A Spatial Target Function for Metropolis Photon Tracing

Self Cite

Markov chain Monte Carlo (MCMC) sampling is a powerful approach to generate samples from an arbitrary distribution. The application to light transport simulation allows us to efficiently handle complex light transport such as highly occluded scenes. Since light transport paths in MCMC methods are sampled according to the path contributions over the sampling domain covering the whole image, bright pixels receive more samples than dark pixels to represent differences in the brightness. This variation in the number of samples per pixel is a fundamental property of MCMC methods. This property often leads to uneven convergence over the image, which is a notorious and fundamental issue of any MCMC method to date. We present a novel stratification method of MCMC light transport methods. Our stratification method, for the first time, breaks the fundamental limitation that the number of samples per pixel is uncontrollable. Our method guarantees that every pixel receives a specified number of samples by running a single Markov chain per pixel. We rely on the fact that different MCMC processes should converge to the same result when the sampling domain and the integrand are the same. We thus subdivide an image into multiple overlapping tiles associated with each pixel, run an independent MCMC process in each of them, and then align all of the tiles such that overlapping regions match. This can be formulated as an optimization problem similar to the reconstruction step for gradient‐domain rendering. Further, our method can exploit the coherency of integrands among neighboring pixels via coherent Markov chains and replica exchange. Images rendered with our method exhibit much more predictable convergence compared to existing MCMC methods.

Section: Stratification In MC and Mcmcmentioning

confidence: 99%

Stratified Markov Chain Monte Carlo Light Transport

Gruson

West

Hachisuka

2020

Self Cite

“…Photon mapping [Jen01] is one of the most versatile and robust methods for rendering complex global illumination, with several extensions for making it compatible with motion blur [CJ02], adapting the distribution of photons [SJ09, GRv*16], carefully selecting the radiance estimation kernel [SJ09, KD13, JRJ11], combining it with unbiased techniques [GKDS12, HPJ12] or making it progressive for ensuring consistency within a limited memory budget [HOJ08, KZ11]. Hachisuka et al .…”

Section: Related Workmentioning

confidence: 99%

Progressive Transient Photon Beams

Marco

Guillén

Jarosz

et al. 2019

In this work, we introduce a novel algorithm for transient rendering in participating media. Our method is consistent, robust and is able to generate animations of time‐resolved light transport featuring complex caustic light paths in media. We base our method on the observation that the spatial continuity provides an increased coverage of the temporal domain, and generalize photon beams to transient‐state. We extend stead‐state photon beam radiance estimates to include the temporal domain. Then, we develop a progressive variant of our approach which provably converges to the correct solution using finite memory by averaging independent realizations of the estimates with progressively reduced kernel bandwidths. We derive the optimal convergence rates accounting for space and time kernels, and demonstrate our method against previous consistent transient rendering methods for participating media.

“…Difficult specular transport can be rendered with Markov chain approaches using regularization [KD13] or manifold exploration [JM12]. The Metropolis algorithm can also be used in conjunction with Photon mapping [ŠOHK16,GRŠ*17,HJ11], so as to distribute photons according to visibility, image contribution, or in a way that ensures a uniform error distribution. However, all these methods suffer from the drawbacks common to MCMC approaches.…”

Section: Related Workmentioning

confidence: 99%

“…However, bright, yet far away, caustics might still receive too many photons. One way to improve our method further could therefore be to combine it with previous work trying to distribute photons in a way that achieves a more uniform distribution of error in the image, like [GRŠ*17].…”

Section: Limitations and Future Workmentioning

confidence: 99%

Efficient Caustic Rendering with Lightweight Photon Mapping

Grittmann

Pérard-Gayot

Slusallek

et al. 2018

Self Cite

Robust and efficient rendering of complex lighting effects, such as caustics, remains a challenging task. While algorithms like vertex connection and merging can render such effects robustly, their significant overhead over a simple path tracer is not always justified and – as we show in this paper ‐ also not necessary. In current rendering solutions, caustics often require the user to enable a specialized algorithm, usually a photon mapper, and hand‐tune its parameters. But even with carefully chosen parameters, photon mapping may still trace many photons that the path tracer could sample well enough, or, even worse, that are not visible at all. Our goal is robust, yet lightweight, caustics rendering. To that end, we propose a technique to identify and focus computation on the photon paths that offer significant variance reduction over samples from a path tracer. We apply this technique in a rendering solution combining path tracing and photon mapping. The photon emission is automatically guided towards regions where the photons are useful, i.e., provide substantial variance reduction for the currently rendered image. Our method achieves better photon densities with fewer light paths (and thus photons) than emission guiding approaches based on visual importance. In addition, we automatically determine an appropriate number of photons for a given scene, and the algorithm gracefully degenerates to pure path tracing for scenes that do not benefit from photon mapping.