CAREER: Generalized Separation of Style and Content on Nonlinear Manifolds with Application to Human Motion Analysis

题目：职业：非线性流形上风格与内容的广义分离及其在人体运动分析中的应用视觉输入是各种概念上正交因素的函数。这些因素中的每一个，通常都可以表示为一个潜在的非线性流形。所以，一般来说，每个数据点都在流形的混合上。因此，我们有所有这些因素的乘积空间，这使得问题非常具有挑战性。然而，如果我们在一定程度上从概念上理解产生数据的正交因素的每个单独流形的拓扑结构、维数和性质，就可以解决这个问题。本研究的最终目标是建立数据中多因素分离的通用数学框架。特别是，在人体运动的背景下，目标是建立一个数学框架，将内在的身体结构与影响视觉输入的其他变异性源解耦，从而利用这些模型来恢复身体结构。为了实现这一目标，将研究四个方向：1)从同一流形上的各种风格变化中学习统一的不变内容流形表示。2)为给定的一个或多个底层流形表示的数据学习因式生成模型。3)给定底层流形的表示，如何使用它来选择视觉输入中的判别特征。4)将研究结果应用于恢复内在身体形态。风格与内容的分离问题是视觉感知中的一个重要问题，也是感知的一个基本谜题。我们不知道我们是如何感知一个常见的运动的，比如走路，不管它的外观有各种各样的变化。本研究计划涉及的基础研究问题广泛出现在不同的计算机视觉和机器学习应用中。这一发现将有助于推动计算机视觉和机器学习领域的最新发展，并为认知科学领域的研究人员带来有趣的计算模型。人体运动分析将是本研究的主要应用领域。提出的人体运动分析研究在监控、安全、人机交互等方面有着重要的应用。人体运动分析将成为研究与教育活动相结合的主题，以激励数学与科学教育。该教育计划包括针对研究生水平、本科水平和高中教育工作者和学生的几个综合活动。目标是开发教育工具，通过协作设计、实现和评估计算机视觉虚拟教室，将PI、高中教育者、本科生和高中生的努力整合在一起。URL: http://www.cs.rutgers.edu/ elgammal /研究/ GStyleContent.htm

Title: CAREER: Generalized Separation of Style and Content on Nonlinear Manifolds with Application to Human Motion AnalysisThe visual input is a function of various conceptually orthogonal factors. Each of these factors, typically, can be represented as an underlying nonlinear manifold. So, in general, each data point lies on a mixture of manifolds. Therefore, we have a product space of all these factors, which makes the problem very challenging. However, the problem can be approached if we understand conceptually, to some extent, the topology, dimensionality and the properties of each individual manifold of the orthogonal factors that generated the data. The ultimate goal of this research is to establish general mathematical frameworks for the separation of multiple factors in the data. In particular, in context of human motion, the objective is to establish a mathematical framework that decouples intrinsic body configuration from other sources of variability that affect the visual input and, consequently, to exploit such models in recovering body configuration. To achieve this goal four research directions will be investigated 1) Learning a unified invariant content manifold representation from various style variations on the same manifold. 2) Learning factorized generative models for the data given representation of one or more of the underlying manifolds. 3) Given representation of the underlying manifold, how that can be used to select discriminative features in the visual input. 4) Applying the findings towards the recovery of intrinsic body configuration.The problem of separation of style and content is an essential task in visual perception and is a fundamental mystery of perception. It is not clear how we perceive a common motion, such as walking, regardless of all sources of variations in its appearance. The fundamental research problems addressed in this research plan appear extensively in different computer vision as well as machine learning applications. The findings will help promote the state-of-the-art in computer vision and machine learning fields as well as bringing interesting computational models to researchers in the cognitive science field. Human motion analysis will be the main applied domain for this research. The proposed research in human motion analysis has various important applications such as surveillance, security, human computer interaction, etc. Human motion analysis will be the integrating theme between the research and the educational activities for motivating Math and Science education. The educational plan consists of several integrated activities targeting the graduate level, the undergraduate level, and high school educators and students. The goal is to develop educational tools that will integrate the efforts of the PI, high school educators, undergraduate and high school students through collaborating in the design, implementation, and evaluation of a computer vision virtual classroom.URL: http://www.cs.rutgers.edu/~elgammal/Research/GStyleContent.htm