Physical Sciences and Mathematics Commons^™

Consistent Monte Carlo Methods For Non-Linear Applications In Light Transport, Zackary T. Misso

Dartmouth College Ph.D Dissertations

The study of light transport focuses on describing the propagation of light from emitters to sensors through accurately describing the interactions light can undergo with everything in between. Physically-based rendering is the process of applying the laws of light transport to formulate practical algorithms which simulate the flow of light for the purpose of synthesizing images of virtual environments.

Unfortunately, there are very few interesting scene configurations which can be computed analytically. Instead, modern solutions predominantly rely on Monte Carlo integration to stochastically estimate the transfer of light since the process is both unbiased and consistent. Meaning, it is expected …

Random Walk Methods For Geometry Representation Agnostic Transport, Dario R. Seyb

Dartmouth College Ph.D Dissertations

In computer graphics, we use geometry representations to model a wide range of virtual scenes—from the fantastical worlds shown in animated movies to intricate mechanical parts.
These representations provide the context for transport problems—light transport is used to produce images of virtual scenes and diffusive transport to simulate distributions of quantities like heat.

There are many types of representations each with their own advantages.
For example, explicit ones make it easy to directly manipulate surfaces, while implicit representations allow for intuitive modeling by non-technical users and straightforward integration into machine learning systems.
Unfortunately, many algorithms that work on these digital …

A Bidirectional Formulation For Walk On Spheres, Yang Qi

Dartmouth College Master’s Theses

Poisson’s equations and Laplace’s equations are important linear partial differential equations (PDEs)
widely used in many applications. Conventional methods for solving PDEs numerically often need to
discretize the space first, making them less efficient for complex shapes. The random walk on spheres
method (WoS) is a grid-free Monte-Carlo method for solving PDEs that does not need to discrete the
space. We draw analogies between WoS and classical rendering algorithms, and find that the WoS
algorithm is conceptually identical to forward path tracing.
We show that solving the Poisson’s equation is equivalent to solving the Green’s function for every
pair of …

Temporally Sliced Photon Primitives For Volumetric Time-Of-Flight Rendering, Yang Liu

Dartmouth College Master’s Theses

Traditional steady-state rendering assumes that the light transport has already reached equilibrium. In contrast, time-of-flight rendering removes this assumption and recovers the pattern of light at extremely high temporal resolutions. This novel rendering modality not only provides a way to visualize the propagation of light, but can also empower the advances in time-of-flight imaging and its corresponding applications.

Building on previous work in steady-state volumetric rendering, this thesis introduces a novel framework for deriving new Monte Carlo estimators for solving the time-of-flight rendering problem in participating media. Conceptually, our method starts with any steady-state photon primitive, like a photon plane …

Correlations And Reuse For Fast And Accurate Physically Based Light Transport, Benedikt Bitterli

Dartmouth College Ph.D Dissertations

Light transport is the study of the transfer of light between emitters, surfaces, media and sensors. Fast simulations of light transport play a pivotal role in photo-realistic image synthesis, and find many applications today, including predictive manufacturing, machine learning, scientific visualization and the movie industry. In order to accurately reproduce the appearance of real scenes, light transport must closely approximate the physical laws governing the flow of light. Physically based rendering is a set of principles for codifying these laws into a mathematical model, and is the predominant rendering methodology today.

The representational power of this model is limited to …