Generalized active learning and design of statistical experiments for manifold-valued data

In computer graphics and computer vision, usually either physically inspired analytic reflectance models, like Cook and Torrance (1981) or He et al. (1991), or parametric reflectance models chosen via qualitative criteria, like Phong (1975), or Lafortune et al. (1997), are used to model BRDFs. These BRDF models are only crude approximations of the reflectance of real materials. In multidimensional reflectometry, an alternative approach is usually taken. One directly measures values of the BRDF for different combinations of the incoming and outgoing angles and then fits the measured data to a selected analytic model using optimization techniques. There were numerous efforts to use modern machine learning techniques to construct datadriven BRDF models. Brady et al. (2014) proposed a method to generate new analytical BRDFs using a heuristic distance-based search procedure called Genetic Programming. In Brochu et al. (2008), an active learning algorithm using discrete perceptional data was developed and applied to learning parameters of BRDF models such as the Ashikhmin - Shirley model Ashikhmin and Shirley (2000), while Langovoy et al. (2016) treated active learning for the Cook - Torrance model Cook and Torrance (1981). Analysis of BRDF data with statistical and machine learning methods was discussed in Langovoy (2015b), Langovoy (2015a), Sole et al. (2018), Doctor and Byers (2018).