Generalized active learning and design of statistical experiments for manifold-valued data
This work addresses the challenge of scarce measurements in BRDF estimation for fields such as computer graphics and vision, but it appears incremental as it builds a foundation rather than presenting a fully novel method or breakthrough results.
The paper tackles the problem of efficiently sampling and measuring BRDF data from high-dimensional manifolds, which is crucial for applications like reflectometry and computer vision, by developing a mathematical framework for generalized active learning and statistical design of experiments.
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). We treat BRDF measurements as samples of points from high-dimensional non-linear non-convex manifolds. BRDF manifolds form an infinite-dimensional space, but typically the available measurements are very scarce for complicated problems such as BRDF estimation. Therefore, an efficient learning strategy is crucial when performing the measurements. In this paper, we build the foundation of a mathematical framework that allows to develop and apply new techniques within statistical design of experiments and generalized proactive learning, in order to establish more efficient sampling and measurement strategies for BRDF data manifolds.