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

摘要：随着数字形式的视觉信息的巨大增长，迫切需要更强大、更有效的图像处理应用。在许多这些图像处理任务的基础是一个有效的表示，可以用一个小的描述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，如傅里叶和小波，并不一定最适合图像。人们有强烈的动机去寻找更强大的方案，能够捕捉到内在的几何结构，这是图像信息的关键。实现这一步骤将导致图像处理许多领域的根本进步。该项目涉及开发新的“真实”二维表示，可以更有效地处理具有光滑轮廓的典型图像。重点是使用不可分离滤波器组开发定向和多分辨率图像扩展，与从滤波器组构建小波的方式大致相同。从本质上讲，研究者追求小波和多分辨率技术的不可分离扩展，以便它们能够捕获方向信息——多维信号的重要和独特特征。与此同时，新开发的图像表示在各种应用中进行了探索，期望对当前方法进行实质性改进。该项目的教育部分通过设计一门新的课程来教授专门为多维信号开发的基本处理方法，从而最大限度地发挥研究成果和最近相关发现的效益；开发计算工具箱和可重复实验，训练学生熟练使用这些方法；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.