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. 

Fotorealistisk rendering och prediktiv bildsyntes har blivit allt viktigare och an-vänds i flera olika tillämpningsområden, allt ifrån produktion av visuella effekter och produktvisualisering till digital design och generering av syntetiska data för tillämpningar inom visuell maskininlärning. Utvecklingen har tagit en ordentlig fart under de senaste decennierna för många av de väsentliga komponenterna i det fotorealistiska bildsyntes-området. En nyckelkomponent inom området är att noggrant kunna mäta, modellera och simulera ljusets spridning från ytan hos ett material. Ljusspridningen från en punkt på en yta med reflektion och färg, beskrivs av en funktion (eng. BRDF); vilket är det huvudsakliga forskningsområdet i den här avhandlingen. BRDF beskriver hur strålning, ljus i detta fall, träffar en punkt på en yta och sprids mot varje observerad synvinkel. En noggrann uppmätning och representation av materialegenskaper är en fundamental del i fotorealistisk bildsyntes och omger ett väldigt intressant forskningsområde med många tillämpningar.

Den här avhandlingen har utforskat och studerat modellering för materialytors utseende, glesa representationer och glesa mätningar av ljusspridningsfunktioner. Avhandlingen täcker två huvudområden. Inom det första området, BRDF-modellering, så presenterar vi ett flertal nya BRDF-modeller för noggrann representation av ljusspridningens beteende från materialets yta genom att använda simpla men effektiva metoder. Forskningsutmaningarna inom BRDF-modellering inkluderar både metoder för tensoruppdelning och glesa approximationer baserat på uppmätt BRDF-data. Den andra delen fokuserar på gles BRDF-sampling och en ny och effektiv mätningsmetod för att mäta BRDF. Syftet med den glesa BRDF-samplingen är för att förenkla och snabba upp de enormt tidskrävande processerna som krävs för att mäta BRDF. Detta utmanande problem löses genom att använda glesa modeller och tekniker från compressed sensing som möjliggör att BRDF kan be uppmätt och noggrant rekonstruerad genom att endast använda ett fåtal uppmätta sampel. Slutligen så visar avhandlingen ett flertal exempel på tillämpningsområden från forskningen, så väl som tekniker för BRDF-editering och interpolation.

De BRDF-databaser som är öppna och tillgängliga för allmänheten är en vital del av de datadrivna metoderna som presenteras I denna avhandling. De uppmätta BRDF-data som använts har öppnat nya insikter för vidare utveckling av de framtagna metoderna. Resultaten, algoritmerna och teknikerna presenterade i den här avhandlingen visar på att det finns en nära koppling mellan BRDF modellering och BRDF-mätning; effektiv och noggrann BRDF-modellering är en biprodukt av gles BRDF-sampling.  

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.