Realism has always been a major goal in visual content creation - from oil painting to motion pictures, from graphic arts to scientific data visualization. Computer graphics creates a virtual reality with digital representations. Trading between accuracy and speed, realistic rendering either creates photorealistic renders that follow strict rules of physics or approximates them with interactive alternatives. The two approaches have their distinctive strengths and constraints. In this thesis, we focus on working from both ends towards realistic rendering. We study the highly accurate process of physically based rendering and introduce three novel methods dedicated to making it more efficient. We also investigate real-time depth of field rendering and develop a new model for an effect that is currently missing in state of the art systems. Part i concerns sampling in numerical integration. Two methods are presented in Chapter 2 and Chapter 3. We first propose to perform path guiding in primary sample space, resulting in an effective and efficient scheme that is easy to plug into existing rendering pipelines. Secondly, we map visibility relations in a matrix-like table to steer the sampling process, which improves processes, such as visible light samples and light subpaths. Part ii tackles the subsequent step after sampling in numerical integration. We present a new integration scheme in Chapter 4 that associates a weight to samples based on their adjacency, while remaining unbiased. The method delivers similar performance using uniform random samples as one can obtain with costly low-discrepancy sequences. In Part iii this thesis revisits the optics behind depth of field effects and models distortion and shrinking effects that are missing in modern real-time rendering solutions. We are able to deliver similar effects to that of ray-traced results at a fraction of the cost. Each chapter has detailed depiction and evaluation that helps readers better understand the methods and gain insights as to the applications thereof.@en

Numerical integration is fundamental in multiple Monte Carlo rendering problems. We present a sample reweighting scheme, including underlying theory, and analysis of numerical performance for the integration of an unknown one-dimensional function. Our method is simple to implement and builds upon the insight to link the weights to a function reconstruction process during integration. We provide proof that our solution is unbiased in one-dimensional cases and consistent in multi-dimensional cases. We illustrate its effectiveness in several use cases.

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Monte-Carlo rendering requires determining the visibility between scene points as the most common and compute intense operation to establish paths between camera and light source. Unfortunately, many tests reveal occlusions and the corresponding paths do not contribute to the final image. In this work, we present next event estimation++ (NEE++): a visibility mapping technique to perform visibility tests in a more informed way by caching voxel to voxel visibility probabilities. We show two scenarios: Russian roulette style rejection of visibility tests and direct importance sampling of the visibility. We show applications to next event estimation and light sampling in a uni-directional path tracer, and light-subpath sampling in Bi-Directional Path Tracing. The technique is simple to implement, easy to add to existing rendering systems, and comes at almost no cost, as the required information can be directly extracted from the rendering process itself. It discards up to 80% of visibility tests on average, while reducing variance by 20% compared to other state-of-the-art light sampling techniques with the same number of samples. It gracefully handles complex scenes with efficiency similar to Metropolis light transport techniques but with a more uniform convergence.@en

We demonstrate multi-scale multi-parameter optical coherence tomography (OCT) imaging and visualization of Johannes Vermeer’s painting Girl with a Pearl Earring. Through automated acquisition, OCT image segmentation, and 3D volume stitching we realize OCT imaging at the scale of an entire painting. This makes it possible to image, with micrometer axial and lateral resolution, an entire painting over more than 5 orders of length scale. From the multi-scale OCT data we quantify multiple parameters in a fully automated way: the surface height, the scattering strength, and the combined glaze and varnish layer thickness. The multi-parameter OCT data of Girl with a Pearl Earring shows various features: Vermeer’s brushstrokes, surface craquelure, paint losses, and restorations. Through an interactive visualization of the Girl, based on the OCT data and the optical properties of historical reconstructions of Vermeer’s paint, we can virtually study the effect of the lighting condition, viewing angle, zoom level and presence/absence of glaze layer. The interactive visualization shows various new painting features. It demonstrates that the glaze layer structure and its optical properties were essential to Vermeer to create an extremely strong light to dark contrast between the figure and the background that gives the painting such an iconic aesthetic appeal.@en

We present a scheme for unbiased path guiding. Different from existing methods that focus on constructing structures in spatial-directional domain, we work in primary sample space. We collect records containing a few dimensions of random numbers as well as the luminance that the resulting path contributes. A multiple dimensional structure is built with collected information. After this, random numbers are drawn from this structure and is used to feed the path tracer. Using this scheme, we are able to work completely outside the rendering kernel. We demonstrate that our method is practical and can be efficient. We manage to reduce variance and reduce zero radiance paths by only working in the primary sample space.@en

In this extended abstract we present our research statement, motivation and methodology for this PhD project. This PhD research focuses on Monte Carlo methods in the field of realistic image synthesis. According to various studies, widely adopted sampling schemes prove not optimal. The overall goal of this PhD research project is to improve existing Monte Carlo methods and make them more robust and efficient. We will analyze pitfalls of existing methods and propose improved mathematical models and methods accordingly. We will verify and implement our proposed models. Performance will be analyzed following rigorous design science guidelines. @en