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

摘要本文的研究重点是利用统计学、微分几何和计算机图形学等工具开发自动目标识别方法。主要目标是设计从（2D）相机图像中识别（3D）物体的算法，重点是自动人脸识别。最大的挑战来自图像中表现出来的可变性。我们如何对它进行建模，可以使用什么有效的程序来分析它？许多当前的方法寻求观察图像的主导子空间（例如PCA， ICA， Fisher判别）来捕获和表征这种变异性。尽管硬件技术在计算和成像方面都有了很大的进步，但目前计算机视觉的数学技术和算法在根本上处理图像可变性的能力方面仍然有限。最近的技术进步，如3D成像、超快速图形和高性能计算，使这个项目既可行又及时。我们的方法建立在物理考虑的基础上，这将导致随机几何中的表示。我们强调了图像变异性背后的物理因素，并提出了建模方法。对物理因素建模的一个明显优势是能够将上下文信息合并到结果识别算法中。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形状、姿态、运动、反射率、光照及其时间变化，并表明这些变量在李群及其商空间上取值。遵循“综合分析”范式，将观察到的图像与合成图像进行统计比较，我们提出对干扰变量的推论，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合并为先验模型，以添加到观察到的信息中。推理引擎基于特定于这些表示的蒙特卡罗方法。这些既定的目标需要来自统计学、几何、计算和图形等遥远领域的专业知识。通过这次FRG合作，我们将为协同的多学科研究创造一种氛围，这将支持许多未来的努力。

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.