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

标题：Career：非线性流形上风格和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。通常，这些因素中的每一个都可以表示为潜在的非线性流形。因此，一般而言，每个数据点都位于流形的混合体上。因此，我们拥有所有这些因素的产品空间，这使得这个问题非常具有挑战性。然而，如果我们在某种程度上概念性地了解产生数据的正交因子的每个单独流形的拓扑、维度和性质，就可以解决这个问题。这项研究的最终目标是为分离数据中的多个因素建立通用的数学框架。特别是，在人类运动的背景下，目标是建立一种数学框架，该框架将固有的身体结构与影响视觉输入的其他可变性来源解耦，并因此在恢复身体结构时利用这种模型。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)学习给定一个或多个潜在流形表示的数据的因式分解生成模型。3)给定底层流形的表示，如何使用它来选择视觉输入中的区别性特征。4)将研究结果应用于身体内在形态的恢复。形式与内容的分离问题是视觉知觉中的一个基本任务，也是知觉的一个基本谜团。目前还不清楚我们如何感知一个常见的动作，如行走，而不考虑其外观的所有来源的变化。这项研究计划中涉及的基本研究问题广泛地出现在不同的计算机视觉以及机器学习应用中。这些发现将有助于促进计算机视觉和机器学习领域的最先进技术，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。人体运动分析的研究在监控、安全、人机交互等方面都有重要的应用，人体运动分析将成为研究与教育活动相结合的主题，以激励数学和科学教育。该教育计划包括几项针对研究生、本科生以及高中教育工作者和学生的综合活动。目标是开发教育工具，通过合作设计、实施和评估计算机视觉虚拟教室，整合PI、高中教育工作者、本科生和高中生的努力。URL：http://www.cs.rutgers.edu/~elgammal/Research/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