Photo-realistic rendering and predictive image synthesis are becoming increasingly important and utilized in many application areas ranging from production of visual effects and product visualization to digital design and the generation of synthetic data for visual machine learning applications. Many essential components of the realistic image synthesis pipelines have been developed tremendously over the last decades. One key component is accurate measurement, modeling, and simulation of how a surface material scatters light. The scattering of light at a point on a surface (reflectance and color) is described by the Bidirectional Reflectance Distribution Function (BRDF); which is the main research topic of this thesis. The BRDF describes how radiance, light, incident at a point on a surface is scattered towards any view-point from which the surface is observed. Accurate acquisition and representation of material properties play a fundamental role in photo-realistic image synthesis, and form a highly interesting research topic with many applications. 

The thesis has explored and studied appearance modeling, sparse representation and sparse acquisition of BRDFs. The topics of this thesis cover two main areas. Within the first area, BRDF modeling, we propose several new BRDF models for accurate representation of material scattering behaviour using simple but efficient methods. The research challenges in BRDF modeling include tensor decomposition methods and sparse approximations based on measured BRDF data. The second part of the contributions focuses on sparse BRDF sampling and novel highly efficient BRDF acquisition. The sparse BRDF sampling is to tackle tedious and time-consuming processes for acquiring BRDFs. This challenging problem is addressed using sparse modeling and compressed sensing techniques and enables a BRDF to be measured and accurately reconstructed using only a small number of samples. Additionally, the thesis provides example applications based on the research, as well as a techniques for BRDF editing and interpolation. 

Publicly available BRDF databases are a vital part of the data-driven methods proposed in this thesis. The measured BRDF data used has revealed insights to facilitate further development of the proposed methods. The results, algorithms, and techniques presented in this thesis demonstrate that there is a close connection between BRDF modeling and BRDF acquisition; efficient and accurate BRDF modeling is a by-product of sparse BRDF sampling. 

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.

Electroencephalography (EEG) is another method for performing person identification (PI). Due to the nature of the EEG signals, EEG-based PI is typically done while a person is performing a mental task such as motor control. However, few studies used EEG-based PI while the person is in different mental states (affective EEG). The aim of this paper is to improve the performance of affective EEG-based PI using a deep learning (DL) approach. We proposed a cascade of DL using a combination of convolutional neural networks (CNNs) and recurrent neural networks (RNNs). CNNs are used to handle the spatial information from the EEG while RNNs extract the temporal information. We evaluated two types of RNNs, namely long short-term memory (LSTM) and gated recurrent unit (GRU). The proposed method is evaluated on the state-of-the-art affective data set DEAP. The results indicate that CNN-GRU and CNN-LSTM can perform PI from different affective states and reach up to 99.90%-100% mean correct recognition rate. This significantly outperformed a support vector machine baseline system that used power spectral density features. Notably, the 100% mean CRR came from 32 subjects in DEAP data set. Even after the reduction of the number of EEG electrodes from 32 to 5 for more practical applications, the model could still maintain an optimal result obtained from the frontal region, reaching up to 99.17%. Amongst the two DL models, we found that CNN-GRU and CNN-LSTM performed similarly while CNN-GRU expended faster training time. In conclusion, the studied DL approaches overcame the influence of affective states in EEG-Based PI reported in the previous works.

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.

This paper presents a novel approach for efficient sampling of isotropic Bidirectional Reflectance Distribution Functions (BRDFs). Our approach builds upon a new parameterization, the Projected Deviation Vector parameterization, in which isotropic BRDFs can be described by two 1D functions. We show that BRDFs can be efficiently and accurately measured in this space using simple mechanical measurement setups. To demonstrate the utility of our approach, we perform a thorough numerical evaluation and show that the BRDFs reconstructed from measurements along the two 1D bases produce rendering results that are visually comparable to the reference BRDF measurements which are densely sampled over the 4D domain described by the standard hemispherical parameterization.

Data driven reflectance models using BRDF data measured from real materials, e.g. [Matusik et al. 2003], are becoming increasingly popular in product visualization, digital design and other applications driven by the need for predictable rendering and highly realistic results. Although recent analytic, parametric BRDFs provide good approximations for many materials, some effects are still not captured well [Löw et al. 2012]. Thus, it is hard to accurately model real materials using analytic models, even if the parameters are fitted to data. In practice, it is often desirable to apply small edits to the measured data for artistic purposes, or to model similar materials that are not available in measured form. A drawback of data driven models is that they are often difficult to edit and do not easily lend themselves well to artistic adjustments. Existing editing techniques for measured data [Schmidt et al. 2014], often use complex decompositions making them difficult to use in practice.