Seeking Optimal Representations, Classifiers, and Generalizations for Image Based Recognition

Robotics and Human Augmentation ProgramabSTRACTProposal #：0307998 Title：Seeking Optimal Representations，Classifiers，and Generalizations for Image Based Augmentation PI：Liu，Xiuwen佛罗里达州立大学线性表示在计算科学的所有领域都是普遍存在的。图像分析和计算机视觉中的许多应用涉及通过将高维数据线性投影到低维子空间来分析高维数据。鉴于其计算效率，这种线性投影在某些应用中已经成为标准。然而，对于从图像中识别物体，很少有关于寻找“最佳”线性表示的讨论。许多社会、商业和科学操作，如国土安全和生物识别，严重依赖于基于图像的识别，识别性能成为一个至关重要的因素。这个项目的目的是提供有效的算法，寻找线性和非线性表示，在对象识别的上下文中执行最佳。我们建议通过以下方式实现这一目标：（i）将对最优线性表示的搜索公式化为格拉斯曼流形上的优化，（ii）使用格拉斯曼流形的几何来开发用于寻找最优线性表示的算法，（iii）分析所提出的优化技术的收敛性质和理论极限，以及（iv）在线性表示适用的情况下，证明对问题的潜在显著性能改进。由于有许多应用程序利用降维使用线性投影，包括对象识别，图像和文本检索，子空间跟踪，和非线性滤波，所提出的研究的潜在好处是巨大的。这项研究将建立在非线性流形上的随机优化和统计推断的工具上，这些工具将在许多其他应用中被证明是有益的。这项研究还将显著增强佛罗里达州立大学计算机视觉的学习和研究环境。几何和统计方法在计算机视觉应用中的应用使这成为一项多学科的努力，使所有参与者受益，包括研究生和本科生。这项研究的成果将被纳入最近设计的计算机视觉和计算统计课程。

Robotics and Human Augmentation ProgramABSTRACTProposal #: 0307998Title: Seeking Optimal Representations, Classifiers, and Generalizations for Image Based RecognitionPI: Liu, XiuwenFlorida State UniversityLinear representations are ubiquitous in all areas of computational sciences. Many applications in image analysis and computer vision involve analysis of large-dimensional data by projecting them linearly to low-dimensional subspaces. In view of their computational efficiency such linear projections have become standard in certain applications. However, for recognizing objects from their images, there is seldom a discussion on finding "optimal" linear representations. Many societal, commercial, and scientific operations, such as homeland security and biometrics, rely heavily on image-based recognition and the recognition performance becomes a vital factor. This project aims to provide efficient algorithms for finding linear and non-linear representations that perform optimally in the context of object recognition. We propose to achieve this goal by: (i) formulating the search for optimal linear representations as that of optimization on Grassmann manifolds, (ii) using the geometry of Grassmannians to develop algorithms for finding optimal linear representations, (iii) analyzing the convergence properties and the theoretical limits of the proposed optimization techniques, and (iv) demonstrating the potential significant performance improvement on problems wherever linear representations are applicable. Since there are numerous applications utilizing dimension reduction using linear projections, including object recognition, image and text retrieval, subspace tracking, and nonlinear filtering, the potential benefits of the proposed research are tremendous. This research will be built on tools for stochastic optimization and statistical inferences on nonlinear manifolds, tools that will prove beneficial in many other applications.This research will also enhance significantly the learning and research environment on computer vision at the Florida State University. Utilization of geometric and statistical approaches to applications in computer vision makes this a multidisciplinary effort to the benefit of all participants, including both graduate and undergraduate students. Outcomes of this research will be incorporated in recently designed courses on Computer Vision and Computational Statistics.