Shu-Jheng Huang 1 / 25 Structured Importance Sampling of Environment Maps Agarwal, S., R. Ramamoorthi, S. Belongie, and H. W. Jensen.

Slides:

Advertisements

Similar presentations

Sample Approximation Methods for Stochastic Program Jerry Shen Zeliha Akca March 3, 2005.

Advertisements

Kartic Subr, Derek Nowrouzezahrai, Wojciech Jarosz, Jan Kautz and Kenny Mitchell Disney Research, University of Montreal, University College London.

Photorealistic Rendering. Ray tracing v. photorealistic rendering What illumination effects are not captured by ray tracing? What illumination effects.

Path Differentials for MC Rendering Frank Suykens Department of Computer Science K.U.Leuven, Belgium Dagstuhl 2001: Stochastic methods in Rendering.

Importance Sampling. What is Importance Sampling ? A simulation technique Used when we are interested in rare events Examples: Bit Error Rate on a channel,

Monte Carlo Integration Robert Lin April 20, 2004.

Advanced Computer Graphics (Spring 2005) COMS 4162, Lectures 18, 19: Monte Carlo Integration Ravi Ramamoorthi Acknowledgements.

Photon Tracing with Arbitrary Materials Patrick Yau.

Chapters 7-8 Key Points and JMP Instructions. Example 1: Comparing Two Sample Means Means are different at the  =.05 level.

Advanced Computer Graphics (Fall 2009) CS 294, Rendering Lecture 5: Monte Carlo Path Tracing Ravi Ramamoorthi

Computational statistics, course introduction Course contents  Monte Carlo Methods  Random number generation  Simulation methodology  Bootstrap  Markov.

Advanced Computer Graphics (Fall 2010) CS 283, Lecture 10: Global Illumination Ravi Ramamoorthi Some images courtesy.

1 Lecture 9 Lighting Light Sources Reflectance Camera Models.

Advanced Computer Graphics (Spring 2006) COMS 4162, Lecture 20: Monte Carlo Path Tracing Ravi Ramamoorthi Acknowledgements.

Normal and Sampling Distributions A normal distribution is uniquely determined by its mean, , and variance,  2 The random variable Z = (X-  /  is.

Mean, Variance, and Standard Deviation for Grouped Data Section 3.3.

Direct Illumination with Lazy Visibility Evaluation David Hart Philip Dutré Donald P. Greenberg Cornell University SIGGRAPH 99.

Hashed Samples Selectivity Estimators for Set Similarity Selection Queries.

Analysis of Monte Carlo Integration Fall 2012 By Yaohang Li, Ph.D.

01/24/05© 2005 University of Wisconsin Last Time Raytracing and PBRT Structure Radiometric quantities.

Selected Topics in Global Illumination Computation Jaroslav Křivánek Charles University, Prague

Chapter 14 Monte Carlo Simulation Introduction Find several parameters Parameter follow the specific probability distribution Generate parameter.

Optimal Allocation in the Multi-way Stratification Design for Business Surveys (*) Paolo Righi, Piero Demetrio Falorsi 

Monte Carlo Integration II Digital Image Synthesis Yung-Yu Chuang with slides by Pat Hanrahan and Torsten Moller.

Monte Carlo I Previous lecture Analytical illumination formula This lecture Numerical evaluation of illumination Review random variables and probability.

M. Zwicker Univ. of Bern W. Jarosz Disney Research J. Lehtinen

Sampling Distributions. What is a sampling distribution? Grab a sample of size N Compute a statistic (mean, variance, etc.) Record it Do it again (until.

7821 Monte Carlo Techniques Basic Concepts Chapter (13)14, 15 of “Physically Based Rendering” by Pharr&Humphreys.

4. Numerical Integration. Standard Quadrature We can find numerical value of a definite integral by the definition: where points x i are uniformly spaced.

1 Rendering translucent materials using SSS Implemented by João Pedro Jorge & Willem Frishert.

An Enhanced Splatting Method Graphics and Visualization Group Department of Computer Science The University of Auckland Peter Kulka & Richard Lobb.

Optimally Combining Sampling Techniques for Monte Carlo Rendering Eric Veach and Leonidas J. Guibas Computer Science Department Stanford University SIGGRAPH.

Importance Resampling for Global Illumination Justin F. Talbot Master’s Thesis Defense Brigham Young University Provo, UT.

Covariance Estimation For Markowitz Portfolio Optimization Ka Ki Ng Nathan Mullen Priyanka Agarwal Dzung Du Rezwanuzzaman Chowdhury 14/7/2010.

Importance Resampling for Global Illumination Justin Talbot, David Cline, and Parris Egbert Brigham Young University Provo, UT.

Instant Radiosity Alexander Keller University Kaiserslautern Present by Li-Fong Lin.

A Theory of Monte Carlo Visibility Sampling

Prabhas Chongstitvatana1 Monte Carlo integration It is a numerical probabilistic algorithm ab I/(b-a) f.

Quasi-Random Techniques Don P. Mitchell. MC Integration for Rendering Ray tracing yields point samples f(x i ) Discontinuous f thwarts efficient methods.

Computer Graphics III – Monte Carlo integration Direct illumination

Variance Reduction Fall 2012

Photo-realistic Rendering and Global Illumination in Computer Graphics Spring 2012 Stochastic Path Tracing Algorithms K. H. Ko School of Mechatronics Gwangju.

Monte Carlo Techniques Basic Concepts

01/26/05© 2005 University of Wisconsin Last Time Raytracing and PBRT Structure Radiometric quantities.

Distributed Ray Tracing. Can you get this with ray tracing?

Distributed Ray Tracing. Can you get this with ray tracing?

親愛的吉姆舅舅：今天吃完晚餐後，奶奶說，在家裡情況變好以前，您要我搬到城裡跟您住。奶奶有沒有跟您說，爸爸已經好久沒有工作，也好久沒有人請媽媽做衣服了？我們聽完都哭了，連爸爸也哭了，但是媽媽說了一個故事讓我們又笑了。她說：您們小的時候，她曾經被您追得爬到樹上去，真的嗎？雖然我個子小，但是我很強壯，

Atmospheric Effects Interactive Rendering of Atmospheric Scattering Effects Using Graphics Hardware Tsuyoshi Yamamoto Tomoyuki Nishita Tokyo University.

Презентацию подготовила Хайруллина Ч.А. Муслюмовская гимназия Подготовка к части С ЕГЭ.

Introduction to Monte Carlo Method

Robust Diffuse Final Gathering on the GPU

Sampling and Reconstruction of Visual Appearance

Sampling and Reconstruction of Visual Appearance

Energy Preserving Non-linear Filters

Hire Toyota Innova in Delhi for Outstation Tour

عمل الطالبة : هايدى محمد عبد المنعم حسين

© 2005 University of Wisconsin

Homework #3 Environment Lights

Monte Carlo I Previous lecture Analytical illumination formula

Monte Carlo Rendering Central theme is sampling:

Determining Which Method to use

VQMC J. Planelles.

And portfolio variance

C.2.10 Sample Questions.

C.2.8 Sample Questions.

C.2.8 Sample Questions.

Monte Carlo Path Tracing and Caching Illumination

Monte Carlo Integration

Presentation transcript:

Shu-Jheng Huang 1 / 25 Structured Importance Sampling of Environment Maps Agarwal, S., R. Ramamoorthi, S. Belongie, and H. W. Jensen

Shu-Jheng Huang 2 / 25 Outline Monte Carlo Sampling and Importance metric Variance Analysis for Visibility Hierarchical Environment Map Stratification Rendering Optimizations

Shu-Jheng Huang 3 / 25

Shu-Jheng Huang 4 / 25 Monte Carlo Sampling and Importance Area based stratified sampling Illumination-based importance sampling

Shu-Jheng Huang 5 / 25 Importance Metric Illumination-based importance sampling ( a=1 b=0 ) Area based stratified sampling ( a=0 b=1 )

Shu-Jheng Huang 6 / 25 Variance Analysis for Visibility (variance) (empirical)

Shu-Jheng Huang 7 / 25 Variance Analysis for Visibility Correlation model for visibility

Shu-Jheng Huang 8 / 25 Variance Analysis for Visibility Mean visibility = ½ (assuming) P(S=0) = P(S=1) = ½ θ-> 0, α(θ) = 1 θbecomes large α(θ) = ½ (T is the correlation angle)

Shu-Jheng Huang 9 / 25 Variance Analysis for Visibility

Shu-Jheng Huang 10 / 25 Variance Analysis for Visibility

Shu-Jheng Huang 11 / 25 Variance Analysis for Visibility

Shu-Jheng Huang 12 / 25 The Number of Samples The number of samples is proportional to Uniform lighting

Shu-Jheng Huang 13 / 25 Hierarchical Environment Map Stratification Hierarchical Thresholding Hierarchical Stratification

Shu-Jheng Huang 14 / 25 Hierarchical Thresholding σ:Standard deviation of the illumnation in the map

Shu-Jheng Huang 15 / 25 Hierarchical Thresholding

Shu-Jheng Huang 16 / 25 Hierarchical Thresholding N1N1 N2N2 N3N3 N4

Shu-Jheng Huang 17 / 25 Hierarchical Stratification Hochbaum-Shmoys Algorithm (K-center problem)

Shu-Jheng Huang 18 / 25 Hochbaum-Shmoys Algorithm

Shu-Jheng Huang 19 / 25 Hochbaum-Shmoys Algorithm

Shu-Jheng Huang 20 / 25 Hochbaum-Shmoys Algorithm

Shu-Jheng Huang 21 / 25 Hochbaum-Shmoys Algorithm

Shu-Jheng Huang 22 / 25 Rendering Optimizations Pre-integrating the illumination Jittering Sorting

Shu-Jheng Huang 23 / 25

Shu-Jheng Huang 24 / 25

Shu-Jheng Huang 25 / 25