CAREER: Directional Multiresolution Image Processing: Theory, Algorithms and Applications

伊利诺伊州的Minh N.Dou@Urbana Champain数字形式的视觉信息的巨大增长产生了对更强大和更有效的图像处理应用的迫切需求。其中许多图像处理任务的基础是一种有效的表示，它可以使用较小的描述来捕获重要的图像信息。最近，很明显，常用的一维变换的可分离扩展，如傅立叶变换和小波变换，并不一定最适合图像。有强烈的动机寻找更强大的方案，可以捕捉内在的几何结构，这是图片信息的关键。实现这一步将在图像处理的许多领域带来根本性的进步。该项目涉及开发新的真正的二维表示法，该表示法可以更有效地处理具有平滑轮廓的典型图像。重点放在使用不可分离的滤波器组进行定向和多分辨率图像扩展的发展上，这与从滤波器组构造小波的方式大致相同。本质上，研究人员追求小波和多分辨率技术的不可分离扩展，以便它们能够捕捉方向信息--多维信号的一个重要而独特的特征。与此同时，新开发的图像表示法在各种应用中都得到了探索，在这些应用中，预计会比现有方法有实质性的改进。该项目的教育部分通过以下方式最大限度地发挥研究成果和最近相关发现的好处：设计一门新课程，教授专门为多维信号开发的基本处理方法；开发计算工具箱和可重复的实验，以培训熟练使用这些方法的学生；以及让学生接触精心设计的项目，以获得实践经验。

ABSTRACT0237633Minh N. DoU of Illinois @ Urbana ChampaignThe enormous growth of visual information in digital form has produced an urgent need for more powerful and effective image processing applications. At the foundation of many of these image processing tasks is an efficient representation that can capture significant image information using a small description. Recently, it has become evident that the commonly used separable extensions from one-dimensional transforms, such as Fourier and wavelet, are not necessarily best suited for images. There is strong motivation to search for more powerful schemes that can capture the intrinsic geometrical structure that is key in pictorial information. Achieving this step will lead to fundamental advances in a number of areas in image processing.This project involves developing new "true" two-dimensional representations that can deal more effectively with typical images having smooth contours. The focus is on the development of directional and multiresolution image expansions using non-separable filter banks, in much the same way that wavelets were constructed from filter banks. In essence, the investigator pursues non-separable extensions of wavelets and multiresolution techniques so that they can capture the directional information -- an important and unique feature of multidimensional signals. In parallel, newly developed image representations are explored in a variety of applications, where substantial improvements over current methods are expected. The educational part of the project maximizes the benefits of the research results and recent related discoveries through: designing a new course to teach fundamental processing methods that werespecially developed for multidimensional signals; developing computational toolboxes and reproducible experiments to train students using these methods proficiently; and exposing students to well-designed projects to gain hands-on experiences.