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研究生:吳昱霆
研究生(外文):Yu-Ting Wu
論文名稱:使用取樣與重建技術的高效率蒙地卡羅渲染法
論文名稱(外文):Sampling and Reconstruction Techniques for Efficient Monte Carlo Rendering
指導教授:莊永裕
指導教授(外文):Yung-Yu Chuang
口試委員:歐陽明王傑智施仁忠莊榮宏張鈞法蔡侑庭賴祐吉
口試委員(外文):Ming OuhyoungChieh-Chih (Bob) WangZen-Chung ShihJung-Hong ChuangChun-Fa ChangYu-Ting TsaiYu-Chi Lai
口試日期:2014-05-30
學位類別:博士
校院名稱:國立臺灣大學
系所名稱:資訊工程學研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2014
畢業學年度:102
語文別:英文
論文頁數:109
中文關鍵詞:三維計算機圖學以物理為基礎的渲染法重要性取樣法半透明物質渲染法自適應採樣與重建技術
外文關鍵詞:three-dimensional computer graphicsphysically-based renderingimportance samplingtranslucent material renderingadaptive sampling and reconstruction
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產生視覺逼真的影像以及進行數值精確的科學模擬為電腦圖學技術的兩個重要目的,基於物理性質的渲染繪製(physically-based rendering)因為可以同時滿足這兩個目的而受到重視。為了能夠使用一套完整的理論來考慮各式各樣複雜的光線傳播路徑,其通常會採用蒙地卡羅光線追蹤法(Monte Carlo ray tracing)來進行模擬。雖然蒙地卡羅法能用簡潔的方式模擬多種光影效果,其收斂速度並不理想。當繪製一個擁有大量的三維模型、逼真的材質、以及複雜光源的場景時,蒙地卡羅光線追蹤法往往需要非常大量的取樣數才能才能得到一張沒有雜訊的影像。
在這篇博士論文中我們共提出三種取樣與重建技術來增進蒙地卡羅光線追蹤法的效率。首先,我們觀察到在繪製複雜的場景時,比起光源和材質,物體表面兩點的可視度(visibility) 計算通常是造成雜訊的主要原因。因此為了增加取樣的效率,我們提出了可適度群聚(VisibilityCluster)演算法來快速並準確地預測場景中的可視度。此演算法可以被整合進重要性取樣(importance sampling)的架構中並大量減少雜訊。接著為了加速繪製需要龐大計算量的半透明材質,我們首先提出一個雙重矩陣(Dual-matrix)表示法來詮釋渲染半透明材質的問題。同時,我們發展一套取樣與重建技術來減少不重要的計算,大幅加速半透明材質的繪製。最後,我們提出一個有效率的自適應取樣與重建(adaptive sampling and reconstruction) 架構來處理淺景深,動態模糊,以及全域照明等光線傳遞效果。藉著導入統計學中估計誤差的方法到三維繪製的領域,我們成功的決定每個像素需要的取樣數量,並估計出一個最好的濾波器(filter)來大幅減少雜訊。與之前的研究相比,以上的這三個方法皆能大幅改善蒙地卡羅光線追蹤法的繪製效率。

Two of the important tasks that computer graphics techniques try to solve are rendering photo-realistic images and performing numerically accurate simulation. Physically-based rendering can naturally satisfy these two goals. It is usually simulated by Monte Carlo ray tracing for handling a variety of sophisticated light transport paths in a unified manner. Despite its generality and simplicity, however, Monte Carlo integration converges slowly. Rendering scenes with a large number of complex geometries and realistic materials under complex illumination usually requires a large number of samples to produce a noise-free image.
In this dissertation, we proposed three advanced sampling and reconstruction algorithms for improving the performance of Monte Carlo integration. First, realizing that in complex scenes visibility is usually the major source of noise during sampling the shading function, we developed a method called VisibilityCluster for efficiently approximating visibility function. By integrating it into importance sampling framework, we achieve superior noise reduction
compared to previous approaches. Second, to reduce the computation overhead of rendering translucent materials, we proposed an algorithm, Dual-matrix sampling, to avoid evaluating unimportant surface samples which contribute
little to the final image. Finally, a general adaptive sampling and reconstruction framework named SURE-based optimization is proposed to render a wide range of distributed effects, including depth of field, motion blur, and global illumination. All of the three methods achieve significant performance improvement compared to the state-of-the-art rendering algorithms.

Abstract viii
List of Figures xiv
Chapter 1 Introduction 1
Chapter 2 Light Transport, Monte Carlo, and Path Integration 8
2.1 Light Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Monte Carlo Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Importance Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4 Path Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4.1 Path integral formulation . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4.2 Antialiasing, depth of field, and motion blur . . . . . . . . . . . . . 16
2.5 Path-based Rendering Algorithms . . . . . . . . . . . . . . . . . . . . . . . 17
2.5.1 Path tracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.5.2 Virtual point light . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Chapter 3 VisibilityCluster: Average Directional Visibility for Many-Light Rendering
20
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2.1 Importance sampling . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2.2 Visibility algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2.3 Directional occlusion . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.4 VisibilityCluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.4.1 Initial clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.4.2 Average visibility estimation . . . . . . . . . . . . . . . . . . . . . 32
3.4.3 Local refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4.4 Bias avoidance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.5.1 Triple-product importance sampling . . . . . . . . . . . . . . . . . 36
3.5.2 Directional occlusion . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.6 Conclusion and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Chapter 4 Dual-Matrix Sampling for Scalable Translucent Material Rendering 48
4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2.1 BSSRDF models for subsurface scattering . . . . . . . . . . . . . . 52
4.2.2 Subsurface scattering rendering . . . . . . . . . . . . . . . . . . . . 53
4.3 Algorithm Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.3.1 Dual-matrix representation . . . . . . . . . . . . . . . . . . . . . . . 56
4.3.2 Flow of the algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.4 Dual-Matrix Representation and Sampling . . . . . . . . . . . . . . . . . . 57
4.4.1 Light-to-Surface matrix reconstruction (the first pass) . . . . . . . 58
4.4.2 Surface-to-Camera matrix reconstruction (the second pass) . . . . 61
4.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.5.1 Tested scenes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.5.2 Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.6 Conclusion and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . 70
Chapter 5 SURE-based Optimization for Adaptive Sampling and Reconstruction
72
5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.2.1 Adaptive sampling and reconstruction . . . . . . . . . . . . . . . . 75
5.2.2 Denoising using SURE . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.3 Stein’s Unbiased Risk Estimator (SURE) . . . . . . . . . . . . . . . . . . . 77
5.4 SURE-based Adaptive Rendering . . . . . . . . . . . . . . . . . . . . . . . 78
5.4.1 Initial samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.4.2 Filter selection using SURE . . . . . . . . . . . . . . . . . . . . . . 80
5.4.3 Adaptive sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.5.1 Parameter setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.5.2 Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.5.3 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.5.4 Other filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.5.5 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.6 Conclusion and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Chapter 6 Conclusions 98
Chapter A Derivatives for Filters 1
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