Geometric Particle Filters for Visual Tracking (Attn. Dr. Kishan Baheti)

B.项目总结在这个研究项目中，PI提出了一种新的结合几何活动轮廓/粒子滤波的方法来跟踪对象的边界(即平面形状)，当观测对象是可能是闭合曲线的复杂非线性函数的图像时。使用几何活动轮廓线的优点是它们允许拓扑变化(自动合并和断开)，因此可以用于跟踪多个对象。更具体地说，粒子滤波框架将应用于连续闭合曲线空间，这是一个无限维空间。这是一个特别困难的问题，因为从一个非常大的维度(理论上是无限的)系统生成蒙特卡罗样本是一个计算复杂的问题。此外，精确滤波所需的样本数随着系统噪声的大小而增加。PI将表明，只要系统噪声的维度很小，即使总状态空间维度非常大(或无穷大)，也可以实现粒子滤波算法，这将使他能够开发出实用的鲁棒跟踪算法。特别是，PI建议使用时变的有限维表示来近似曲线变形。他将把问题描述为具有未知静态参数的粒子滤波，并使用已被证明是渐近稳定的粒子过滤器的修改来跟踪静态参数。主要假设是，即使曲线可以被视为无限维空间中的一个点，给定时间段的“它的大部分变形”可以用少量的有限维来近似。但随着时间的推移，这种近似可能不再适用，因此当当前的近似不能足够准确地跟踪时，必须允许改变维数和有限维基。对于一些关键场景，这一假设似乎是合理的，并允许使用无限维观察者技术进行视觉跟踪。智力优势：该项目的关键目标是开发在反馈回路中使用视觉信息的新方法，这是受控主动视觉的根本问题。从知识和实践的角度来看，这都是一个棘手的问题。事实上，受控主动视觉，特别是视觉跟踪，需要控制理论、信号处理和计算机视觉技术的集成。这项研究计划指出了利用所有上述模块找到一种新的稳健且有望实时的视觉跟踪方案的方法。研究活动的广泛影响：PI认为本提案中描述的视觉、过滤和控制的拟议协同可能会对跟踪和主动视觉产生强烈影响。事实上，视觉跟踪提供了一个基本的例子，说明需要受控的主动视觉。虽然干扰情况下的跟踪是一个经典的控制问题，但视觉跟踪提出了新的问题。首先，由于摄像机是系统的一部分，所以必须考虑来自成像传感器的干扰的性质。其次，反馈信号可能需要对图像进行某种解释，例如，将目标从其背景中分割出来，或者关于遮挡物的推断。最后，随着视觉处理变得越来越复杂，处理时间的问题就出现了。在目标检测之前，这些问题都必须得到回答，并且可以为医疗、商业或先进武器系统提供视觉中介控制。

B. PROJECT SUMMARYIn this research program, the PI proposes a novel combined geometric active contour/particlefiltering approach for tracking the boundaries of objects (i.e., planar shapes), when the observationis an image which may be a complicated nonlinear function of the closed curve. The advantageof using geometric active contours is that they allow topological changes (automatic merging andbreaking), and hence can be used to track multiple objects.More specifically, the particle filtering framework will be applied to the space of continuousclosed curves which is an infinite dimensional space. This is a particularly difficult problem sincegenerating Monte Carlo samples from a very large dimensional (theoretically infinite) system noisedistribution is computationally complex. Moreover, the number of samples required for accuratefiltering increases with the dimension of the system noise. The PI will show that as long as thenumber of dimensions of the system noise is small, even if the total state space dimension isvery large (or infinite), a particle filtering algorithm can be implemented which will allow himto develop practical robust tracking algorithms. In particular, the PI proposes to approximatecurve deformation using a time- varying finite dimensional representation. He will formulate theproblem as particle filtering with unknown static parameters and use a modification of a particlefilter that has been shown to be asymptotically stable for tracking static parameters.The main assumption is that even though the curve may be regarded as a point of an infinitedimensional space, "most of its deformation" for a given period of time can be approximated usinga small finite number of dimensions. But over time, this approximation may no longer sufficeand hence one must allow the number of dimensions and the finite dimensional basis to changewhenever the current approximation is unable to track with suffcient accuracy. For a numberof key scenarios, this assumption seems reasonable, and allows the use of infinite dimensionalobserver techniques for visual tracking.Intellectual Merit:The key objective of this project is the development of new methodologies for employing visualinformation in a feedback loop, the underlying problem of controlled active vision. This is achallenging problem both from the intellectual and practical points of view. Indeed, controlledactive vision, and in particular visual tracking requires the integration of techniques from controltheory, signal processing, and computer vision. This research program points the way to finding anew class of robust and hopefully real-time visual tracking schemes making use of all of the abovebuilding blocks.Broader Impact of Research Activity:The PI believes that the proposed synergy of vision, filtering, and control described in thisproposal may have a strong impact on tracking and active vision. Indeed, visual tracking providesa fundamental example of the need for controlled active vision. While tracking in the presence of adisturbance is a classical control problem, visual tracking raises new issues. Firstly, since camerasare part of the system, one must consider the nature of the disturbance from imaging sensors.Secondly, the feedback signal may require some interpretation of the image, e.g., segmentationof a target from its background, or an inference about an occluder. Finally, as visual processingbecomes more complex, the issue of processing time arises. Each of these problems must beanswered before target detection, and visually-mediated control can be provided for medical,commercial, or advanced weapon systems.