CAREER: Unifying Segmentation and Other Image Processing Problems via Variational PDE's

0133736本研究围绕图像处理中的分割问题展开。分割可以被描述为在图像中定位有意义的区域的问题，在医学成像、军事成像和各种其他基于图像的应用中是一个关键的问题。这项研究的两个目标是(1)促进图像分割的发展和(2)开发框架来解决分割和其他图像处理问题。一个关键的例子(2)将集中在图像配准(对齐两个或更多图像中的常见对象)的问题上。传统上，分割(定位每幅图像中的对象)和配准(排列它们)的问题是分开解决的，本研究探索了同时解决这两个问题的方法，重要的好处是其中一个问题不需要在开始解决另一个问题之前完全解决。首席研究人员处理问题(1)和(2)的方法将主要借鉴微分几何、曲线和曲面演化、变分和偏微分方程(PDE)的数学理论。PDE包含非常自然和强大的数学工具，因为它们具有灵活性、易于实现和数学严谨性。他们目前和以前在图像处理(包括分割)问题上的应用表明了他们在这一领域的强大潜力。在建议的支持水平下，PI将尽一切努力满足本项目最初的范围和努力水平。

0133736Yezzi, AnthonyGA Tech Res CorpThis research is centered around problems of segmentation in image processing. Segmentation, which may be described as the problem of locating meaningful regions within an image, is a crucial problem in medical imaging, military imaging, and a variety of other image based applications. The two goals of this research are to (1) advance the state of the art in image segmentation and (2) develop frameworks to solve segmentation jointly with other image processing problems. A key an example of (2) will focus around the problem of image registration (aligning common objects seen within two or more images). Tradiditionally, the problems of segmentation (locating the objects in each image) and registration (lining them up) are solved separately.This research explores methods for solving such problems simultaneously, with the important benefit that one of the problems need not be fully solved before starting the solution of the other problem. The Principal Investigator's approach to problems (1) and (2) will draw strongly from the mathematical theories of differential geometry, curve and surface evolution, the calculus of variations, and partial differential equations (PDE's). PDE's comprise very natural and powerful mathematical tools due to their flexibility, ease of implementation, and mathematical rigor. Their current and previous applications to problems in image processing (including segmentation) have demonstrated their strong potential in this field.Under the recommended level of support, the PI will make every attempt to meet the original scope and level of effort of this project.