QR-RLS algorithm for error diffusion of color images

Printing color images on color printers and displaying them on computer monitors requires a significant reduction of physically distinct colors, which causes degradation in image quality. An efficient method to improve the display quality of a quantized image is error diffusion, which works by distributing the previous quantization errors to neighboring pixels, exploiting the eye's averaging of colors in the neighborhood of the point of interest. This creates the illusion of more colors. A new error diffusion method is presented in which the adaptive recursive least-squares (RLS) algorithm is used. This algorithm provides local optimization of the error diffusion filter along with smoothing of the filter coefficients in a neighborhood. To improve the performance, a diagonal scan is used in processing the image, (C) 2000 Society of Photo-Optical Instrumentation Engineers. [S0091-3286(00)00611-5]

QR-RLS algorithm for error diffusion of color images

Printing color images on color printers and displaying them on computer monitors requires a significant reduction of physically distinct colors, which causes degradation in image quality. An efficient method to improve the display quality of a quantized image is error diffusion, which works by distributing the previous quantization errors to neighboring pixels, exploiting the eye's averaging of colors in the neighborhood of the point of interest. This creates the illusion of more colors. A new error diffusion method is presented in which the adaptive recursive least-squares (RLS) algorithm is used. This algorithm provides local optimization of the error diffusion filter along with smoothing of the filter coefficients in a neighborhood. To improve the performance, a diagonal scan is used in processing the image

Novel methods in image halftoning

Ankara : Department of Electrical and Electronics Engineering and Institute of Engineering and Science, Bilkent Univ., 1998.Thesis (Master's) -- Bilkent University, 1998.Includes bibliographical references leaves 97-101Halftoning refers to the problem of rendering continuous-tone (contone) images on display and printing devices which are capable of reproducing only a limited number of colors. A new adaptive halftoning method using the adaptive QR- RLS algorithm is developed for error diffusion which is one of the halftoning techniques. Also, a diagonal scanning strategy to exploit the human visual system properties in processing the image is proposed. Simulation results on color images demonstrate the superior quality of the new method compared to the existing methods. Another problem studied in this thesis is inverse halftoning which is the problem of recovering a contone image from a given halftoned image. A novel inverse halftoning method is developed for restoring a contone image from the halftoned image. A set theoretic formulation is used where sets are defined using the prior information about the problem. A new space domain projection is introduced assuming the halftoning is performed ,with error diffusion, and the error diffusion filter kernel is known. The space domain, frequency domain, and space-scale domain projections are used alternately to obtain a feasible solution for the inverse halftoning problem which does not have a unique solution. Simulation results for both grayscale and color images give good results, and demonstrate the effectiveness of the proposed inverse halftoning method.Bozkurt, GözdeM.S

Fully-resolved simulations of coal particle combustion using a detailed multi-step approach for heterogeneous kinetics

Fully-resolved simulations of the heating, ignition, volatile flame combustion and char conversion of single coal particles in convective gas environments are conducted and compared to experimental data (Molina and Shaddix, 2007). This work extends a previous computational study (Tufano et al., 2016) by adding a significant level of model fidelity and generality, in particular with regard to the particle interior description and hetero- geneous kinetics. The model considers the elemental analysis of the given coal and interpolates its properties by linear superposition of a set of reference coals. The improved model description alleviates previously made assumptions of single-step pyrolysis, fixed volatile composition and simplified particle interior properties, and it allows for the consideration of char conversion. The results show that the burning behavior is affected by the oxygen concentration, i.e. for enhanced oxygen levels ignition occurs in a single step, whereas decreasing the oxygen content leads to a two-stage ignition process. Char conversion becomes dominant once the volatiles have been depleted, but also causes noticeable deviations of temperature, released mass, and overall particle con- version during devolatilization already, indicating an overlap of the two stages of coal conversion which are usually considered to be consecutive. The complex pyrolysis model leads to non-monotonous profiles of the combustion quantities which introduce a minor dependency of the ignition delay time $τ_{ign}$ on its definition. Regardless of the chosen extraction method, the simulations capture the measured values of $τ_{ign}$ very well

Adaptive filtering algorithms for quaternion-valued signals

Advances in sensor technology have made possible the recoding of three and four-dimensional signals which afford a better representation of our actual three-dimensional world than the ``flat view'' one and two-dimensional approaches. Although it is straightforward to model such signals as real-valued vectors, many applications require unambiguous modeling of orientation and rotation, where the division algebra of quaternions provides crucial advantages over real-valued vector approaches. The focus of this thesis is on the use of recent advances in quaternion-valued signal processing, such as the quaternion augmented statistics, widely-linear modeling, and the HR-calculus, in order to develop practical adaptive signal processing algorithms in the quaternion domain which deal with the notion of phase and frequency in a compact and physically meaningful way. To this end, first a real-time tracker of quaternion impropriety is developed, which allows for choosing between strictly linear and widely-linear quaternion-valued signal processing algorithms in real-time, in order to reduce computational complexity where appropriate. This is followed by the strictly linear and widely-linear quaternion least mean phase algorithms that are developed for phase-only estimation in the quaternion domain, which is accompanied by both quantitative performance assessment and physical interpretation of operations. Next, the practical application of state space modeling of three-phase power signals in smart grid management and control systems is considered, and a robust complex-valued state space model for frequency estimation in three-phase systems is presented. Its advantages over other available estimators are demonstrated both in an analytical sense and through simulations. The concept is then expanded to the quaternion setting in order to make possible the simultaneous estimation of the system frequency and its voltage phasors. Furthermore, a distributed quaternion Kalman filtering algorithm is developed for frequency estimation over power distribution networks and collaborative target tracking. Finally, statistics of stable quaternion-valued random variables, that include quaternion-valued Gaussian random variables as a special case, is investigated in order to develop a framework for the modeling and processing of heavy-tailed quaternion-valued signals.Open Acces

Color Sparse Representations for Image Processing: Review, Models, and Prospects

International audienceSparse representations have been extended to deal with color images composed of three channels. A review of dictionary-learning-based sparse representations for color images is made here, detailing the differences between the models, and comparing their results on real data and simulated data. These models are considered in a unifying framework that is based on the degrees of freedom of the linear filtering/transformation of the color channels. Moreover, this allows it to be shown that the scalar quaternionic linear model is equivalent to constrained matrix-based color filtering, which highlights the filtering implicitly applied through this model. Based on this reformulation, the new color filtering model is introduced, using unconstrained filters. In this model, spatial morphologies of color images are encoded by atoms, and colors are encoded by color filters. Color variability is no longer captured in increasing the dictionary size, but with color filters, this gives an efficient color representation

Sensor Signal and Information Processing II

In the current age of information explosion, newly invented technological sensors and software are now tightly integrated with our everyday lives. Many sensor processing algorithms have incorporated some forms of computational intelligence as part of their core framework in problem solving. These algorithms have the capacity to generalize and discover knowledge for themselves and learn new information whenever unseen data are captured. The primary aim of sensor processing is to develop techniques to interpret, understand, and act on information contained in the data. The interest of this book is in developing intelligent signal processing in order to pave the way for smart sensors. This involves mathematical advancement of nonlinear signal processing theory and its applications that extend far beyond traditional techniques. It bridges the boundary between theory and application, developing novel theoretically inspired methodologies targeting both longstanding and emergent signal processing applications. The topic ranges from phishing detection to integration of terrestrial laser scanning, and from fault diagnosis to bio-inspiring filtering. The book will appeal to established practitioners, along with researchers and students in the emerging field of smart sensors processing

Robust convex optimisation techniques for autonomous vehicle vision-based navigation

This thesis investigates new convex optimisation techniques for motion and pose estimation. Numerous computer vision problems can be formulated as optimisation problems. These optimisation problems are generally solved via linear techniques using the singular value decomposition or iterative methods under an L2 norm minimisation. Linear techniques have the advantage of offering a closed-form solution that is simple to implement. The quantity being minimised is, however, not geometrically or statistically meaningful. Conversely, L2 algorithms rely on iterative estimation, where a cost function is minimised using algorithms such as Levenberg-Marquardt, Gauss-Newton, gradient descent or conjugate gradient. The cost functions involved are geometrically interpretable and can statistically be optimal under an assumption of Gaussian noise. However, in addition to their sensitivity to initial conditions, these algorithms are often slow and bear a high probability of getting trapped in a local minimum or producing infeasible solutions, even for small noise levels. In light of the above, in this thesis we focus on developing new techniques for finding solutions via a convex optimisation framework that are globally optimal. Presently convex optimisation techniques in motion estimation have revealed enormous advantages. Indeed, convex optimisation ensures getting a global minimum, and the cost function is geometrically meaningful. Moreover, robust optimisation is a recent approach for optimisation under uncertain data. In recent years the need to cope with uncertain data has become especially acute, particularly where real-world applications are concerned. In such circumstances, robust optimisation aims to recover an optimal solution whose feasibility must be guaranteed for any realisation of the uncertain data. Although many researchers avoid uncertainty due to the added complexity in constructing a robust optimisation model and to lack of knowledge as to the nature of these uncertainties, and especially their propagation, in this thesis robust convex optimisation, while estimating the uncertainties at every step is investigated for the motion estimation problem. First, a solution using convex optimisation coupled to the recursive least squares (RLS) algorithm and the robust H filter is developed for motion estimation. In another solution, uncertainties and their propagation are incorporated in a robust L convex optimisation framework for monocular visual motion estimation. In this solution, robust least squares is combined with a second order cone program (SOCP). A technique to improve the accuracy and the robustness of the fundamental matrix is also investigated in this thesis. This technique uses the covariance intersection approach to fuse feature location uncertainties, which leads to more consistent motion estimates. Loop-closure detection is crucial in improving the robustness of navigation algorithms. In practice, after long navigation in an unknown environment, detecting that a vehicle is in a location it has previously visited gives the opportunity to increase the accuracy and consistency of the estimate. In this context, we have developed an efficient appearance-based method for visual loop-closure detection based on the combination of a Gaussian mixture model with the KD-tree data structure. Deploying this technique for loop-closure detection, a robust L convex posegraph optimisation solution for unmanned aerial vehicle (UAVs) monocular motion estimation is introduced as well. In the literature, most proposed solutions formulate the pose-graph optimisation as a least-squares problem by minimising a cost function using iterative methods. In this work, robust convex optimisation under the L norm is adopted, which efficiently corrects the UAV’s pose after loop-closure detection. To round out the work in this thesis, a system for cooperative monocular visual motion estimation with multiple aerial vehicles is proposed. The cooperative motion estimation employs state-of-the-art approaches for optimisation, individual motion estimation and registration. Three-view geometry algorithms in a convex optimisation framework are deployed on board the monocular vision system for each vehicle. In addition, vehicle-to-vehicle relative pose estimation is performed with a novel robust registration solution in a global optimisation framework. In parallel, and as a complementary solution for the relative pose, a robust non-linear H solution is designed as well to fuse measurements from the UAVs’ on-board inertial sensors with the visual estimates. The suggested contributions have been exhaustively evaluated over a number of real-image data experiments in the laboratory using monocular vision systems and range imaging devices. In this thesis, we propose several solutions towards the goal of robust visual motion estimation using convex optimisation. We show that the convex optimisation framework may be extended to include uncertainty information, to achieve robust and optimal solutions. We observed that convex optimisation is a practical and very appealing alternative to linear techniques and iterative methods

Greedy adaptive algorithms for sparse representations

A vector or matrix is said to be sparse if the number of non-zero elements is significantly smaller than the number of zero elements. In estimation theory the vectors of model parameters can be known in advance to have a sparse structure, and solving an estimation problem taking into account this constraint can improve substantially the accuracy of the solution. The theory of sparse models has advanced significantly in recent years providing many results that can guarantee certain properties of the sparse solutions. These performance guarantees can be very powerful in applications and they have no correspondent in the estimation theory for non-sparse models. Model sparsity is an inherent characteristic of many applications (image compressing, wireless channel estimation, direction of arrival) in signal processing and other related areas.Due to the continuous technological advances that allow faster numerical computations, optimization problems, too complex to be solved in the past, are now able to provide better solutions by considering also sparsity constraints. However, an exhaustive search to finding sparse solutions generally requires a combinatorial search for the correct support, a very limiting factor due to the huge numerical complexity. This motivated a growing interest towards developing batch sparsity aware algorithms in the past twenty years. More recently, the main goal for the continuous research related to sparsity is the quest for faster, less computational intensive, adaptive methods able to recursively update the solution. In this thesis we present several such algorithms. They are greedy in nature and minimize the least squares criterion under the constraint that the solution is sparse. Similarly to other greedy sparse methods, two main steps are performed once new data are available: update the sparse support by changing the positions that contribute to the solution; compute the coefficients towards the minimization of the least squares criterion restricted to the current support. Two classes of adaptive algorithms were proposed. The first is derived from the batch matching pursuit algorithm. It uses a coordinate descent approach to update the solution, each coordinate being selected by a criterion similar to the one used by matching pursuit. We devised two algorithms that use a cyclic update strategy to improve the solution at each time instant. Since the solution support and coefficient values are assumed to vary slowly, a faster and better performing approach is later proposed by spreading the coordinate descent update in time. It was also adapted to work in a distributed setup in which different nodes communicate with their neighbors to improve their local solution towards a global optimum. The second direction can be linked to the batch orthogonal least squares. The algorithms maintain a partial QR decomposition with pivoting and require a permutation based support selection strategy to ensure a low complexity while allowing the tracking of slow variations in the support. Two versions of the algorithm were proposed. They allow past data to be forgotten by using an exponential or a sliding window, respectively. The former was modified to improve the solution in a structured sparsity case, when the solution is group sparse. We also propose mechanisms for estimating online the sparsity level. They are based on information theoretic criteria, namely the predictive least squares and the Bayesian information criterion. The main contributions are the development of the adaptive greedy algorithms and the use of the information theoretic criteria enabling the algorithms to behave robustly. The algorithms have good performance, require limited prior information and are computationally efficient. Generally, the configuration parameters, if they exist, can be easily chosen as a tradeoff between the stationary error and the convergence speed