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1. Residual path integrals for re‐rendering

   https://doi.org/10.1111/cgf.15152  

   Xu, Bing; Li, Tzu‐Mao; Georgiev, Iliyan; Hedstrom, Trevor; Ramamoorthi, Ravi (July 2024, Computer Graphics Forum)

   Abstract Conventional rendering techniques are primarily designed and optimized for single‐frame rendering. In practical applications, such as scene editing and animation rendering, users frequently encounter scenes where only a small portion is modified between consecutive frames. In this paper, we develop a novel approach to incremental re‐rendering of scenes with dynamic objects, where only a small part of a scene moves from one frame to the next. We formulate the difference (or residual) in the image between two frames as a (correlated) light‐transport integral which we call the residual path integral. Efficient numerical solution of this integral then involves (1) devising importance sampling strategies to focus on paths with non‐zero residual‐transport contributions and (2) choosing appropriate mappings between the native path spaces of the two frames. We introduce a set of path importance sampling strategies that trace from the moving object(s) which are the sources of residual energy. We explore path mapping strategies that generalize those from gradient‐domain path tracing to our importance sampling techniques specially for dynamic scenes. Additionally, our formulation can be applied to material editing as a simpler special case. We demonstrate speed‐ups over previous correlated sampling of path differences and over rendering the new frame independently. Our formulation brings new insights into the re‐rendering problem and paves the way for devising new types of sampling techniques and path mappings with different trade‐offs. 

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2. Path Sampling Methods for Differentiable Rendering

   https://doi.org/10.2312/sr.20241148  

   Su, Tanli; Gkioulekas, Ioannis (January 2024, The Eurographics Association)

   We introduce a suite of path sampling methods for differentiable rendering of scene parameters that do not induce visibility-driven discontinuities, such as BRDF parameters. We begin by deriving a path integral formulation for differentiable rendering of such parameters, which we then use to derive methods that importance sample paths according to this formulation. Our methods are analogous to path tracing and path tracing with next event estimation for primal rendering, have linear complexity, and can be implemented efficiently using path replay backpropagation. Our methods readily benefit from differential BRDF sampling routines, and can be further enhanced using multiple importance sampling and a loss-aware pixel-space adaptive sampling procedure tailored to our path integral formulation. We show experimentally that our methods reduce variance in rendered gradients by potentially orders of magnitude, and thus help accelerate inverse rendering optimization of BRDF parameters. 

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3. Doppler Time-of-Flight Rendering

   https://doi.org/10.1145/3618335  

   Kim, Juhyeon; Jarosz, Wojciech; Gkioulekas, Ioannis; Pediredla, Adithya (December 2023, ACM Transactions on Graphics)

   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. 

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4. Warped-Area Reparameterization of Differential Path Integrals

   https://doi.org/10.1145/3618330  

   Xu, Peiyu; Bangaru, Sai; Li, Tzu-Mao; Zhao, Shuang (December 2023, ACM Transactions on Graphics)

   Physics-based differentiable rendering is becoming increasingly crucial for tasks in inverse rendering and machine learning pipelines. To address discontinuities caused by geometric boundaries and occlusion, two classes of methods have been proposed: 1) the edge-sampling methods that directly sample light paths at the scene discontinuity boundaries, which require nontrivial data structures and precomputation to select the edges, and 2) the reparameterization methods that avoid discontinuity sampling but are currently limited to hemispherical integrals and unidirectional path tracing. We introduce a new mathematical formulation that enjoys the benefits of both classes of methods. Unlike previous reparameterization work that focused on hemispherical integral, we derive the reparameterization in the path space. As a result, to estimate derivatives using our formulation, we can apply advanced Monte Carlo rendering methods, such as bidirectional path tracing, while avoiding explicit sampling of discontinuity boundaries. We show differentiable rendering and inverse rendering results to demonstrate the effectiveness of our method. 

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5. Dense Lissajous sampling and interpolation for dynamic light-transport

   https://doi.org/10.1364/OE.425061  

   Liu, Xiaomeng; Henderson, Kristofer; Rego, Joshua; Jayasuriya, Suren; Koppal, Sanjeev (May 2021, Optics Express)

   Light-transport represents the complex interactions of light in a scene. Fast, compressed, and accurate light-transport capture for dynamic scenes is an open challenge in vision and graphics. In this paper, we integrate the classical idea of Lissajous sampling with novel control strategies fordynamic light-transport applicationssuch as relighting water drops and seeing around corners. In particular, this paper introduces an improved Lissajous projector hardware design and discusses calibration and capture for a microelectromechanical (MEMS) mirror-based projector. Further, we show progress towards speeding up the hardware-based Lissajous subsampling for dual light transport frames, and investigate interpolation algorithms for recovering back the missing data. Our captured dynamic light transport results show complex light scattering effects for dense angular sampling, and we also show dual non-line-of-sight (NLoS) capture of dynamic scenes. This work is the first step towards adaptive Lissajous control for dynamic light-transport. 

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