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，用于跟踪被描述为水平集的现象或对象的边界。轮廓的随机估计在活动轮廓的文献中已经显示出其强大的功能，并且水平集方法已经被证明对于描述频繁改变拓扑结构的边界非常有效，并且形状非常迅速。拟议的活动有一部分是理论性的：理论必须从头开始形成，若干数学和计算方面的挑战有待克服，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;在水平集的背景下，发明了用于重新估计、最大似然估计和最大后验估计的新方法;以及发展用于边界估计的更新和传播的数值有效方法。该提案的另一个重要组成部分是应用方面的工作，包括由一群机器人跟踪漏油或污染物云;识别和解释图像序列中的手势;以及分析皮肤病的生长情况以进行皮肤病诊断。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蔓延对社会具有明确和直接的用处。用于视频分析的跟踪技术对于公共场所的监视、活动的监控以及言语或听力受损者的帮助具有迫切的重要性。此外，随机估计和水平集的结合足以在计算机视觉以外的领域取得进展。

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.