90 research outputs found

    Image filtering with past parametrized biorthogonal transforms implemented on a new GUI research aid system

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    In this paper the authors show that fast parametrized biorthogonal transforms (FPBT) are well suited for adaptive generalized Wiener image ïŹltering. Research results are obtained with a use of a new graphical user interface system for implementing various fast adaptive techniques, designed, implemented and published by the authors as a part of a project Innovative Economy Programme 2007-2013 „Platforma Informatyczna TEWI”

    Sieve-based inference for infinite-variance linear processes

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    We extend the available asymptotic theory for autoregressive sieve estimators to cover the case of stationary and invertible linear processes driven by independent identically distributed (i.i.d.) infinite variance (IV) innovations. We show that the ordinary least squares sieve estimates, together with estimates of the impulse responses derived from these, obtained from an autoregression whose order is an increasing function of the sample size, are consistent and exhibit asymptotic properties analogous to those which obtain for a finite-order autoregressive process driven by i.i.d. IV errors. As these limit distributions cannot be directly employed for inference because they either may not exist or, where they do, depend on unknown parameters, a second contribution of the paper is to investigate the usefulness of bootstrap methods in this setting. Focusing on three sieve bootstraps: the wild and permutation bootstraps, and a hybrid of the two, we show that, in contrast to the case of finite variance innovations, the wild bootstrap requires an infeasible correction to be consistent, whereas the other two bootstrap schemes are shown to be consistent (the hybrid for symmetrically distributed innovations) under general conditions

    Discrete Wavelet Transforms

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    The discrete wavelet transform (DWT) algorithms have a firm position in processing of signals in several areas of research and industry. As DWT provides both octave-scale frequency and spatial timing of the analyzed signal, it is constantly used to solve and treat more and more advanced problems. The present book: Discrete Wavelet Transforms: Algorithms and Applications reviews the recent progress in discrete wavelet transform algorithms and applications. The book covers a wide range of methods (e.g. lifting, shift invariance, multi-scale analysis) for constructing DWTs. The book chapters are organized into four major parts. Part I describes the progress in hardware implementations of the DWT algorithms. Applications include multitone modulation for ADSL and equalization techniques, a scalable architecture for FPGA-implementation, lifting based algorithm for VLSI implementation, comparison between DWT and FFT based OFDM and modified SPIHT codec. Part II addresses image processing algorithms such as multiresolution approach for edge detection, low bit rate image compression, low complexity implementation of CQF wavelets and compression of multi-component images. Part III focuses watermaking DWT algorithms. Finally, Part IV describes shift invariant DWTs, DC lossless property, DWT based analysis and estimation of colored noise and an application of the wavelet Galerkin method. The chapters of the present book consist of both tutorial and highly advanced material. Therefore, the book is intended to be a reference text for graduate students and researchers to obtain state-of-the-art knowledge on specific applications

    Pattern Recognition

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    Pattern recognition is a very wide research field. It involves factors as diverse as sensors, feature extraction, pattern classification, decision fusion, applications and others. The signals processed are commonly one, two or three dimensional, the processing is done in real- time or takes hours and days, some systems look for one narrow object class, others search huge databases for entries with at least a small amount of similarity. No single person can claim expertise across the whole field, which develops rapidly, updates its paradigms and comprehends several philosophical approaches. This book reflects this diversity by presenting a selection of recent developments within the area of pattern recognition and related fields. It covers theoretical advances in classification and feature extraction as well as application-oriented works. Authors of these 25 works present and advocate recent achievements of their research related to the field of pattern recognition

    Short-Term Visual Object Tracking in Real-Time

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    In the thesis, we propose two novel short-term object tracking methods, the Flock of Trackers (FoT) and the Scale-Adaptive Mean-Shift (ASMS), a framework for fusion of multiple trackers and detector and contributions to the problem of tracker evaluation within the Visual Object Tracking (VOT) initiative. The Flock of Trackers partitions the object of interest to an equally sized parts. For each part, the FoT computes an optical flow correspondence and estimates its reliability. Reliable correspondences are used to robustly estimates a target pose using RANSAC technique, which allows for range of complex rigid transformation (e.g. affine transformation) of a target. The scale-adaptive mean-shift tracker is a gradient optimization method that iteratively moves a search window to the position which minimizes a distance of a appearance model extracted from the search window to the target model. The ASMS propose a theoretically justified modification of the mean-shift framework that addresses one of the drawbacks of the mean-shift trackers which is the fixed size search window, i.e. target scale. Moreover, the ASMS introduce a technique that incorporates a background information into the gradient optimization to reduce tracker failures in presence of background clutter. To take advantage of strengths of the previous methods, we introduce a novel tracking framework HMMTxD that fuses multiple tracking methods together with a proposed feature-based online detector. The framework utilizes a hidden Markov model (HMM) to learn online how well each tracking method performs using sparsely ”annotated” data provided by a detector, which are assumed to be correct, and confidence provided by the trackers. The HMM estimates the probability that a tracker is correct in the current frame given the previously learned HMM model and the current tracker confidence. This tracker fusion alleviates the drawbacks of the individual tracking methods since the HMMTxD learns which trackers are performing well and switch off the rest. All of the proposed trackers were extensively evaluated on several benchmarks and publicly available tracking sequences and achieve excellent results in various evaluation criteria. The FoT achieved state-of-the-art performance in the VOT2013 benchmark, finishing second. Today, the FoT is used as a building block in complex applications such as multi-object tracking frameworks. The ASMS achieved state-of-the-art results in the VOT2015 benchmark and was chosen as the best performing method in terms of a trade-off between performance and running time. The HMMTxD demonstrated state-of-the-art performance in multiple benchmarks (VOT2014, VOT2015 and OTB). The thesis also contributes, and provides an overview, to the Visual Object Tracking (VOT) evaluation methodology. This methodology provides a means for unbiased comparison of different tracking methods across publication, which is crucial for advancement of the state-of-the-art over a longer timespan and also provides a tools for deeper performance analysis of tracking methods. Furthermore, a annual workshops are organized on major computer vision conferences, where the authors are encouraged to submit their novel methods to compete against each other and where the advances in the visual object tracking are discussed.Katedra kybernetik

    Matemaattisten mallien dimension redusointi neurotieteessÀ

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    Dimensionality reduction is a commonly used method in engineering sciences, such as control theory, for improving computational efficiency of simulations of complex nonlinear mathematical models. Additionally, it is a way of surfacing the most important factors that drive the dynamics of the system. In the field of neuroscience, there is a great demand to incorporate molecular and cellular level detail in large-scale models of the brain in order to produce phenomena such as learning and behavior. This cannot be achieved with the computing power available today, since the detailed models are unsuitable for large-scale network or system level simulations. In this thesis, methods for mathematical model reduction are reviewed. In the field of systems biology, models are typically simplified by completely eliminating variables, such as molecules, from the system, and making assumptions of the system behavior, for example regarding the steady state of the chemical reactions. However, this approach is not meaningful in neuroscience since comprehensive models are needed in order to increase understanding of the target systems. This information loss problem is solved by mathematical reduction methods that strive to approximate the entire system with a smaller number of dimensions compared to the original system. In this study, mathematical model reduction is applied in the context of an experimentally verified signaling pathway model of plasticity. The chosen biophysical model is one of the most comprehensive models out of those that are currently able to explain aspects of plasticity on the molecular level with chemical interactions and the law of mass action. The employed reduction method is Proper Orthogonal Decomposition with Discrete Empirical Interpolation Method (POD+DEIM), a subspace projection method for reducing the dimensionality of nonlinear systems. By applying these methods, the simulation time of the plasticity model was radically shortened although approximation errors are present if the model is reviewed on large time scales. It is up to the final application of the model whether some error or none at all is tolerated. Based on these promising results, subspace projection methods are recommended for dimensionality reduction in computational neuroscience

    Cooperative Game Theory and its Insurance Applications

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    This survey paper presents the basic concepts of cooperative game theory, at an elementary level. Five examples, including three insurance applications, are progressively developed throughout the paper. The characteristic function, the core, the stable sets, the Shapley value, the Nash and Kalai-Smorodinsky solutions are defined and computed for the different examples

    Binokulare EigenbewegungsschĂ€tzung fĂŒr Fahrerassistenzanwendungen

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    Driving can be dangerous. Humans become inattentive when performing a monotonous task like driving. Also the risk implied while multi-tasking, like using the cellular phone while driving, can break the concentration of the driver and increase the risk of accidents. Others factors like exhaustion, nervousness and excitement affect the performance of the driver and the response time. Consequently, car manufacturers have developed systems in the last decades which assist the driver under various circumstances. These systems are called driver assistance systems. Driver assistance systems are meant to support the task of driving, and the field of action varies from alerting the driver, with acoustical or optical warnings, to taking control of the car, such as keeping the vehicle in the traffic lane until the driver resumes control. For such a purpose, the vehicle is equipped with on-board sensors which allow the perception of the environment and/or the state of the vehicle. Cameras are sensors which extract useful information about the visual appearance of the environment. Additionally, a binocular system allows the extraction of 3D information. One of the main requirements for most camera-based driver assistance systems is the accurate knowledge of the motion of the vehicle. Some sources of information, like velocimeters and GPS, are of common use in vehicles today. Nevertheless, the resolution and accuracy usually achieved with these systems are not enough for many real-time applications. The computation of ego-motion from sequences of stereo images for the implementation of driving intelligent systems, like autonomous navigation or collision avoidance, constitutes the core of this thesis. This dissertation proposes a framework for the simultaneous computation of the 6 degrees of freedom of ego-motion (rotation and translation in 3D Euclidean space), the estimation of the scene structure and the detection and estimation of independently moving objects. The input is exclusively provided by a binocular system and the framework does not call for any data acquisition strategy, i.e. the stereo images are just processed as they are provided. Stereo allows one to establish correspondences between left and right images, estimating 3D points of the environment via triangulation. Likewise, feature tracking establishes correspondences between the images acquired at different time instances. When both are used together for a large number of points, the result is a set of clouds of 3D points with point-to-point correspondences between clouds. The apparent motion of the 3D points between consecutive frames is caused by a variety of reasons. The most dominant motion for most of the points in the clouds is caused by the ego-motion of the vehicle; as the vehicle moves and images are acquired, the relative position of the world points with respect to the vehicle changes. Motion is also caused by objects moving in the environment. They move independently of the vehicle motion, so the observed motion for these points is the sum of the ego-vehicle motion and the independent motion of the object. A third reason, and of paramount importance in vision applications, is caused by correspondence problems, i.e. the incorrect spatial or temporal assignment of the point-to-point correspondence. Furthermore, all the points in the clouds are actually noisy measurements of the real unknown 3D points of the environment. Solving ego-motion and scene structure from the clouds of points requires some previous analysis of the noise involved in the imaging process, and how it propagates as the data is processed. Therefore, this dissertation analyzes the noise properties of the 3D points obtained through stereo triangulation. This leads to the detection of a bias in the estimation of 3D position, which is corrected with a reformulation of the projection equation. Ego-motion is obtained by finding the rotation and translation between the two clouds of points. This problem is known as absolute orientation, and many solutions based on least squares have been proposed in the literature. This thesis reviews the available closed form solutions to the problem. The proposed framework is divided in three main blocks: 1) stereo and feature tracking computation, 2) ego-motion estimation and 3) estimation of 3D point position and 3D velocity. The first block solves the correspondence problem providing the clouds of points as output. No special implementation of this block is required in this thesis. The ego-motion block computes the motion of the cameras by finding the absolute orientation between the clouds of static points in the environment. Since the cloud of points might contain independently moving objects and outliers generated by false correspondences, the direct computation of the least squares might lead to an erroneous solution. The first contribution of this thesis is an effective rejection rule that detects outliers based on the distance between predicted and measured quantities, and reduces the effects of noisy measurement by assigning appropriate weights to the data. This method is called Smoothness Motion Constraint (SMC). The ego-motion of the camera between two frames is obtained finding the absolute orientation between consecutive clouds of weighted 3D points. The complete ego-motion since initialization is achieved concatenating the individual motion estimates. This leads to a super-linear propagation of the error, since noise is integrated. A second contribution of this dissertation is a predictor/corrector iterative method, which integrates the clouds of 3D points of multiple time instances for the computation of ego-motion. The presented method considerably reduces the accumulation of errors in the estimated ego-position of the camera. Another contribution of this dissertation is a method which recursively estimates the 3D world position of a point and its velocity; by fusing stereo, feature tracking and the estimated ego-motion in a Kalman Filter system. An improved estimation of point position is obtained this way, which is used in the subsequent system cycle resulting in an improved computation of ego-motion. The general contribution of this dissertation is a single framework for the real time computation of scene structure, independently moving objects and ego-motion for automotive applications.Autofahren kann gefĂ€hrlich sein. Die Fahrleistung wird durch die physischen und psychischen Grenzen des Fahrers und durch externe Faktoren wie das Wetter beeinflusst. Fahrerassistenzsysteme erhöhen den Fahrkomfort und unterstĂŒtzen den Fahrer, um die Anzahl an UnfĂ€llen zu verringern. Fahrerassistenzsysteme unterstĂŒtzen den Fahrer durch Warnungen mit optischen oder akustischen Signalen bis hin zur Übernahme der Kontrolle ĂŒber das Auto durch das System. Eine der Hauptvoraussetzungen fĂŒr die meisten Fahrerassistenzsysteme ist die akkurate Kenntnis der Bewegung des eigenen Fahrzeugs. Heutzutage verfĂŒgt man ĂŒber verschiedene Sensoren, um die Bewegung des Fahrzeugs zu messen, wie zum Beispiel GPS und Tachometer. Doch Auflösung und Genauigkeit dieser Systeme sind nicht ausreichend fĂŒr viele Echtzeitanwendungen. Die Berechnung der Eigenbewegung aus Stereobildsequenzen fĂŒr Fahrerassistenzsysteme, z.B. zur autonomen Navigation oder Kollisionsvermeidung, bildet den Kern dieser Arbeit. Diese Dissertation prĂ€sentiert ein System zur Echtzeitbewertung einer Szene, inklusive Detektion und Bewertung von unabhĂ€ngig bewegten Objekten sowie der akkuraten SchĂ€tzung der sechs Freiheitsgrade der Eigenbewegung. Diese grundlegenden Bestandteile sind erforderlich, um viele intelligente Automobilanwendungen zu entwickeln, die den Fahrer in unterschiedlichen Verkehrssituationen unterstĂŒtzen. Das System arbeitet ausschließlich mit einer Stereokameraplattform als Sensor. Um die Eigenbewegung und die Szenenstruktur zu berechnen wird eine Analyse des Rauschens und der Fehlerfortpflanzung im Bildaufbereitungsprozess benötigt. Deshalb werden in dieser Dissertation die Rauscheigenschaften der durch Stereotriangulation erhaltenen 3D-Punkte analysiert. Dies fĂŒhrt zu der Entdeckung eines systematischen Fehlers in der SchĂ€tzung der 3D-Position, der sich mit einer Neuformulierung der Projektionsgleichung korrigieren lĂ€sst. Die Simulationsergebnisse zeigen, dass eine bedeutende Verringerung des Fehlers in der geschĂ€tzten 3D-Punktposition möglich ist. Die EigenbewegungsschĂ€tzung wird gewonnen, indem die Rotation und Translation zwischen Punktwolken geschĂ€tzt wird. Dieses Problem ist als „absolute Orientierung” bekannt und viele Lösungen auf Basis der Methode der kleinsten Quadrate sind in der Literatur vorgeschlagen worden. Diese Arbeit rezensiert die verfĂŒgbaren geschlossenen Lösungen zu dem Problem. Das vorgestellte System gliedert sich in drei wesentliche Bausteine: 1. Registrierung von Bildmerkmalen, 2. EigenbewegungsschĂ€tzung und 3. iterative SchĂ€tzung von 3D-Position und 3D-Geschwindigkeit von Weltpunkten. Der erster Block erhĂ€lt eine Folge rektifizierter Bilder als Eingabe und liefert daraus eine Liste von verfolgten Bildmerkmalen mit ihrer entsprechenden 3D-Position. Der Block „EigenbewegungsschĂ€tzung” besteht aus vier Hauptschritten in einer Schleife: 1. Bewegungsvorhersage, 2. Anwendung der Glattheitsbedingung fĂŒr die Bewegung (GBB), 3. absolute Orientierungsberechnung und 4. Bewegungsintegration. Die in dieser Dissertation vorgeschlagene GBB ist eine mĂ€chtige Bedingung fĂŒr die Ablehnung von Ausreißern und fĂŒr die Zuordnung von Gewichten zu den gemessenen 3D-Punkten. Simulationen werden mit gaußschem und slashschem Rauschen ausgefĂŒhrt. Die Ergebnisse zeigen die Überlegenheit der GBB-Version ĂŒber die Standardgewichtungsmethoden. Die StabilitĂ€t der Ergebnisse hinsichtlich Ausreißern wurde analysiert mit dem Resultat, dass der „break down point” grĂ¶ĂŸer als 50% ist. Wenn die vier Schritte iterativ ausgefĂŒhrt, werden wird ein PrĂ€diktor-Korrektor-Verfahren gewonnen.Wir nennen diese SchĂ€tzung Multi-frameschĂ€tzung im Gegensatz zur ZweiframeschĂ€tzung, die nur die aktuellen und vorherigen Bildpaare fĂŒr die Berechnung der Eigenbewegung betrachtet. Die erste Iteration wird zwischen der aktuellen und vorherigen Wolke von Punkten durchgefĂŒhrt. Jede weitere Iteration integriert eine zusĂ€tzliche Punktwolke eines vorherigen Zeitpunkts. Diese Methode reduziert die Fehlerakkumulation bei der Integration von mehreren SchĂ€tzungen in einer einzigen globalen SchĂ€tzung. Simulationsergebnisse zeigen, dass obwohl der Fehler noch superlinear im Laufe der Zeit zunimmt, die GrĂ¶ĂŸe des Fehlers um mehrere GrĂ¶ĂŸenordnungen reduziert wird. Der dritte Block besteht aus der iterativen SchĂ€tzung von 3D-Position und 3D-Geschwindigkeit von Weltpunkten. Hier wird eine Methode basierend auf einem Kalman Filter verwendet, das Stereo, Featuretracking und Eigenbewegungsdaten fusioniert. Messungen der Position eines Weltpunkts werden durch das Stereokamerasystem gewonnen. Die Differenzierung der Position des geschĂ€tzten Punkts erlaubt die zusĂ€tzliche SchĂ€tzung seiner Geschwindigkeit. Die Messungen werden durch das Messmodell gewonnen, das Stereo- und Bewegungsdaten fusioniert. Simulationsergebnisse validieren das Modell. Die Verringerung der Positionsunsicherheit im Laufe der Zeit wird mit einer Monte-Carlo Simulation erzielt. Experimentelle Ergebnisse werden mit langen Sequenzen von Bildern erzielt. ZusĂ€tzliche Tests, einschließlich einer 3D-Rekonstruktion einer Waldszene und der Berechnung der freien Kamerabewegung in einem Indoor-Szenario, wurden durchgefĂŒhrt. Die Methode zeigt gute Ergebnisse in allen FĂ€llen. Der Algorithmus liefert zudem akzeptable Ergebnisse bei der SchĂ€tzung der Lage kleiner Objekte, wie Köpfe und Beine von realen Crash-Test-Dummies

    Multipoint Okounkov bodies, strong topology of ω-plurisubharmonic functions and K\ue4hler-Einstein metrics with prescribed singularities

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    The most classical topic in K\ue4hler Geometry is the study of K\ue4hler-Einstein metrics as solution of complex Monge-Amp\ue8re equations. This thesis principally regards the investigation of a strong topology for ω-plurisubharmonic functions on a fixed compact K\ue4hler manifold (X,ω), its connection with complex Monge-Amp\ue8re equations with prescribed singularities and the consequent study of singular K\ue4hler-Einstein metrics. However the first part of the thesis, Paper I, provides a generalization of Okounkov bodies starting from a big line bundle over a projective manifold and a bunch of distints points. These bodies encode renowned global and local invariants as the volume and the multipoint Seshadri constant.In Paper II the set of all ω-psh functions slightly more singular than a fixed singularity type are endowed with a complete metric topology whose distance represents the analog of the L1 Finsler distance on the space of K\ue4hler potentials. These spaces can be also glued together to form a bigger complete metric space when the singularity types are totally ordered. Then Paper III shows that the corresponding metric topology is actually a strong topology given as coarsest refinement of the usual topology for ω-psh functions such that the relative Monge-Amp\ue8re energy becomes continuous. Moreover the main result of Paper III proves that the extended Monge-Amp\ue8re operator produces homeomorphisms between these complete metric spaces and natural sets of singular volume forms endowed their strong topologies. Such homeomorphisms extend Yau\u27s famous solution to the Calabi\u27s conjecture and the strong topology becomes a significant tool to study the stability of solutions of complex Monge-Amp\ue8re equations with prescribed singularities. Indeed Paper IV introduces a new continuity method with movable singularities for classical families of complex Monge-Amp\ue8re equations typically attached to the search of log K\ue4hler-Einstein metrics. The idea is to perturb the prescribed singularities together with the Lebesgue densities and asking for the strong continuity of the solutions. The results heavily depend on the sign of the so-called cosmological constant and the most difficult and interesting case is related to the search of K\ue4hler-Einstein metrics on a Fano manifold. Thus Paper V contains a first analytic characterization of the existence of K\ue4hler-Einstein metrics with prescribed singularities on a Fano manifold in terms of the relative Ding and Mabuchi functionals. Then extending the Tian\u27s α-invariant into a function on the set of all singularity types, a first study of the relationships between the existence of singular K\ue4hler-Einstein metrics and genuine K\ue4hler-Einstein metrics is provided, giving a further motivation to study these singular special metrics since the existence of a genuine K\ue4hler-Einstein metric is equivalent to an algebrico-geometric stability notion called K-stability which in the last decade turned out to be very important in Algebraic Geometry
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