Path Guiding with Vertex Triplet Distributions

Good importance sampling strategies are decisive for the quality and robustness of photorealistic image synthesis with Monte Carlo integration. Path guiding approaches use transport paths sampled by an existing base sampler to build and refine a guiding distribution. This distribution then guides subsequent paths in regions that are otherwise hard to sample. We observe that all terms in the measurement contribution function sampled during path construction depend on at most three consecutive path vertices. We thus propose to build a 9D guiding distribution over vertex triplets that adapts to the full measurement contribution with a 9D Gaussian mixture model (GMM). For incremental path sampling, we query the model for the last two vertices of a path prefix, resulting in a 3D conditional distribution with which we sample the next vertex along the path. To make this approach scalable, we partition the scene with an octree and learn a local GMM for each leaf separately. In a learning phase, we sample paths using the current guiding distribution and collect triplets of path vertices. We resample these triplets online and keep only a fixed-size subset in reservoirs. After each progression, we obtain new GMMs from triplet samples by an initial hard clustering followed by expectation maximization. Since we model 3D vertex positions, our guiding distribution naturally extends to participating media. In addition, the symmetry in the GMM allows us to query it for paths constructed by a light tracer. Therefore our method can guide both a path tracer and light tracer from a jointly learned guiding distribution

GPU 상에서의 빠르고 가벼운 Path Guiding 알고리즘

학위논문(석사) -- 서울대학교대학원 : 공과대학 전기·정보공학부, 2022.2. 김영민.We propose a simple, yet practical path guiding algorithm that runs on GPU. Path guiding renders photo-realistic images by simulating the iterative bounces of rays, which are sampled from the radiance distribution. The radiance distribution is often learned by serially updating the hierarchical data structure to represent complex scene geometry, which is not easily implemented with GPU. In contrast, we employ a regular data structure and allow fast updates by processing a significant number of rays with GPU. We further increase the efficiency of radiance learning by employing SARSA used in reinforcement learning. SARSA does not include aggregation of incident radiance from all directions nor storing all of the previous paths. The learned distribution is then importance-sampled with an optimized rejection sampling, which adapts the current surface normal to reflect finer geometry than the grid resolution. All of the algorithms have been implemented on GPU using megakernal architecture with NVIDIA OptiX. Through numerous experiments on complex scenes, we demonstrate that our proposed path guiding algorithm works efficiently on GPU, drastically reducing the number of wasted paths.본 연구는 GPU 상에서 작동하는 간단하지만 효과적인 path guiding 알고리즘을 제안한다. Path guiding은 path tracing의 노이즈를 줄이기 위해 제안된 기법으로 샘플링 과정에서 복사 휘도(radiance)를 배우고 이를 이용해 중요도 샘플링(importance sampling)을 수행한다. 복사 휘도의 복잡한 분포를 배우기 위해 이전의 논문들에서는 복잡한 재귀적 데이터 구조를 제안하고 이를 순차적으로 업데이트 하였지만 이는 CPU상에서의 path tracing만을 가정한 것으로 GPU상에서는 쉽게 구현하기 어려우며 효과적으로 작동하지 않는다. 본 논문에서는 GPU 친화적인 간단한 그리드 형태의 데이터를 사용해 path guiding 알고리즘을 진행하였다. 또한 path guiding의 두 가지 목표-(1) 복사 휘도 학습과 (2) 학습된 복사 휘도 분포를 이용한 중요도 샘플링-를 GPU 상에서 효과적으로 구현하기 위해 다음과 같은 방법을 제시한다. 우선 복사 휘도 학습의 경우, 강화학습과 복사 휘도 학습의 구조적 유사성을 밝힌 이전 연구를 확장하여 가볍고 빠른 SARSA를 이용한 학습 방법을 제안하였다. 학습된 복사 휘도는 공간-방향을 그리드 형태로 분할한 GPU상의 데이터 구조에 저장된다. 학습된 복사 휘도를 사용한 중요도 샘플링의 경우 법선 벡터 방향에 유효하지 않은 샘플들은 제외한 뒤, 리젝션 샘플링(rejection sampling)을 이용해 중요도 샘플링(importance sampling)을 수행하였다. 모든 알고리즘은 NVIDIA OptiX를 사용해 GPU상에서 megakernel 구조로 구현되었다. 복잡한 구조의 씬 데이터에 대해 여러 번 실험을 수행하였으며 본 연구에서 제안한 방법의 우수성을 확인하였다.Abstract i Chapter 1 Introduction 1 Chapter 2 Background and Related Works 4 2.1 Ray Tracing on GPU 4 2.2 Path Guiding 5 2.3 Reinforcement Learning and Light Transport 6 Chapter 3 Problem Setting and Overview 7 Chapter 4 Fast and Lightweight Radiance Learning 10 4.1 Analogy between the Rendering Equation and Reinforcement Learning 10 4.2 Fast and Lightweight Radiance Learning with SARSA 12 Chapter 5 Efficient Importance Sampling from Learned Radiance 16 5.1 Importance Sampling on Hemispherical Domain 16 5.2 Fast and Efficient Importance Sampling with Optimized Rejection Sampling 18 5.3 Normalizing Term Calculation with Memoization 20 Chapter 6 Experiments and Results 22 6.1 GPU-based Path Guiding with a Regular Grid 23 6.2 Comparison for Radiance Learning Methods 25 6.3 Comparison for Radiance Sampling Methods 27 Chapter 7 Conclusion 35 Appendix A Additional Experimental Results 36 A.1 Comparison for Spatial Directional Resolution 36 A.2 Equal SPP Comparison 36 Appendix B Pseudocode for the Algorithm 39 초록 46 Acknowledgements 47석

Online Neural Path Guiding with Normalized Anisotropic Spherical Gaussians

The variance reduction speed of physically-based rendering is heavily affected by the adopted importance sampling technique. In this paper we propose a novel online framework to learn the spatial-varying density model with a single small neural network using stochastic ray samples. To achieve this task, we propose a novel closed-form density model called the normalized anisotropic spherical gaussian mixture, that can express complex irradiance fields with a small number of parameters. Our framework learns the distribution in a progressive manner and does not need any warm-up phases. Due to the compact and expressive representation of our density model, our framework can be implemented entirely on the GPU, allowing it produce high quality images with limited computational resources

Towards a unified linear kinetic transport model with the trace ion module for EIRENE

Linear kinetic Monte Carlo particle transport models are frequently employed in fusion plasma simulations to quantify atomic and surface effects on the main plasma flow dynamics. Separate codes are used for transport of neutral particles (incl. radiation) and charged particles (trace impurity ions). Integration of both modules into main plasma fluid solvers provides then self consistent solutions, in principle. The required interfaces are far from trivial, because rapid atomic processes in particular in the edge region of fusion plasmas require either smoothing and resampling, or frequent transfer of particles from one into the other Monte Carlo code. We propose a different scheme here, in which despite the inherently different mathematical form of kinetic equations for ions and neutrals (e.g. Fokker-Planck vs. Boltzmann collision integrals) both types of particle orbits can be integrated into one single code. We show that the approximations and shortcomings of this "single sourcing" concept (e.g., restriction to explicit ion drift orbit integration) can be fully tolerable in a wide range of typical fusion edge plasma conditions, and be overcompensated by the code-system simplicity, as well as by inherently ensured consistency in geometry (one single numerical grid only) and (the common) atomic and surface process modulesComment: 15 pages, 7 figure