Mathematical Sciences: Probabilistic Methods for Image Generation and Encoding

该奖项将允许继续研究使用 随机迭代函数系统（IFS）生成和编码 数字图像。 在IFS生成中，遍历马尔可夫链是 通过随机仿射的乘积在R2或R3中模拟 变换，并绘制其轨迹以创建 形象 IFS编码问题涉及到构建 这样的马尔可夫链，以便生成给定的目标图像。 通过 利用涉及的变换的线性， 这些链，一个可以编码任何数字图像，并为广泛的 这提供了大量的数据压缩。 是 计划分析和测试各种编码方案，并 开发算法来实现它们的向量和并行 机械. 这对于处理大规模的 成像和编码问题，特别是涉及真实的时间 图像传输和通信的应用，图像 构建和处理以及图像恢复。 潜在 应用包括3-D机械成像，视觉（例如， 飞行）模拟器，语音和模式识别，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 图像和高清电视。

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.