SGER ACT: Stochastic Shape Analysis for Recognizing and Tracking Objects in Images and Videos

成像设备已成为监视公共区域、偏远位置、受限访问区域和其他需要加强安全的场所的普遍工具。对收集到的图像的详细分析可以提供关于人、物体、他们的特征和行为模式的宝贵信息。因此，与其他战略相结合，图像分析可为预防恐怖主义和国家安全作出重大贡献。然而，由于监视设备产生的大量图像，这项任务的执行带来了具有挑战性的问题。为了使这项任务可行，需要先进的自动化系统来筛选图像，并将非常可能包含相关信息的材料发送给人类操作员。拟议的跨学科研究涉及形状和数字图像分析的接口问题，其解决方案将有助于实施这种智能监视系统，并将在许多其他应用中发挥作用。图像包含有关对象的两个主要属性的信息：它们的形状和纹理。作者将利用微分几何、微分拓扑学和统计学的方法和工具开发一种新的框架来定量地表示和分析平面形状。统计纹理分析和合成将与形状研究相结合，以产生更精细的成像对象模型。将开发、实现和应用新的形状和图像分析算法：(A)检测和识别噪声图像中的目标；(B)跟踪视频序列中可能受到遮挡的动态形状；(C)组织大型形状数据库，以便有效地检索和处理信息。目前的算法形状分析技术在范围或性能上有所限制：一些使用地标的粗略集合来表示形状，这些地标的选择可能很难自动化，并且一些涉及大量的计算成本。计算效率问题也限制了现有图像分析方法的使用；尽管基于偏微分方程的方法在许多应用中取得了显著的成功，但与典型实现相关的计算成本很高，并且性能不足以应用于视频监控。迫切需要高效、健壮的算法来分析、处理和模拟连续闭合曲线的形状动态。本文提出的主要思想是利用计算随机微分几何来研究形状，即在统计框架下对连续曲线的微分几何表示进行算法分析。提出者将：(I)通过角度或曲率函数将闭合形状表示为无穷维黎曼流形的元素来分析闭合形状；(Ii)开发基于几何的工具来解决形状空间上的统计推理问题；(Iii)推导无限维形状流形中形状的非线性过滤和跟踪技术；(Iv)研究轮廓和纹理的完备性，以发现遵循可观察模式的隐藏几何特征；(V)实现算法并将其应用于形状和图像分析中的问题的解决。这种方法的关键新元素是使用曲线空间的几何来研究形状，而不仅仅是单个曲线的几何。这项研究的结果可能会对形状、图像和视频分析产生深远的影响。提出的形状算法方法有可能为曲线演化的处理设定一种新的范式。该团队在微分几何和拓扑学、统计学、计算和图像分析领域拥有专业知识。这一分组反映了拟议调查的跨学科性质，并将进一步加强私营部门主管及其研究生之间存在的合作研究气氛。此外，将被调查的申请将有助于教育更多的学生，并使更多的学生参与到与国家安全有关的领域。PIS将继续开发和提供从入门到高级的课程和研讨会，面向广大理科学生，目标是增加这一研究领域的整体影响。为了鼓励本科生和来自代表不足群体的学生参与，有积极性的学生将完全可以进入佛罗里达州立大学计算视觉实验室，在那里亲身实践的学习环境将允许他们用自己的实验探索这一领域。为了传播研究成果，提名者将继续在发行量很大的期刊上发表文章，在各种电子预印本档案中公布成果，制作光盘的多媒体演示文稿，在杂志或手册上撰写介绍性文章，并在区域、国家和国际会议上展示成果。该奖项由国家科学基金会和情报界共同支持。数学和物理科学局的反恐方法方案支持基础研究和劳动力发展方面的新概念，有可能对国家安全作出贡献。

Imaging devices have become ubiquitous tools of surveillance of public areas, remote locations, areas of restricted access, and other sites where additional security is needed. The detailed analysis of collected images can provide invaluable information about people, objects, their characteristics and patterns of behavior. Thus, combined with other strategies, image analysis can contribute significantly to the prevention of terrorism and national security. However, the execution of this task poses challenging problems due to the vast amount of imagery generated by surveillance devices. To make this task feasible, advanced automated systems are needed to screen images and route to human operators only material that is very likely to contain relevant information. The proposed interdisciplinary research addresses problems on the interface of shape and digital image analysis, whose solutions will contribute to the implementation of such intelligent surveillance systems, and will be useful in numerous other applications. Images contain information about two main attributes of objects: their shapes and textures. The proposers will develop a novel framework to represent and analyze planar shapes quantitatively using methods and tools of differential geometry, differential topology, and statistics. Statistical texture analysis and synthesis will be combined with the study of shapes to produce finer models of imaged objects. New algorithms of shape and image analysis will be developed, implemented, and applied to: (a) the detection and recognition of objects in noisy images; (b) tracking dynamic shapes possibly subject to occlusions in video sequences; (c) the organization of large databases of shapes for efficient retrieval and processing of information. Current techniques of algorithmic shape analysis are somewhat limited in scope or performance: some represent shapes using coarse collections of landmarks whose selection may be difficult to automate, and some involve heavy computational costs. Computational efficiency issues also limit the use of existing methods of image analysis; in spite of the remarkable success that methods based on partial differential equations have had in many applications, computational costs associated with typical implementations are high and the performance is not adequate for applications in video surveillance. There is a pressing need for efficient, robust algorithms that can analyze, process, and simulate the dynamics of shapes of continuous closed curves. The main idea proposed here is the use of computational stochastic differential geometry to study shapes, i.e., the algorithmic analysis of differential geometric representations of continuous curves in a statistical framework. The proposers will: (i) analyze closed shapes by representing them as elements of infinite-dimensional Riemannian manifolds via their angle or curvature functions; (ii) develop geometry-based tools for statistical inference problems on shape spaces; (iii) derive techniques for nonlinear filtering and tracking of shapes in infinite-dimensional shape manifolds; (iv) study completions of contours and textures with the goal of discovering hidden geometric features that follow an observable pattern; (v) implement algorithms and apply them to the solution of problems in shape and image analysis. The key new element in this approach is the use of the geometry of spaces of curves to study shapes, not only the geometry of individual curves. Results originating from this research may have far-reaching implications in shape, image and video analysis. The proposed algorithmic approach to shapes has the potential to set a new paradigm for the treatment of curve evolution. The team has expertise in the areas of differential geometry and topology, statistics, computing, and image analysis. This grouping reflects the interdisciplinary nature of the proposed investigation and will further enhance the atmosphere of collaborative research that exists among the PIs and their graduate students. Moreover, the applications to be investigated will contribute to the education and involvement of more students in areas related to national security. The PIs will continue to develop and offer courses and seminars from the introductory to the advanced levels targeting a broad audience of science students with the goal of increasing the overall impact of this line of research. To encourage the participation of undergraduates and students from underrepresented groups, motivated students will have full access to the Florida State University Laboratory of Computational Vision, where a hands-on learning environment will allow them to explore the area with their own experiments. To disseminate research results the proposers will continue to publish articles in well-circulated journals, post results in various electronic preprint archives, produce multimedia presentations on CD-ROMs, write introductory articles in magazines or handbooks, and present results at regional, national and international conferences.This award is supported jointly by the NSF and the Intelligence Community. The Approaches to Combat Terrorism Program in the Directorate for Mathematical and Physical Sciences supports new concepts in basic research and workforce development with the potential to contribute to national security.