Research in Manipulating Fractal Images and Fractal Analysis

网络计算机的世界导致了数字信息的爆炸式增长。这在信息的传输和存储方面都造成了问题。因为“一张图片胜过千言万语”，很多信息都是以图像数据的形式存在的。然而，图片比文字需要更多的数据来存储。因此，有必要以某种方式减少这种存储需求。已经发现了许多不同的“压缩”这些信息的方法，其中一种涉及到分形的使用。分形为描述自然现象提供了一种方便的方法，因此在各种技术领域中得到了广泛的应用。与其他流行的方法相比，分形已被证明提供了一种有效的图像压缩方案。这个项目将采取下一步——使用分形作为压缩工具和分析工具。在使用分形方法压缩图像数据的情况下，尝试使用分形描述来分析图像是很自然的。一种方法是提取图像的某些部分进行处理，比如识别照片中的人脸。另一个例子是使用岩石表面图像的分形描述来识别岩石类型或预测岩石的物理性质。本研究项目将开发使用分形压缩图像的数据来提取有关图像的进一步有意义的信息的方法。使用分形来压缩和分析信息。该GOALI项目由MPS多学科活动办公室（OMA）和数学科学司（DMS）联合支持。

The world of networked computers has resulted in an explosion of digital information. This causes a problem in both transmission and storage of this information. Since "a picture is worth a thousand words", much of this information is in the form of image data. However, pictures require much more data to store than words. Thus, it is necessary to reduce this storage requirement somehow. Many different ways of "compressing" this information have been discovered, among them one that involves the use of fractals. Fractals provide a convenient way of describing natural phenomena, thus they have found many uses in various technical fields. Fractals have proven to provide an efficient scheme to compress images, comparing favorably with other popular methods. This project will take the next step -- using fractals as both a compression tool as well as an analysis tool. Given image data comresses using the method of fractals, it is natural to try to use the fractal description to analyze the image. One would like to extract parts of the image for processing -- say to recognize a face in a picture. Another example would be to use the fractal description of an image of a rock face to recognize the rock type or to predict physical properties of the rock. This research project will develop methods to use the data from a fractal compressed image to extract further meaningful information about the image. Use fractals to compress as well as analyze information. This GOALI project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).