures, their consistency and functional quantification. It is a design imperative that a hierarchically decomposed structure maintains compatibility and consistency between the functional and realisation solutions. Complex systems are normally simplified by the use of hierarchical decomposition so that lower level components are precisely defined and simpler than higher-level components. To enable such systems to be reconstructed from their components, the hierarchical construction must provide vertical intra-relationship consistency, horizontal interrelationship consistency, and inter-component functional consistency. Firstly, a modified process design model is proposed that incorporates the generic structural representation of system architectures. Secondly, a system architecture design knowledge domain is proposed that enables viewpoint evaluations to be aggregated into a coherent set of domains that are both necessary and sufficient to determine the integrity of system architectures. Thirdly, four methods of structural analysis are proposed to assure the integrity of the architecture. The first enables the structural compatibility between the 'building blocks' that provide the emergent functional properties and implementation solution properties to be determined. The second enables the compatibility of the functional causality structure and the implementation causality structure to be determined. The third method provides a graphical representation of architectural structures. The fourth method uses the graphical form of structural representation to provide a technique that enables quantitative estimation of performance estimates of emergent properties for large scale or complex architectural structures. These methods have been combined into a procedure of formal design. This is a design process that, if rigorously executed, meets the requirements for reconstructability

Segmentation and quantification of spinal cord gray matter–white matter structures in magnetic resonance images

This thesis focuses on finding ways to differentiate the gray matter (GM) and white matter (WM) in magnetic resonance (MR) images of the human spinal cord (SC). The aim of this project is to quantify tissue loss in these compartments to study their implications on the progression of multiple sclerosis (MS). To this end, we propose segmentation algorithms that we evaluated on MR images of healthy volunteers. Segmentation of GM and WM in MR images can be done manually by human experts, but manual segmentation is tedious and prone to intra- and inter-rater variability. Therefore, a deterministic automation of this task is necessary. On axial 2D images acquired with a recently proposed MR sequence, called AMIRA, we experiment with various automatic segmentation algorithms. We first use variational model-based segmentation approaches combined with appearance models and later directly apply supervised deep learning to train segmentation networks. Evaluation of the proposed methods shows accurate and precise results, which are on par with manual segmentations. We test the developed deep learning approach on images of conventional MR sequences in the context of a GM segmentation challenge, resulting in superior performance compared to the other competing methods. To further assess the quality of the AMIRA sequence, we apply an already published GM segmentation algorithm to our data, yielding higher accuracy than the same algorithm achieves on images of conventional MR sequences. On a different topic, but related to segmentation, we develop a high-order slice interpolation method to address the large slice distances of images acquired with the AMIRA protocol at different vertebral levels, enabling us to resample our data to intermediate slice positions. From the methodical point of view, this work provides an introduction to computer vision, a mathematically focused perspective on variational segmentation approaches and supervised deep learning, as well as a brief overview of the underlying project's anatomical and medical background

NASA thesaurus. Volume 3: Definitions

Publication of NASA Thesaurus definitions began with Supplement 1 to the 1985 NASA Thesaurus. The definitions given here represent the complete file of over 3,200 definitions, complimented by nearly 1,000 use references. Definitions of more common or general scientific terms are given a NASA slant if one exists. Certain terms are not defined as a matter of policy: common names, chemical elements, specific models of computers, and nontechnical terms. The NASA Thesaurus predates by a number of years the systematic effort to define terms, therefore not all Thesaurus terms have been defined. Nevertheless, definitions of older terms are continually being added. The following data are provided for each entry: term in uppercase/lowercase form, definition, source, and year the term (not the definition) was added to the NASA Thesaurus. The NASA History Office is the authority for capitalization in satellite and spacecraft names. Definitions with no source given were constructed by lexicographers at the NASA Scientific and Technical Information (STI) Facility who rely on the following sources for their information: experts in the field, literature searches from the NASA STI database, and specialized references

On continuous maximum ow image segmentation algorithm

Ces dernières années avec les progrès matériels, les dimensions et le contenu des images acquises se sont complexifiés de manière notable. Egalement, le différentiel de performance entre les architectures classiques mono-processeur et parallèles est passé résolument en faveur de ces dernières. Pourtant, les manières de programmer sont restées largement les mêmes, instituant un manque criant de performance même sur ces architectures. Dans cette thèse, nous explorons en détails un algorithme particulier, les flots maximaux continus. Nous explicitons pourquoi cet algorithme est important et utile, et nous proposons plusieurs implémentations sur diverses architectures, du mono-processeur à l'architecture SMP et NUMA, ainsi que sur les architectures massivement parallèles des GPGPU. Nous explorons aussi des applications et nous évaluons ses performances sur des images de grande taille en science des matériaux et en biologie à l'échelle nanoIn recent years, with the advance of computing equipment and image acquisition techniques, the sizes, dimensions and content of acquired images have increased considerably. Unfortunately as time passes there is a steadily increasing gap between the classical and parallel programming paradigms and their actual performance on modern computer hardware. In this thesis we consider in depth one particular algorithm, the continuous maximum flow computation. We review in detail why this algorithm is useful and interesting, and we propose efficient and portable implementations on various architectures. We also examine how it performs in the terms of segmentation quality on some recent problems of materials science and nano-scale biologyPARIS-EST-Université (770839901) / SudocSudocFranceF