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.

通过压缩感知技术中的稀疏表示方法，本论文提出了 Fast and Robust Optimal Sampling Technique (FROST) 用于设计一种能够以最小化恢复误差的方式放置采样方向的压缩采样算子，从而加速 BRDF 材料的获取，具有从压缩感知领域得到的强理论保证和与现有方法相比的显著优势。