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Quantization
 IEEE TRANS. INFORM. THEORY
, 1998
"... The history of the theory and practice of quantization dates to 1948, although similar ideas had appeared in the literature as long ago as 1898. The fundamental role of quantization in modulation and analogtodigital conversion was first recognized during the early development of pulsecode modula ..."
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Cited by 639 (11 self)
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The history of the theory and practice of quantization dates to 1948, although similar ideas had appeared in the literature as long ago as 1898. The fundamental role of quantization in modulation and analogtodigital conversion was first recognized during the early development of pulsecode modulation systems, especially in the 1948 paper of Oliver, Pierce, and Shannon. Also in 1948, Bennett published the first highresolution analysis of quantization and an exact analysis of quantization noise for Gaussian processes, and Shannon published the beginnings of rate distortion theory, which would provide a theory for quantization as analogtodigital conversion and as data compression. Beginning with these three papers of fifty years ago, we trace the history of quantization from its origins through this decade, and we survey the fundamentals of the theory and many of the popular and promising techniques for quantization.
Precomputed Radiance Transfer for RealTime Rendering in Dynamic, LowFrequency Lighting Environments
 ACM Transactions on Graphics
, 2002
"... We present a new, realtime method for rendering diffuse and glossy objects in lowfrequency lighting environments that captures soft shadows, interreflections, and caustics. As a preprocess, a novel global transport simulator creates functions over the object's surface representing transfer of arbi ..."
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Cited by 353 (23 self)
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We present a new, realtime method for rendering diffuse and glossy objects in lowfrequency lighting environments that captures soft shadows, interreflections, and caustics. As a preprocess, a novel global transport simulator creates functions over the object's surface representing transfer of arbitrary, lowfrequency incident lighting into transferred radiance which includes global effects like shadows and interreflections from the object onto itself. At runtime, these transfer functions are applied to actual incident lighting. Dynamic, local lighting is handled by sampling it close to the object every frame; the object can also be rigidly rotated with respect to the lighting and vice versa. Lighting and transfer functions are represented using loworder spherical harmonics. This avoids aliasing and evaluates efficiently on graphics hardware by reducing the shading integral to a dot product of 9 to 25 element vectors for diffuse receivers. Glossy objects are handled using matrices rather than vectors. We further introduce functions for radiance transfer from a dynamic lighting environment through a preprocessed object to neighboring points in space. These allow soft shadows and caustics from rigidly moving objects to be cast onto arbitrary, dynamic receivers. We demonstrate realtime global lighting effects with this approach.
Clustering with Bregman Divergences
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2005
"... A wide variety of distortion functions are used for clustering, e.g., squared Euclidean distance, Mahalanobis distance and relative entropy. In this paper, we propose and analyze parametric hard and soft clustering algorithms based on a large class of distortion functions known as Bregman divergence ..."
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Cited by 310 (52 self)
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A wide variety of distortion functions are used for clustering, e.g., squared Euclidean distance, Mahalanobis distance and relative entropy. In this paper, we propose and analyze parametric hard and soft clustering algorithms based on a large class of distortion functions known as Bregman divergences. The proposed algorithms unify centroidbased parametric clustering approaches, such as classical kmeans and informationtheoretic clustering, which arise by special choices of the Bregman divergence. The algorithms maintain the simplicity and scalability of the classical kmeans algorithm, while generalizing the basic idea to a very large class of clustering loss functions. There are two main contributions in this paper. First, we pose the hard clustering problem in terms of minimizing the loss in Bregman information, a quantity motivated by ratedistortion theory, and present an algorithm to minimize this loss. Secondly, we show an explicit bijection between Bregman divergences and exponential families. The bijection enables the development of an alternative interpretation of an ecient EM scheme for learning models involving mixtures of exponential distributions. This leads to a simple soft clustering algorithm for all Bregman divergences.
SharedDistribution Hidden Markov Models for Speech Recognition
, 1991
"... Parameter sharing plays an important role in statistical modeling since training data are usually limited. On the one hand, we would like to use models that are as detailed as possible. On the other hand, with models too detailed, we can no longer reliably estimate the parameters. Triphone generaliz ..."
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Cited by 275 (7 self)
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Parameter sharing plays an important role in statistical modeling since training data are usually limited. On the one hand, we would like to use models that are as detailed as possible. On the other hand, with models too detailed, we can no longer reliably estimate the parameters. Triphone generalization may force two models to be merged together when only parts of the model output distributions are similar, while the rest of the output distributions are different. This problem can be avoided if clustering is carried out at the distribution level. In this paper, a shareddistribution model is proposed to replace generalized triphone models for speakerindependent continuous speech recognition. Here, output distributions in the hidden Markov model are shared with each other if they exhibit acoustic similarity. In addition to detailed representation, it also gives us the freedom to use a large number of states for each phonetic model. Although an increase in the number of states will inc...
Deterministic Annealing for Clustering, Compression, Classification, Regression, and Related Optimization Problems
 Proceedings of the IEEE
, 1998
"... this paper. Let us place it within the neural network perspective, and particularly that of learning. The area of neural networks has greatly benefited from its unique position at the crossroads of several diverse scientific and engineering disciplines including statistics and probability theory, ph ..."
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Cited by 248 (11 self)
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this paper. Let us place it within the neural network perspective, and particularly that of learning. The area of neural networks has greatly benefited from its unique position at the crossroads of several diverse scientific and engineering disciplines including statistics and probability theory, physics, biology, control and signal processing, information theory, complexity theory, and psychology (see [45]). Neural networks have provided a fertile soil for the infusion (and occasionally confusion) of ideas, as well as a meeting ground for comparing viewpoints, sharing tools, and renovating approaches. It is within the illdefined boundaries of the field of neural networks that researchers in traditionally distant fields have come to the realization that they have been attacking fundamentally similar optimization problems.
Centroidal Voronoi tessellations: Applications and algorithms
 SIAM Rev
, 1999
"... Abstract. A centroidal Voronoi tessellation is a Voronoi tessellation whose generating points are the centroids (centers of mass) of the corresponding Voronoi regions. We give some applications of such tessellations to problems in image compression, quadrature, finite difference methods, distributio ..."
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Cited by 237 (25 self)
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Abstract. A centroidal Voronoi tessellation is a Voronoi tessellation whose generating points are the centroids (centers of mass) of the corresponding Voronoi regions. We give some applications of such tessellations to problems in image compression, quadrature, finite difference methods, distribution of resources, cellular biology, statistics, and the territorial behavior of animals. We discuss methods for computing these tessellations, provide some analyses concerning both the tessellations and the methods for their determination, and, finally, present the results of some numerical experiments.
Hidden Markov processes
 IEEE Trans. Inform. Theory
, 2002
"... Abstract—An overview of statistical and informationtheoretic aspects of hidden Markov processes (HMPs) is presented. An HMP is a discretetime finitestate homogeneous Markov chain observed through a discretetime memoryless invariant channel. In recent years, the work of Baum and Petrie on finite ..."
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Cited by 170 (3 self)
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Abstract—An overview of statistical and informationtheoretic aspects of hidden Markov processes (HMPs) is presented. An HMP is a discretetime finitestate homogeneous Markov chain observed through a discretetime memoryless invariant channel. In recent years, the work of Baum and Petrie on finitestate finitealphabet HMPs was expanded to HMPs with finite as well as continuous state spaces and a general alphabet. In particular, statistical properties and ergodic theorems for relative entropy densities of HMPs were developed. Consistency and asymptotic normality of the maximumlikelihood (ML) parameter estimator were proved under some mild conditions. Similar results were established for switching autoregressive processes. These processes generalize HMPs. New algorithms were developed for estimating the state, parameter, and order of an HMP, for universal coding and classification of HMPs, and for universal decoding of hidden Markov channels. These and other related topics are reviewed in this paper. Index Terms—Baum–Petrie algorithm, entropy ergodic theorems, finitestate channels, hidden Markov models, identifiability, Kalman filter, maximumlikelihood (ML) estimation, order estimation, recursive parameter estimation, switching autoregressive processes, Ziv inequality. I.
Acoustical and Environmental Robustness in Automatic Speech Recognition
, 1990
"... This dissertation describes a number of algorithms developed to increase the robustness of automatic speech recognition systems with respect to changes in the environment. These algorithms attempt to improve the recognition accuracy of speech recognition systems when they are trained and tested in d ..."
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Cited by 169 (9 self)
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This dissertation describes a number of algorithms developed to increase the robustness of automatic speech recognition systems with respect to changes in the environment. These algorithms attempt to improve the recognition accuracy of speech recognition systems when they are trained and tested in different acoustical environments, and when a desktop microphone (rather than a closetalking microphone) is used for speech input. Without such processing, mismatches between training and testing conditions produce an unacceptable degradation in recognition accuracy. Two kinds of
Spacefrequency Quantization for Wavelet Image Coding
, 1997
"... Recently, a new class of image coding algorithms coupling standard scalar quantization of frequency coefficients with treestructured quantization (related to spatial structures) has attracted wide attention because its good performance appears to confirm the promised efficiencies of hierarchical re ..."
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Cited by 152 (15 self)
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Recently, a new class of image coding algorithms coupling standard scalar quantization of frequency coefficients with treestructured quantization (related to spatial structures) has attracted wide attention because its good performance appears to confirm the promised efficiencies of hierarchical representation [1, 2]. This paper addresses the problem of how spatial quantization modes and standard scalar quantization can be applied in a jointly optimal fashion in an image coder. We consider zerotree quantization (zeroing out treestructured sets of wavelet coefficients) and the simplest form of scalar quantization (a single common uniform scalar quantizer applied to all nonzeroed coefficients), and we formalize the problem of optimizing their joint application and we develop an image coding algorithm for solving the resulting optimization problem. Despite the basic form of the two quantizers considered, the resulting algorithm demonstrates coding performance that is competitive (often...
Continuous Probabilistic Transform for Voice Conversion
 IEEE Transactions on Speech and Audio Processing
, 1998
"... Abstract — Voice conversion, as considered in this paper, is defined as modifying the speech signal of one speaker (source speaker) so that it sounds as if it had been pronounced by a different speaker (target speaker). Our contribution includes the design of a new methodology for representing the r ..."
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Cited by 129 (4 self)
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Abstract — Voice conversion, as considered in this paper, is defined as modifying the speech signal of one speaker (source speaker) so that it sounds as if it had been pronounced by a different speaker (target speaker). Our contribution includes the design of a new methodology for representing the relationship between two sets of spectral envelopes. The proposed method is based on the use of a Gaussian mixture model of the source speaker spectral envelopes. The conversion itself is represented by a continuous parametric function which takes into account the probabilistic classification provided by the mixture model. The parameters of the conversion function are estimated by least squares optimization on the training data. This conversion method is implemented in the context of the HNM (harmonic C noise model) system, which allows highquality modifications of speech signals. Compared to earlier methods based on vector quantization, the proposed conversion scheme results in a much better match between the converted envelopes and the target envelopes. Evaluation by objective tests and formal listening tests shows that the proposed transform greatly improves the quality and naturalness of the converted speech signals compared with previous proposed conversion methods. I.