SGER: Tracking Level Sets

研究人员建议探索一种新的、成熟的随机估计理论的基础，以跟踪被描述为水平集的现象或对象的边界。轮廓线的随机估计在活动轮廓线的文献中已经显示出其强大的能力，水平集方法被证明对于描述频繁变化的拓扑和形状非常迅速的边界非常有效。拟议活动的一部分是理论性质的：理论必须从头开始形式化，需要克服几个数学和计算挑战，包括以随机控制的方式制定扰动边界的方法；边界形状估计与轮廓运动分析的交错；在水平集背景下发明重采样、最大似然和最大后验估计的新方法；以及开发更新和传播边界估计的数值有效方法。这项提议的另一个重要组成部分是开展各种应用，包括由一群机器人跟踪溢油或污染物云；识别和解释图像序列中的手势；以及为皮肤病诊断分析皮肤病变的生长情况。拟议的应用本身就很重要：跟踪石油泄漏、污染物、森林火灾和类似现象的传播对社会具有明确而直接的作用。用于视频分析的跟踪技术对于监视公共场所、监视活动以及帮助言语或听力受损的人具有迫切的重要性。此外，随机估计和水平集的结合足够基础，使计算机视觉以外的领域也有可能取得进展。

The investigator proposes to explore the foundations for a new, full-fledged theory of stochastic estimation for tracking boundaries of phenomena or objects that are described as level sets. Stochastic estimation for contours has shown its power in the literature of active contours, and level set methods have been shown to be very effective for describing boundaries that change topology frequently, and shape very rapidly. Part of the proposed activities are theoretical in nature: the theory must be formalized from scratch, and several mathematical and computational challenges are to be overcome, including the formulation of methods for perturbing boundaries in a stochastically controlled way; the interleaving of boundary shape estimation with contour motion analysis; the invention of new methods for resampling, Maximum Likelihood, and Maximum A Posteriori estimation in the context of level sets; and the development of numerically efficient methods for the update and propagation of boundary estimates. Another important component of this proposal is work on applications ranging from the tracking of oil spills or clouds of pollutants by a swarm of robots; the identification and interpretation of hand gestures in image sequences; and the analysis of growth of skin lesions for dermatological diagnosis. The proposed applications are important in their own right: tracking the spread of oil spills, pollutants, forest fires and similar phenomena is of clear and immediate usefulness to society. Tracking techniques for video analysis are of urgent importance for surveillance of public sites, monitoring of activities, and aiding of the speech or hearing impaired. In addition, the marriage of stochastic estimation and level sets is fundamental enough to make possible advances also in fields beyond computer vision.