FRG: Development of Geometrical and Statistical Models for Automated Object Recognition

FRG：自动对象识别的几何和统计模型的开发

• 批准号: 0101429
• 负责人: Anuj Srivastava
• 金额: $ 52.2万
• 依托单位: Florida State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-08-01 至 2005-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0101429&HistoricalAwards=false
• 关键词: FRG; Development; Geometrical; Statistical; Models

Anuj Srivastava 0101429AbstractThe proposed research will focus on developing methods for automated object recognition using tools from statistics, differential geometry and computer graphics. The main objective is to design algorithms for recognizing (3D) objects from their (2D) camera images, with an emphasis on automated face recognition. The biggest challenge comes from the variability manifested in the images. How do we model it and what efficient procedures can be used to analyze it? Many current methods seek dominant subspaces (e.g. PCA, ICA, Fisher discriminant) of the observed images to capture and characterize this variability. Although the hardware technology has advanced significantly for both computing and imaging,the current mathematical techniques and algorithms for computer vision remain limited in their ability to fundamentally handle the image variability. Recent technological advances, such as 3D imaging, super fast graphics, and high-performance computing, make this project both feasible and timely.Our approach builds upon the physical considerations that will lead to representations in stochastic geometry. We highlight the physical factors behind the image variability and propose methods to model them. A distinct advantage of modeling the physical factors is the ability to incorporate the contextual information in the resulting recognition algorithms. In particular, we will develop (i) geometric models for facial shape variability, (ii) tools for synthetic illumination and facial rendering, and (iii) algorithms for statistical inference on these models/parameters. We use coordinate and differential geometry to characterize object shapes, pose, motion, reflectance, illumination, and their time variations, and show that these variables take values on the Lie groups and their quotient spaces. Following the "analysis by synthesis" paradigm, where the observed images are statistically compared to the synthesized images, we propose inferences over the nuisance variables to seek the best match, and thus perform recognition. In a Bayesian framework, the contextual knowledge of these physical representations can be incorporated as a prior model, to add to the observed information. The inference engine is based on the Monte-Carlo methods particularized to these representations. These stated goals require expertise from distant areas of statistics, geometry, computing, and graphics. Through this FRG collaboration, we will create an atmosphere for synergistic, multi-disciplinary research that will support many future endeavors.

Anuj Srivastava 0101429摘要拟议的研究将集中在开发方法，自动物体识别使用的工具，从统计，微分几何和计算机图形学。 主要目标是设计算法，用于从（2D）相机图像中识别（3D）对象，重点是自动人脸识别。最大的挑战来自图像中表现出的可变性。我们如何建模它，什么有效的程序可以用来分析它？ 目前的许多方法寻求占主导地位的子空间（例如PCA，伊卡，Fisher判别）的观察到的图像捕捉和表征这种变化。虽然硬件技术在计算和成像方面都有了很大的进步，但目前用于计算机视觉的数学技术和算法在从根本上处理图像变化的能力方面仍然有限。最近的技术进步，如3D成像，超快的图形和高性能计算，使这个项目既可行又及时。我们的方法建立在物理考虑，将导致在随机几何表示。 我们强调图像变化背后的物理因素，并提出方法来模拟它们。对物理因素进行建模的一个明显优势是能够将上下文信息纳入最终的识别算法中。 特别是，我们将开发（i）面部形状变化的几何模型，（ii）合成照明和面部渲染的工具，以及（iii）对这些模型/参数进行统计推断的算法。我们使用坐标和微分几何来表征物体的形状，姿态，运动，反射率，照明，和它们的时间变化，并表明这些变量的李群和他们的商空间的值。 在“合成分析”的范例，观察到的图像进行统计比较的合成图像，我们提出的滋扰变量的推断，以寻求最佳匹配，从而进行识别。 在贝叶斯框架中，这些物理表示的上下文知识可以被合并为先验模型，以添加到观察到的信息中。推理机是基于蒙特-卡罗方法具体到这些表示。这些既定的目标需要来自统计、几何、计算和图形等遥远领域的专业知识。 通过这种FRG合作，我们将创造一个协同的，多学科的研究，将支持许多未来的努力的氛围。