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 analog-to-digital 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 high-resolution 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 analog-to-digital 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.

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 ill-defined 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.

Recently, a new class of image coding algorithms coupling standard scalar quantization of frequency coefficients with tree-structured 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 tree-structured sets of wavelet coefficients) and the simplest form of scalar quantization (a single common uniform scalar quantizer applied to all non-zeroed 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...

Algorithms for approximately optimal quantization of color images are discussed. The distortion measure used is the distance in RGB space. These algorithms are used to compute the color map for low-depth frame buffers in order to allow high-quality static images to be displayed. It is demonstrated that most color images can be very well displayed using only 256 or 512 colors. Thus frame buffers of only 8 or 9 bits can display images that normally require 15 bits or more per pixel. Work reported herein was sponsored by the IBM Corporation though a general grant agreement to MIT dated July 1, 1979. ----------------------------------------------------------------- TABLE OF CONTENTS page I. Introduction ............................................. 4 II. Frame Buffers and Colormaps .............................. 6 III. 1-Dimensional Tapered Quantization .......................17 IV. 3-Dimensional Tapered Quantization .......................27 V. Conclusions and Ideas for Further Study .......

We introduce multi-chart geometry images, a new representation for arbitrary surfaces. It is created by resampling a surface onto a regular 2D grid. Whereas the original scheme of Gu et al. maps the entire surface onto a single square, we use an atlas construction to map the surface piecewise onto charts of arbitrary shape. We demonstrate that this added flexibility reduces parametrization distortion and thus provides greater geometric fidelity, particularly for shapes with long extremities, high genus, or disconnected components. Traditional atlas constructions suffer from discontinuous reconstruction across chart boundaries, which in our context create unacceptable surface cracks. Our solution is a novel zippering algorithm that creates a watertight surface. In addition, we present a new atlas chartification scheme based on clustering optimization.

in the area of digital color imaging. In order to establish the background and lay down terminology, fundamental concepts of color perception and measurement are first presented using vector-space notation and terminology. Present-day color recording and reproduction systems are reviewed along with the common mathematical models used for representing these devices. Algorithms for processing color images for display and communication are surveyed, and a forecast of research trends is attempted. An extensive bibliography is provided. I.

A fundamental problem in the transmission of analog information across a noisy discrete channel is the choice of channel code rate that optimally allocates the available transmission rate between lossy source coding and block channel coding. We establish tight bounds on the channel code rate that minimizes the average distortion of a vector quantizer cascaded with a channel coder and a binary-symmetric channel. Analytic expressions are derived in two cases of interest: small bit-error probability and arbitrary source vector dimension; arbitrary bit-error probability and large source vector dimension. We demonstrate that the optimal channel code rate is often substantially smaller than the channel capacity, and obtain a noisy-channel version of the Zador high-resolution distortion formula. Index Terms---Combined source and channel coding, error exponents, high-resolution vector quantization, separation theorem. I. INTRODUCTION S UPPOSE a lossy source coder (vector quantizer) takes an...

This paper describes two methodologies for performing distributed particle filtering in a sensor network. It considers the scenario in which a set of sensor nodes make multiple, noisy measurements of an underlying, time-varying state that describes the monitored system. The goal of

Subband and wavelet decompositions are powerful tools in image coding, because of their decorrelating effects on image pixels, the concentration of energy in a few coefficients, their multirate/multiresolution framework, and their frequency splitting which allows for efficient coding matched to the statistics of each frequency band and to the characteristics of the human visual system. Vector quantization provides a means of converting the decomposed signal into bits in a manner that takes advantage of remaining inter- and intra-band correlation as well as of the more flexible partitions of higher dimensional vector spaces. Since 1988 a growing body of research has examined the use of vector quantization for subband/wavelet transform coefficients. We present a survey of these methods. 1 Introduction Image compression maps an original image into a bit stream suitable for communication over or storage in a digital medium. The number of bits required to represent the coded image should b...

The wavelet transform has become a cutting-edge technology in image compression research. This article explains what wavelets are and provides a practical, nuts-andbolts tutorial on wavelet-based compression that will help readers to understand and experiment with this important new technology. Keywords: image coding, signal compression, wavelet transform, image transforms 1 Introduction The advent of multimedia computing has lead to an increased demand for digital images. The storage and manipulation of these images in their raw form is very expensive; for example, a standard 35mm photograph digitized at 12 ¯m per pixel requires about 18 MBytes of storage and one second of NTSC-quality color video requires almost 23 MBytes of storage. To make widespread use of digital imagery practical, some form of data compression must be used. Digital images can be compressed by eliminating redundant information. There are three types of redundancy that can be exploited by image compression system...