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 paper, 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.

翻译：真实世界材质的高效准确BRDF采集是一个具有挑战性的研究问题，需要对数百万个入射光方向和观察方向进行采样。为加速采集过程，需找到一组最小采样方向集合，使得基于这些样本的全BRDF恢复既准确又鲁棒。本文将BRDF采集问题建模为压缩感知问题，其中感知算子根据一组最优样本方向对BRDF信号进行子采样。为解决该问题，我们提出快速鲁棒最优采样技术（FROST），用于设计可证明最优的子采样算子，放置光-视图样本以最小化恢复误差。FROST将压缩感知中最优子采样算子设计问题，转化为基于多测量向量（MMV）信号模型的稀疏表示形式。该重述是精确的（即不含任何近似），从而将不可解的组合优化问题转化为可通过标准优化技术求解的问题。因此，FROST附有来自压缩感知领域的强理论保证。我们使用公开BRDF数据集进行10折交叉验证，对FROST-BRDF进行深入分析，证明其在重建质量上相比现有技术具有显著优势。最后，FROST在概念和实现上均简洁明了，每次运行结果一致，且速度比现有方法快至少两个数量级。