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.

This paper presents a novel sparse non-parametric Bidirectional Reflectance Distribution Function (BRDF) model derived using a machine learning approach to represent the space of possible BRDFs using a set of multidimensional sub-spaces, or dictionaries. By training the dictionaries under a sparsity constraint, the model guarantees high-quality representations with minimal storage requirements and an inherent clustering of the BDRF-space. The model can be trained once and then reused to represent a wide variety of measured BRDFs. Moreover, the proposed method is flexible to incorporate new unobserved data sets, parameterizations, and transformations. In addition, we show that any two, or more, BRDFs can be smoothly interpolated in the coefficient space of the model rather than the significantly higher-dimensional BRDF space. The proposed sparse BRDF model is evaluated using the MERL, DTU, and RGL-EPFL BRDF databases. Experimental results show that the proposed approach results in about 9.75dB higher signal-to-noise ratio on average for rendered images as compared to current state-of-the-art models.

Measured materials are rapidly becoming a core component in the photo-realistic image synthesis pipeline. The reason is that data-driven models can easily capture the underlying, fine details that represent the visual appearance of materials, which can be difficult or even impossible to model by hand. There are, however, a number of key challenges that need to be solved in order to enable efficient capture, representation and interaction with real materials. This paper presents two new data-driven BRDF models specifically designed for 1D separability. The proposed 3D and 2D BRDF representations can be factored into three or two 1D factors, respectively, while accurately representing the underlying BRDF data with only small approximation error. We evaluate the models using different parameterizations with different characteristics and show that both the BRDF data itself and the resulting renderings yield more accurate results in terms of both numerical errors and visual results compared to previous approaches. To demonstrate the benefit of the proposed factored models, we present a new Monte Carlo importance sampling scheme and give examples of how they can be used for efficient BRDF capture and intuitive editing of measured materials.