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

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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.