Gauss Mixture Quantization for Image Compression and Segmentation

用于图像压缩和分割的高斯混合量化

• 批准号: 0073050
• 负责人: Robert Gray
• 金额: $ 60.05万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-05-15 至 2004-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0073050&HistoricalAwards=false
• 关键词: Gauss; Mixture; Quantization; Image; Compression

The research is concerned with techniques from statistical signal processing and information theory as they apply to communication systems with multiple goals. Such systems arise in multimedia communications networks like the Internet. The decomposition of data streams into different types is critical to finding information desired by a user among vast available sources, and it can also provide methods for displaying, rendering, printing, or playing the received signal that take advantage of its particular structure. Signal processing and coding theory have provided powerful mathematical models of information sources and algorithms by which these sources can be communicated and processed. Typically systems are designed as a collection of separate, unrelated, components. This can result in much less than optimal overall performance. Furthermore, it can hamper theoretical understanding of the fundamental limits on achievable performance.We treat the simultaneous design of mathematical models that account at once for information sources, data compression, and signal processing and apply to extracting information from the received data. Our emphasis is on image communication and processing. Because, the techniques draw heavily from demonstrably successful methods in speech coding and recognition they are natural for both signal types, individually or together.The research involves a unified approach to data compression, statistical classification and regression, and density estimation. It is based on a novel combination of vector quantization, Gauss mixture models, measures of minimum discrimination information (relative entropy), and universal coding. Vector quantization provides both a theoretical framework and a method for implementation. Gauss mixture models are a flexible class by which to describe information sources. They can be fit to real data by clustering with respect to a minimum discrimination information measure of distortion. A primary objective is the development and application of conditional versions of rate-distortion extremal properties of Gaussian models in order to design robust algorithms for compression, classification, modeling, and combinations thereof. There are many open questions about relations among modeling, compression, and classification/regression. Our goal is to provide answers to as many of them as possible and in so doing to contribute to understanding the interplay of modeling, signal processing, and coding. We describe optimized and implementable robust codes for compression and classification for a variety of information sources, especially for multimodal imagery. Part of our efforts are devoted to purely mathematical aspects of tree-structured regression, which is related to martingale theory and to the differentiation of integrals.

该研究涉及统计信号处理和信息论技术，因为它们适用于具有多个目标的通信系统。此类系统出现在诸如互联网之类的多媒体通信网络中。将数据流分解为不同类型对于在大量可用源中查找用户所需的信息至关重要，并且它还可以提供利用其特定结构来显示、呈现、打印或播放接收到的信号的方法。信号处理和编码理论提供了强大的信息源数学模型和算法，通过这些模型可以对这些源进行通信和处理。通常，系统被设计为独立的、不相关的组件的集合。这可能会导致整体性能远低于最佳状态。此外，它可能会妨碍对可实现性能的基本限制的理论理解。我们处理数学模型的同步设计，这些模型同时考虑信息源、数据压缩和信号处理，并应用于从接收到的数据中提取信息。我们的重点是图像通信和处理。因为这些技术在很大程度上借鉴了语音编码和识别中明显成功的方法，它们对于两种信号类型（单独或一起）都是自然的。该研究涉及数据压缩、统计分类和回归以及密度估计的统一方法。它基于矢量量化、高斯混合模型、最小区分信息（相对熵）测量和通用编码的新颖组合。矢量量化既提供了理论框架，又提供了实现方法。高斯混合模型是描述信息源的灵活类别。它们可以通过相对于失真的最小辨别信息度量进行聚类来适合真实数据。主要目标是开发和应用高斯模型率失真极值属性的条件版本，以便设计用​​于压缩、分类、建模及其组合的鲁棒算法。关于建模、压缩和分类/回归之间的关系还有许多悬而未决的问题。我们的目标是为尽可能多的问题提供答案，从而有助于理解建模、信号处理和编码之间的相互作用。我们描述了用于各种信息源（尤其是多模态图像）的压缩和分类的优化且可实现的鲁棒代码。我们的部分工作致力于树结构回归的纯数学方面，这与鞅理论和积分微分相关。