There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Monte Carlo methods are revolutionizing the on-line analysis of data in fields as diverse as financial modeling, target tracking and computer vision. These methods, appearing under the names of bootstrap filters, condensation, optimal Monte Carlo filters, particle filters and survival of the fittest, have made it possible to solve numerically many complex, non-standard problems that were previously intractable. This book presents the first comprehensive treatment of these techniques, including convergence results and applications to tracking, guidance, automated target recognition, aircraft navigation, robot navigation, econometrics, financial modeling, neural networks, optimal control, optimal filtering, communications, reinforcement learning, signal enhancement, model averaging and selection, computer vision, semiconductor design, population biology, dynamic Bayesian networks, and time series analysis. This will be of great value to students, researchers and practitioners, who have some basic knowledge of probability. Arnaud Doucet received the Ph. D. degree from the University of Paris-XI Orsay in 1997. From 1998 to 2000, he conducted research at the Signal Processing Group of Cambridge University, UK. He is currently an assistant professor at the Department of Electrical Engineering of Melbourne University, Australia. His research interests include Bayesian statistics, dynamic models and Monte Carlo methods. Nando de Freitas obtained a Ph.D. degree in information engineering from Cambridge University in 1999. He is presently a research associate with the artificial intelligence group of the University of California at Berkeley. His main research interests are in Bayesian statistics and the application of on-line and batch Monte Carlo methods to machine learning. Neil Gordon obtained a Ph.D. in Statistics from Imperial College, University of London in 1993. He is with the Pattern and Information Processing group at the Defence Evaluation and Research Agency in the United Kingdom. His research interests are in time series, statistical data analysis, and pattern recognition with a particular emphasis on target tracking and missile guidance.

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Sequential Monte Carlo methods in practice

The problem of tracking curves in dense visual clutter is challenging. Kalman filtering is inadequate because it is based on Gaussian densities which, being unimo dal, cannot represent simultaneous alternative hypotheses. The Condensation algorithm uses “factored sampling”, previously applied to the interpretation of static images, in which the probability distribution of possible interpretations is represented by a randomly generated set. Condensation uses learned dynamical models, together with visual observations, to propagate the random set over time. The result is highly robust tracking of agile motion. Notwithstanding the use of stochastic methods, the algorithm runs in near real-time.

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C ONDENSATION —Conditional Density Propagation forVisual Tracking

We propose a natural scene statistic-based distortion-generic blind/no-reference (NR) image quality assessment (IQA) model that operates in the spatial domain. The new model, dubbed blind/referenceless image spatial quality evaluator (BRISQUE) does not compute distortion-specific features, such as ringing, blur, or blocking, but instead uses scene statistics of locally normalized luminance coefficients to quantify possible losses of “naturalness” in the image due to the presence of distortions, thereby leading to a holistic measure of quality. The underlying features used derive from the empirical distribution of locally normalized luminances and products of locally normalized luminances under a spatial natural scene statistic model. No transformation to another coordinate frame (DCT, wavelet, etc.) is required, distinguishing it from prior NR IQA approaches. Despite its simplicity, we are able to show that BRISQUE is statistically better than the full-reference peak signal-to-noise ratio and the structural similarity index, and is highly competitive with respect to all present-day distortion-generic NR IQA algorithms. BRISQUE has very low computational complexity, making it well suited for real time applications. BRISQUE features may be used for distortion-identification as well. To illustrate a new practical application of BRISQUE, we describe how a nonblind image denoising algorithm can be augmented with BRISQUE in order to perform blind image denoising. Results show that BRISQUE augmentation leads to performance improvements over state-of-the-art methods. A software release of BRISQUE is available online: http://live.ece.utexas.edu/research/quality/BRISQUE_release.zip for public use and evaluation.

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No-Reference Image Quality Assessment in the Spatial Domain

From the Publisher: 
The accessible presentation of this book gives both a general view of the entire computer vision enterprise and also offers sufficient detail to be able to build useful applications. Users learn techniques that have proven to be useful by first-hand experience and a wide range of mathematical methods. A CD-ROM with every copy of the text contains source code for programming practice, color images, and illustrative movies. Comprehensive and up-to-date, this book includes essential topics that either reflect practical significance or are of theoretical importance. Topics are discussed in substantial and increasing depth. Application surveys describe numerous important application areas such as image based rendering and digital libraries. Many important algorithms broken down and illustrated in pseudo code. Appropriate for use by engineers as a comprehensive reference to the computer vision enterprise.

Computer vision : a modern approach = 计算机视觉 : 一种现代的方法

We introduce a novel geometric framework for separating the phase and the amplitude variability in functional data of the type frequently studied in growth curve analysis. This framework uses the Fisher-Rao Riemannian metric to derive a proper distance on the quotient space of functions modulo the time-warping group. A convenient square-root velocity function (SRVF) representation transforms the Fisher-Rao metric into the standard $\ltwo$ metric, simplifying the computations. This distance is then used to define a Karcher mean template and warp the individual functions to align them with the Karcher mean template. The strength of this framework is demonstrated by deriving a consistent estimator of a signal observed under random warping, scaling, and vertical translation. These ideas are demonstrated using both simulated and real data from different application domains: the Berkeley growth study, handwritten signature curves, neuroscience spike trains, and gene expression signals. The proposed method is empirically shown to be be superior in performance to several recently published methods for functional alignment.

Statistical Analysis and Modeling of Elastic Functions

The elastic shape analysis of surfaces has proven useful in several application areas, including medical image analysis, vision, and graphics.

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Numerical Inversion of SRNFs for Efficient Elastic Shape Analysis of Star-Shaped Objects

The main goal of this paper is to illustrate a geometric analysis of 3D facial shapes in presence of varying facial expressions using the nose region. This approach consists of the following two main steps: (i) Each nasal surface is automatically denoised and preprocessed to result in an indexed collection of nasal curves. During this step one detects the tip of the nose and defines a surface distance function with that tip as the reference point. The level curves of this distance function are the desired nasal curves. (ii) Comparisons between noses are based on optimal deformations from one to another. This, in turn, is based on optimal deformations of the corresponding nasal curves across surfaces under an elastic metric. The experimental results, generated using a subset of FRGC v2 dataset, demonstrate the success of the proposed framework in recognizing people under different facial expressions. The recognition rates obtained here exceed those for a baseline ICP algorithm on the same dataset.

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Nasal Region Contribution in 3D Face Biometrics Using Shape Analysis Framework

The side information (SI) in Distributed Video Coding (DVC) is estimated using the available decoded frames and exploited for the decoding and reconstruction of other frames. The quality of the SI has a strong impact on the performance of DVC. Here, we propose a new approach that combines both global and local SI to improve coding performance. Since the background pixels in a frame are assigned to global estimation and the foreground objects to local estimation, one needs to estimate foreground objects in the SI using the backward and forward foreground objects, the background pixels are directly taken from the global SI. Specifically, elastic curves and local motion compensation are used to generate the foreground objects masks in the SI. Experimental results show that, as far as the rate-distortion performance is concerned, the proposed approach can achieve a PSNR improvement of up to 1.39 dB for a group of picture (GOP) size of 2, and up to 4.73 dB for larger GOP sizes, with respect to the reference DISCOVER codec.

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Fusion of Global and Local Motion Estimation Using Foreground Objects for Distributed Video Coding

Past approaches for statistical shape analysis of objects have focused mainly on objects within the same topological classes, eg, scalar functions, Euclidean curves, or surfaces, etc For objects that differ in more complex ways, the current literature offers only topological methods This paper introduces a far-reaching geometric approach for analyzing shapes of graphical objects, such as road networks, blood vessels, brain fiber tracts, etc It represents such objects, exhibiting differences in both geometries and topologies, as graphs made of curves with arbitrary shapes (edges) and connected at arbitrary junctions (nodes) To perform statistical analyses, one needs mathematical representations, metrics and other geometrical tools, such as geodesics, means, and covariances This paper utilizes a quotient structure to develop efficient algorithms for computing these quantities, leading to useful statistical tools, including principal component analysis and analytical statistical testing and modeling of graphical shapes The efficacy of this framework is demonstrated using various simulated as well as the real data from neurons and brain arterial networks

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Anuj Srivastava

Papers

Statistical Analysis and Modeling of Elastic Functions

Numerical Inversion of SRNFs for Efficient Elastic Shape Analysis of Star-Shaped Objects

Nasal Region Contribution in 3D Face Biometrics Using Shape Analysis Framework

Fusion of Global and Local Motion Estimation Using Foreground Objects for Distributed Video Coding

Representations, Metrics and Statistics for Shape Analysis of Elastic Graphs