Machine Learning and Statistical Analysis for BRDF Data from Computer Graphics and Multidimensional Reflectometry

摘要

Characterizing the appearance of real-world surfaces is a fundamental problem in multidimensional reflectometry, computer vision and computer graphics. For many applications, appearance is sufficiently well characterized by the bidirectional reflectance distribution function. BRDF is one of the fundamental concepts in such diverse fields as multidimensional reflectometry, computer graphics and computer vision. In this paper, we treat BRDF measurements as samples of points from high-dimensional non-linear non-convex manifolds. We argue that any realistic statistical analysis of BRDF measurements, or any parameter or manifold learning procedure applied to BRDF measurements has to account both for nonlinear structure of the data as well as for a very ill-behaved noise. Standard statistical and machine learning methods can not be safely directly applied to BRDF data. We discuss the differences and the common points of data analysis and modelling for BRDFs in both physical as well as in virtual application domains. We outline a mathematical framework that captures some important problems in both types of application domains, and allows for application and performance comparisons of statistical and machine learning methods. For comparisons between the methods, we use criteria that are relevant to both statistics and machine learning, as well as to both virtual and physical application domains. This outlines a possible unified approach to BRDF data analysis and modelling relevant for the whole generality of application domains. Specifically, we apply the notion of Pitman closeness to compare different estimators and learning procedures for BRDF models. This criterion for comparison is loss function-free and seems to be especially appropriate for applications in metrology and in comparing different types of learning methods. Additionally, we propose a class of multiple testing procedures to test a hypothesis that a material has diffuse reflection 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.