Page 219 - Contributed Paper Session (CPS) - Volume 4

CPS2201 Mikhail L.

Generalized active learning and design of
statistical experiments for manifold-valued data
Langovoy, Mikhail
KIT, Kriegsstr. 77, 76133 Karlsruhe, Germany

Abstract
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.

Keywords
Manifold-valued data; BRDF; proactive learning; sampling strategy.

1. Introduction
In computer graphics and computer vision, usually either physically inspired
analytic reactance 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 data-driven 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)

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