Markov Chain Mixture Models for Real-Time Direct Illumination

Addis Dittebrandt, Vincent Schüßler, Johannes Hanika, Sebastian Herholz and Carsten Dachsbacher

Computer Graphics Forum Vol. 42 Issue 4 (Proceedings of Eurographics Symposium on Rendering) 2023

Left: Direct illumination from many small light sources rendered using our mixture model with 8spp (10.8ms at 1080p), without explicit light source sampling. Right: a visualization of the mixture model in latitude/longitude projection. Red insets: At any time step, every pixel holds only a single vMF lobe (red), aimed at one of the light sources (black), the overlap is shown in green. Through a Markov chain process, lobes are adapted and exchanged locally. Blue inset: We can observe the mixture model as different slices of this construction: spatially over an image region, as well as temporally over multiple time steps. For better visibility, we surround lobes with a dark red circle.


We present a novel technique to efficiently render complex direct illumination in real-time. It is based on a spatio-temporal randomized mixture model of von Mises-Fisher (vMF) distributions in screen space. For every pixel we determine the vMF distribution to sample from using a Markov chain process which is targeted to capture important features of the integrand. By this we avoid the storage overhead of finite-component deterministic mixture models, for which, in addition, determining the optimal component count is challenging. We use stochastic multiple importance sampling (SMIS) to be independent of the equilibrium distribution of our Markov chain process, since it cancels out in the estimator. Further, we use the same sample to advance the Markov chain and to construct the SMIS estimator and local Markov chain state permutations avoid the resulting bias due to dependent sampling. As a consequence we require one ray per sample and pixel only. We evaluate our technique using implementations in a research renderer as well as a classic game engine with highly dynamic content. Our results show that it is efficient and quickly readapts to dynamic conditions. We compare to spatio-temporal resampling (ReSTIR), which can suffer from correlation artifacts due to its non-adapting candidate distributions that can deviate strongly from the integrand. While we focus on direct illumination, our approach is more widely applicable and we exemplarily show the rendering of caustics.





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@article {2023_mcmm,
    journal = {Computer Graphics Forum},
    title = {{Markov Chain Mixture Models for Real-Time Direct Illumination}},
    author = {Dittebrandt, Addis and Sch\"u\ss ler, Vincent and Hanika, Johannes and Herholz, Sebastian and Dachsbacher, Carsten},
    year = {2023},
    publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
    ISSN = {1467-8659},
    DOI = {10.1111/cgf.14881}