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Stochastic geometry models have enjoyed immense success in graphics for modeling interactions of light with complex phenomena such as participating media, rough surfaces, fibers, and more. Although each of these models operates on the same principle of replacing intricate geometry by a random process and deriving the average light transport across all instances thereof, they are each tailored to one specific application and are fundamentally distinct. Each type of stochastic geometry present in the scene is firmly encapsulated in its own appearance model, with its own statistics and light transport average, and no cross-talk between different models or deterministic and stochastic geometry is possible. In this paper, we derive a theory of light transport on stochastic implicit surfaces, a geometry model capable of expressing deterministic geometry, microfacet surfaces, participating media, and an exciting new continuum in between containing aggregate appearance, non-classical media, and more. Our model naturally supports spatial correlations, missing from most existing stochastic models. Our theory paves the way for tractable rendering of scenes in which all geometry is described by the same stochastic model, while leaving ample future work for developing efficient sampling and rendering algorithms. 

The constellation of Earth-observing satellites continuously collects measurements of scattered radiance, which must be transformed into geophysical parameters in order to answer fundamental scientific questions about the Earth. Retrieval of these parameters requires highly flexible, accurate, and fast forward and inverse radiative transfer models. Existing forward models used by the remote sensing community are typically accurate and fast, but sacrifice flexibility by assuming the atmosphere or ocean is composed of plane-parallel layers. Monte Carlo forward models can handle more complex scenarios such as 3D spatial heterogeneity, but are relatively slower. We propose looking to the computer graphics community for inspiration to improve the statistical efficiency of Monte Carlo forward models and explore new approaches to inverse models for remote sensing. In Part 2 of this work, we demonstrate that Monte Carlo forward models in computer graphics are capable of sufficient accuracy for remote sensing by extending Mitsuba 3, a forward and inverse modeling framework recently developed in the computer graphics community, to simulate simple atmosphere-ocean systems and show that our framework is capable of achieving error on par with codes currently used by the remote sensing community on benchmark results. 

The constellation of Earth-observing satellites continuously collects measurements of scattered radiance, which must be transformed into geophysical parameters in order to answer fundamental scientific questions about the Earth. Retrieval of these parameters requires highly flexible, accurate, and fast forward and inverse radiative transfer models. Existing forward models used by the remote sensing community are typically accurate and fast, but sacrifice flexibility by assuming the atmosphere or ocean is composed of plane-parallel layers. Monte Carlo forward models can handle more complex scenarios such as 3D spatial heterogeneity, but are relatively slower. We propose looking to the computer graphics community for inspiration to improve the statistical efficiency of Monte Carlo forward models and explore new approaches to inverse models for remote sensing. In Part 1 of this work, we examine the evolution of radiative transfer models in computer graphics and highlight recent advancements that have the potential to push forward models in remote sensing beyond their current periphery of realism. 

We introduce Doppler time-of-flight (D-ToF) rendering, an extension of ToF rendering for dynamic scenes, with applications in simulating D-ToF cameras. D-ToF cameras use high-frequency modulation of illumination and exposure, and measure the Doppler frequency shift to compute the radial velocity of dynamic objects. The time-varying scene geometry and high-frequency modulation functions used in such cameras make it challenging to accurately and efficiently simulate their measurements with existing ToF rendering algorithms. We overcome these challenges in a twofold manner: To achieve accuracy, we derive path integral expressions for D-ToF measurements under global illumination and form unbiased Monte Carlo estimates of these integrals. To achieve efficiency, we develop a tailored time-path sampling technique that combines antithetic time sampling with correlated path sampling. We show experimentally that our sampling technique achieves up to two orders of magnitude lower variance compared to naive time-path sampling. We provide an open-source simulator that serves as a digital twin for D-ToF imaging systems, allowing imaging researchers, for the first time, to investigate the impact of modulation functions, material properties, and global illumination on D-ToF imaging performance. 

Null-collision approaches for estimating transmittance and sampling free-flight distances are the current state-of-the-art for unbiased rendering of general heterogeneous participating media. However, null-collision approaches have a strict requirement for specifying a tightly bounding total extinction in order to remain both robust and performant; in practice this requirement restricts the use of null-collision techniques to only participating media where the density of the medium at every possible point in space is known a-priori. In production rendering, a common case is a medium in which density is defined by a black-box procedural function for which a bounding extinction cannot be determined beforehand. Typically in this case, a bounding extinction must be approximated by using an overly loose and therefore computationally inefficient conservative estimate. We present an analysis of how null-collision techniques degrade when a more aggressive initial guess for a bounding extinction underestimates the true maximum density and turns out to be non-bounding. We then build upon this analysis to arrive at two new techniques: first, a practical, efficient, consistent progressive algorithm that allows us to robustly adapt null-collision techniques for use with procedural media with unknown bounding extinctions, and second, a new importance sampling technique that improves ratio-tracking based on zero-variance sampling. 

In recent years, reservoir-based spatiotemporal importance resampling (ReSTIR) algorithms appeared out of nowhere to take parts of the realtime rendering community by storm, with sample reuse speeding direct lighting from millions of dynamic lights [1], diffuse multi-bounce lighting [2], participating media [3], and even complex global illumination paths [4]. Highly optimized variants (e.g. [5]) can give 100x efficiency improvement over traditional ray- and path-tracing methods; this is key to achieve 30 or 60 Hz framerates. In production engines, tracing even one ray or path per pixel may only be feasible on the highest-end systems, so maximizing image quality per sample is vital. ReSTIR builds on the math in Talbot et al.'s [6] resampled importance sampling (RIS), which previously was not widely used or taught, leaving many practitioners missing key intuitions and theoretical grounding. A firm grounding is vital, as seemingly obvious "optimizations" arising during ReSTIR engine integration can silently introduce conditional probabilities and dependencies that, left ignored, add uncontrollable bias to the results. In this course, we plan to: 1. Provide concrete motivation and intuition for why ReSTIR works, where it applies, what assumptions it makes, and the limitations of today's theory and implementations; 2. Gently develop the theory, targeting attendees with basic Monte Carlo sampling experience but without prior knowledge of resampling algorithms (e.g., Talbot et al. [6]); 3. Give explicit algorithmic samples and pseudocode, pointing out easily-encountered pitfalls when implementing ReSTIR; 4. Discuss actual game integrations, highlighting the gotchas, challenges, and corner cases we encountered along the way, and highlighting ReSTIR's practical benefits. 

We propose a novel system for low-cost multi-color Fused Filament Fabrication (FFF) 3D printing, allowing for the creation of customizable colored filament using a pre-processing approach. We developed an open-source device to automatically ink filament using permanent markers. Our device can be built using 3D printed parts and off-the-shelf electronics. An accompanying web-based interface allows users to view GCODE toolpaths for a multi-color print and quickly generate filament color profiles. Taking a pre-processing approach makes this system compatible with the majority of desktop 3D printers on the market, as the processed filament behaves no differently from conventional filaments. Furthermore, inked filaments can be produced economically, reducing the need for excessive purchasing of material to expand color options. We demonstrate the efficacy of our system by fabricating monochromatic objects, objects with gradient colors, objects with bi-directional properties, as well as multi-color objects with up to four colors in a single print. 

We propose a novel design for a do-it-yourself hyperspectral imaging system which operates by taking multiple photographs through tunable, polarization-induced, spectral filters. Prior approaches in this do-it-yourself arena achieve hyperspectral imaging by selecting from a discrete set of spectra baked into existing products. In contrast, our approach is capable of generating a continuous family of broadband transmission spectra by simple rotations of stacked polarizers and waveplates. This greatly expands the potential range of representable spectra from a fixed-dimensional to an arbitrary-dimensional space. We analyze the theoretical spectral gamut of our approach and demonstrate its viability for spectral surface reflectance reconstruction both in simulation and with a low-cost physical prototype. Our prototype demonstrates that our approach can achieve comparable quality to prior work at reduced cost, while the new design space holds ample opportunity for increased quality and flexibility with professional manufacturing.