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

机器人和人类增强程序建议#：0307998标题：为基于图像的识别寻求最佳表示、分类器和泛化PI：刘，修文佛罗里达州立大学线性表示在计算科学的所有领域中无处不在。图像分析和计算机视觉中的许多应用包括通过将高维数据线性投影到低维子空间来分析高维数据。鉴于它们的计算效率，这种线性投影在某些应用中已成为标准。然而，为了从图像中识别物体，很少有人讨论如何找到“最佳”的线性表示法。许多社会、商业和科学活动，如国土安全和生物识别，都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来寻找在目标识别环境中表现最佳的线性和非线性表示。我们建议通过以下方法来实现这一目标：(I)将寻找最优线性表示表示为Grassmann流形上的最优化问题，(Ii)利用Grassmannians几何来开发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)展示在线性表示适用的情况下潜在的显著性能改进。由于利用线性投影的降维有许多应用，包括对象识别、图像和文本检索、子空间跟踪和非线性滤波，因此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工具的基础上，这些工具将被证明在许多其他应用中是有益的。这项研究还将显著增强佛罗里达州立大学关于计算机视觉的学习和研究环境。利用几何和统计方法在计算机视觉中的应用，使这项多学科的努力造福于所有参与者，包括研究生和本科生。这项研究的成果将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.