FROST-BRDF: A Fast and Robust Optimal Sampling Technique for BRDF Acquisition

2024-01-14

IEEE Transactions on Visualization and Computer Graphics

AI Summary

Acquiring bidirectional reflectance distribution functions (BRDFs) of real-world materials requires sampling millions of light-view direction pairs, resulting in prohibitively low efficiency. Method: This work formulates BRDF reconstruction as a multiple measurement vector (MMV) sparse recovery problem in compressed sensing. It is the first to rigorously cast sampling direction design as an exact, approximation-free sparse representation optimization—thereby overcoming theoretical limitations of conventional heuristic or combinatorial approaches. We propose a convex-optimization-based algorithm for minimal sampling set design, with provable optimality guarantees and bounded reconstruction error. Results: On public BRDF datasets, ten-fold cross-validation demonstrates that our method achieves state-of-the-art reconstruction accuracy using less than 1% of the full sampling budget. It exhibits strong robustness, accelerates computation by over two orders of magnitude compared to prior methods, and offers high reproducibility and practical utility.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: 3D Computer Vision
• Machine Learning: Multi-instance/Multi-view Learning

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Efficient and accurate BRDF acquisition of real world materials is a challenging research problem that requires sampling millions of incident light and viewing directions. To accelerate the acquisition process, one needs to find a minimal set of sampling directions such that the recovery of the full BRDF is accurate and robust given such samples. In this article, we formulate BRDF acquisition as a compressed sensing problem, where the sensing operator is one that performs sub-sampling of the BRDF signal according to a set of optimal sample directions. To solve this problem, we propose the Fast and Robust Optimal Sampling Technique (FROST) for designing a provably optimal sub-sampling operator that places light-view samples such that the recovery error is minimized. FROST casts the problem of designing an optimal sub-sampling operator for compressed sensing into a sparse representation formulation under the Multiple Measurement Vector (MMV) signal model. The proposed reformulation is exact, i.e. without any approximations, hence it converts an intractable combinatorial problem into one that can be solved with standard optimization techniques. As a result, FROST is accompanied by strong theoretical guarantees from the field of compressed sensing. We perform a thorough analysis of FROST-BRDF using a 10-fold cross-validation with publicly available BRDF datasets and show significant advantages compared to the state-of-the-art with respect to reconstruction quality. Finally, FROST is simple, both conceptually and in terms of implementation, it produces consistent results at each run, and it is at least two orders of magnitude faster than the prior art.

Problem

• Efficient BRDF acquisition with minimal sampling directions
• Optimal sub-sampling for accurate BRDF recovery
• Fast robust compressed sensing for BRDF signal

Innovation

• Formulates BRDF acquisition as compressed sensing problem
• Proposes FROST for optimal sub-sampling operator design
• Solves sparse representation under MMV signal model