New Directions in Active Contours by Reformulating Geometric Gradients

通过重新制定几何梯度来实现主动轮廓的新方向

基本信息

批准号：
0728911
负责人：
Anthony Yezzi
金额：
$ 25.02万
依托单位：
Georgia Tech Research Corporation
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2007
资助国家：
美国
起止时间：
2007-09-01 至 2011-12-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=0728911&HistoricalAwards=false
关键词：
New Directions Active Contours Reformulating

项目摘要

Active contours (deformable curves that evolve within an image in order to capture an object of interest) rank among the most widely used tools in image processing and computer vision. This investigation focuses on the mathematical reformulation of many existing active contour models to improve their robustness and performance as well as the formulation of brand new active contour models that are not possible under the more traditional formulation. The impact of the this investigation is therefore expected to be quite broad given the prominence of active contour applications in many fields ranging from medical imaging, manufacturing, survelliance, target tracking, visual inspection, and video compression.For over twenty years, gradient flow schemes for active contours have been mathematically founded upon a common, though often overlooked, geometric L2 norm. The investigator will study the benefits of changing this fundamental unifying mathematical foundation by proposing alternative classes of norms to greatly improve the behavior of gradient flow schemes for active contours.A tremendous amount of effort has gone into designing more and more sophisticated energy functionals yet not into considering the mathematical foundations behind the "standard recipe" gradient flow calculations.By changing the underlying norm behind gradient descent caluclations for active contours, the investigator will introduce in a mathematically rigorous and principled manner new active contour flows whose behaviors can be improved and tailored regardless of the corresponding energy functional.

主动轮廓（在图像中演变以捕获感兴趣的对象的可变形曲线）在图像处理和计算机视觉中排名最广泛的工具。这项调查着重于许多现有的活跃轮廓模型的数学重新重新制定，以提高其稳健性和性能以及在更传统的表述下不可能的全新主动轮廓模型的制定。因此，鉴于许多领域的主动轮廓应用在医学成像，制造，逃生，目标跟踪，视觉检查和视频压缩中的主动轮廓应用的突出性，预计这项调查的影响将非常广泛。二十年来，梯度流动方案在积极的阶段流动方案上是在数学上建立的，尽管经常忽略了，但经常忽略了。研究者将通过提出替代规范的替代类别来改善梯度流动方案的行为来改善这种基本统一的数学基础的好处以数学上严格和原则性的方式引入新的主动轮廓流，其行为可以改善和量身定制，无论相应的能量功能如何。