A Unied Approach to Data Analysis and Modeling of the Appearance of Materials for Computer Graphics and Multidimensional Reectometry Mikhail Langovoy Abstract Characterizing the appearance of real-world surfaces is a fundamental problem in multidimensional , computer vision and computer graphics. In this paper, we outline a unied perception-based approach to modeling of the appear- ance of materials for computer graphics and reectometry. We discuss the differ- ences and the common points of data analysis and modeling for BRDFs in both physical and in virtual application domains. We outline a mathematical framework that captures important problems in both types of application domains, and allows for application and performance comparisons of statistical and machine learning methods. For comparisons between methods, we use criteria that are relevant to both statistics and machine learning, as well as to both virtual and physical application domains. Additionally, we propose a class of multiple testing proce- dures to test a hypothesis that a material has diffuse reection in a generalized sense. We treat a general case where the number of hypotheses can potentially grow with the number of measurements. Our approach leads to tests that are more powerful than the generic multiple testing procedures. Keywords BRDF Computer graphics Data analysis Light reection Machine learning Metrology Perception Realistic image representation Reectometry Statistics of manifolds 1 Introduction Characterizing the appearance of real-world surfaces is a fundamental problem in multidimensional reectometry, computer vision and computer graphics. For many applications, appearance is suf ciently well characterized by the bidirectional reectance distribution function (BRDF). M. Langovoy (&) The Physikalisch-Technische Bundesanstalt, Abbestrasse 212, 10587 Berlin, Germany e-mail: mikhail.langovoy@ptb.de © Springer Science+Business Media Dordrecht 2015 H.K. Kim et al. (eds.), Transactions on Engineering Technologies, DOI 10.1007/978-94-017-7236-5_2 15