Mathematical Sciences: Probabilistic Methods for Image Generation and Encoding

该合同将允许继续研究使用随机迭代功能系统（IFS）来生成和编码数字图像。在IFS生成中，通过随机仿射变换的乘积在R2或R3中模拟遍历马尔可夫链，并绘制其轨迹以创建图像。IFS编码问题涉及到这样一个马尔可夫链的构造，以产生给定的目标图像。通过利用与这些链相关的变换的线性，可以对任何数字图像进行编码，并且对于广泛的图像类别，这提供了大量的数据压缩。计划分析和测试各种编码方案，并开发算法在向量机和并行机上实现它们。它在处理大规模图像和编码问题，特别是涉及图像传输和通信、图像构建和处理以及图像恢复的实时应用方面具有潜在的巨大价值。潜在的应用包括3-D机械成像、视觉（例如飞行）模拟器、声音和模式识别、光学字符和物体扫描仪、图像理解、指纹和护照编码、动画编码、高分辨率图形和高清晰度电视。

This award will permit the continued study of the use of random iterated function systems (IFS) to generate and encode digital images. In IFS generation an ergodic Markov chain is simulated in R2 or R3 through products of random affine transformations, and its trajectory is plotted to create an image. The IFS encoding problem involves the construction of such a Markov chain so as to generate a given target image. By exploiting the linearity of the transformations involved with these chains, one can encode any digital image, and for a broad class of images this affords substantial data compression. It is planned to analyze and test various encoding schemes, and to develop algorithms to implement them on vector and parallel machines. It is potentially of great value to deal with large-scale image and encoding problems, particularly involving real time applications of image transmission and communication, image construction and processing and image restoration. Potential applications include 3-D mechanical imaging, visual (e.g., flight) simulators, voice and pattern recognition, optical character and object scanners, image understanding, fingerprint and passport encoding, animation encoding, high resolution graphics and high definition TV.