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

## TL;DR

This paper develops a mathematical framework for efficient sampling and measurement strategies of high-dimensional, non-linear BRDF data manifolds, enhancing the process of characterizing real-world surface appearances.

## Contribution

It introduces a novel theoretical foundation combining statistical design of experiments and proactive learning for manifold-valued data, specifically applied to BRDF measurements.

## Key findings

- Framework enables more efficient sampling of BRDF manifolds
- Improves accuracy of surface appearance characterization
- Reduces measurement effort in complex problems

## 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.