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

职业：通过变分偏微分方程统一分割和其他图像处理问题

• 批准号: 0133736
• 负责人: Anthony Yezzi
• 金额: $ 35万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-06-01 至 2008-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0133736&HistoricalAwards=false
• 关键词: CAREER; Unifying; Segmentation; Other; Image

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.

0133736Yezzi，AnthonyGA Tech Res Corp 这项研究主要围绕图像处理中的分割问题。 分割可以被描述为在图像中定位有意义区域的问题，是医学成像、军事成像和各种其他基于图像的应用中的关键问题。这项研究的两个目标是（1）推进图像分割的最新技术；（2）开发框架来共同解决分割和其他图像处理问题。 (2) 的一个关键示例将重点关注图像配准问题（对齐两个或多个图像中看到的常见对象）。 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。本研究探索同时解决这些问题的方法，其重要的好处是在开始解决另一个问题之前不需要完全解决一个问题。首席研究员解决问题（1）和（2）的方法将很大程度上借鉴微分几何、曲线和曲面演化、变分法和偏微分方程（PDE）的数学理论。 由于其灵活性、易于实现和数学严谨性，偏微分方程包含非常自然和强大的数学工具。他们当前和以前在图像处理（包括分割）问题上的应用已经证明了他们在该领域的强大潜力。在建议的支持级别下，PI将尽一切努力满足该项目的原始范围和工作水平。