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

在本研究项目中，PI提出了一种新的组合几何主动轮廓/粒子滤波方法，用于跟踪物体（即平面形状）的边界，当观测到的是一个可能是封闭曲线的复杂非线性函数的图像时。使用几何活动轮廓的优点是它们允许拓扑变化（自动合并和破坏），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）系统噪声分布中生成蒙特卡罗样本是计算复杂的。此外，精确滤波所需的采样数随着系统噪声的大小而增加。PI将表明，只要系统噪声的维数很小，即使总状态空间维非常大（或无限），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。特别地，PI建议使用时变有限维表示来近似曲线变形。他将把这个问题表述为具有未知静态参数的粒子滤波，并使用对粒子滤波器的修改，该粒子滤波器已被证明对跟踪静态参数具有渐近稳定性。主要的假设是，即使曲线可以被看作是无限维空间中的一个点，在给定的时间内，“它的大部分变形”可以用有限的小维度来近似。但随着时间的推移，这种近似可能不再足够，因此，当当前的近似无法以足够的精度跟踪时，必须允许维数和有限维基础发生变化。对于一些关键场景，这个假设似乎是合理的，并且允许使用无限维观察者技术进行视觉跟踪。智力优势：该项目的主要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潜在问题。从理论和实践的角度来看，这都是一个具有挑战性的问题。事实上，控制主动视觉，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。该研究项目指出了利用上述所有构建块寻找新的鲁棒和实时视觉跟踪方案的方法。研究活动的更广泛影响：PI认为，本提案中描述的视觉，过滤和控制的拟议协同作用可能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。在存在干扰的情况下跟踪是一个经典的控制问题，而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，因此必须考虑来自成像传感器的干扰性质。其次，反馈信号可能需要对图像进行一些解释，例如，将目标从其背景中分割出来，或者对遮挡物进行推断。最后，随着视觉处理变得越来越复杂，处理时间的问题也出现了。这些问题都必须在目标检测之前得到解决，并且视觉介导控制可以为医疗，商业或先进的武器系统提供。

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.