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## Advanced Image Synthesis

Instructor: | Prof. Dr. Marc Alexa |
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Contact: | Dr. Bernd Bickel, Christian Lessig |

Course structure: | Seminar |

Room: | E-N 719 |

Date: | Thursday 4pm - 6pm Start : 14 Apr 2011 |

Description: | Computer generated images are used in many applications such as movie production, computer-‐aided design, and scientific visualization. In this course we will study how the physical equations governing light transport can be approximated to obtain computational techniques which are efficient and provide visually convincing, realistic imagery. The course will concentrate on ray tracing techniques and finite element methods but also touch upon algorithms used in real-‐time applications such as pre-‐computed radiance transfer. |

Literature: | The course will loosely follow Physically Based Rendering: From Theory to Implmentation bt Matt Pharr and Greg Humphreys (Morgan Kaufmann Publishers Inc., 2010) Other relevant literature will be posted on the course homepage. |

Requirements: | C/C++ programming, scripting language such as Matlab or python, linear algebra as required for computer graphics (vectors, rotation matrices ...) |

# Syllabus

Date | Topic | Exercises | Readings |
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14.04.2011 | Introduction: Motivation, Examples, Challenges. | First class, no exercises or readings. | |

21.04.2011 | Color, Radiometry, and Images. | pbrt gymnastics: download, install, and compile pbrt and render some of the example scenes; also experiment with the scene descriptions. | Jensen, H. W., and T. Akenine-Möller. The Race for Real-Time Photorealism. American Scientist 98, no. 2 (2010): 132--139. Greenberg, D. P. et al. A Framework for Realistic Image Synthesis. In Proceedings of SIGGRAPH '97, 477-494. New York, New York, USA: ACM Press, 1997. |

28.04.2011 | Signals and their Representation. | 1. Color representation and radiometry. 2. Look at pbrt's spectrum.h / spectrum.cpp and understand the color representation used. Think about possible advantages and disadvantages, with our discussion in class in mind. | Hanrahan, P. Rendering Concepts. In Radiosity and Realistic Image Synthesis, edited by M. F. Cohen and J. Wallace. San Diego, CA, USA: Academic Press Professional, Inc., 1993. Mallat, S. G. Wavelets for Compressing Images. In L'explosion des mathematiques. Societe Mathematique de France, 2007. |

05.05.2011 | Using signal representations for rendering. | Exercises on signal representation and approximation using the starter code. Code containing the solution to your exercise and the Monte Carlo integration example presented in class. | Cook, R. L. Stochastic Sampling in Computer Graphics. ACM Trans. Graph. 5 (1986): 51-72. Green, R. Spherical Harmonic Lighting: The Gritty Details, p. 1-21. |

12.05.2011 | The rendering equation and the operator formulation. | Image sampling and reconstruction in pbrt has three parameters: the sampling pattern used (Sampler), the number of samples per pixel (pixelsamples), and the reconstruction filter (PixelFilter). Use spheres-differentials-texfilt.pbrt, which is available in pbrt's extended scene set, to explore the effect of the different parameters, try to understand the advantages and disadvantages, and connect your observations to our discussions in class. Please make sure the images you generate are available in class. | No reading but the project proposals are due this week. |

19.05.2011 | The Neumann series: solving the rendering equation. | Compute the generalized Gauss-Legendre quadrature weights for the space H_5 spanned by all Legendre polynomials up to L=5 for node locations: [-0.9311,-0.3658,-0.2369, -0.1225,0.3897,0.9004] and [-0.6748,-0.6263,-0.4479, -0.1088,-0.0205,0.2926, 0.3102,0.3594,0.4187, 0.5094,0.5310,0.5904], and verify your result. You might find the discussion in the Numerical Recipes book useful. Matlab script computing generalized Gauss-Legendre quadrature for arbitrary nodes. Code used in class to demonstrate the power series and the effectiveness of finite approximations for the Neumann series. | Kajiya, J. T. The Rendering Equation. ACM SIGGRAPH Computer Graphics 20, no. 4 (1986). He, X. D., K. E. Torrance, F. X. Sillion, and D. P. Greenberg. A Comprehensive Physical Model for Light Reflection. ACM SIGGRAPH Computer Graphics 25, no. 4 (1991). |

26.05.2011 | Finite element methods for light transport simulation: Galerkin projection of the rendering equation. | In class we talked about the matrix representation of operators. Derive an explicit representation for the projection operator of an arbitrary function onto the space spanned by all spherical harmonics up to band L for finite L. Slepian functions are an alternative to spherical harmonics that provide many advantages for computer graphics applications. Derive also an explicit representation for the projection operator of an arbitrary input function onto the first k Slepian functions for some finite L. | Kajiya, J. T. The Rendering Equation. ACM SIGGRAPH Computer Graphics 20, no. 4 (1986). Arvo, J. The Role of Functional Analysis in Global Illumination. In Rendering Techniques '95, edited by P. M. Hanrahan and W. Purgathofer, 115-126. New York: Springer-Verlag, 1995. |

02.06.2011 | No class this week (legal holiday). | ||

09.06.2011 | Monte Carlo integration. | Derive Galerkin projection for the shading equation, using either an abstract basis or spherical harmonics, and simplify the resulting expression as much as possible. What additional simplifications arise in the case of purely diffuse shading? Also consider how the obtained formulas could be implented and what aspects would most likely be challenging to attain high performance. | Arvo, J., K. Torrance, and B. Smits. A Framework for the Analysis of Error in Global Illumination Algorithms. In SIGGRAPH '94: Proceedings of the 21st annual conference on computer graphics and interactive techniques, 75-84. New York, NY, USA: ACM, 1994. |

16.06.2011 | The path integral formulation + interim presentations. | No exercise. In class project interim presentations (15 min. presentation + 5 min. discussion). | Hanrahan, P., E. Veach, and D. Zorin. Mathematical Models for Computer Graphics Lecture Notes, 1997, Chapter 6. The complete lecture notes are worth a look for those interested in the subject. |

23.06.2011 | Path tracing and bi-directional path tracing. | There will be a more comprehensive exercise due to next week. | Lafortune, E. P., and Y. D. Willems. A Theoretical Framework for Physically Based Rendering. Comput. Graph. Forum 13 (1994): 97-107. |

30.06.2011 | Interpolation methods: irradiance caching and photon mapping. | Monte Carlo estimators and Monte Carlo integration on the sphere (combined with last week's exercise). | Veach, E., and L. Guibas. Bidirectional Estimators for Light Transport. In Fifth Eurographics Workshop on Rendering, 147-162, 1994. |

07.07.2011 | Volume transport: media with varying refractive index and scattering media. | Same exercise as last week. Here is some Matlab helper code.7, no. 5 (2008). | Hachisuka, T., S. Ogaki, and H. W. Jensen. Progressive Photon Mapping. ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia 2008) 27, no. 5 (2008). |

14.07.2011 | Final presentations. | Final presentations (20 min. talk + 5 min. discussion). The project reports should in their structure follow a conference publications in computer graphics (e.g. the SIGGRAPH style), possibly with a longer implementation section. The reports are due 5th August 2011. | No reading this week. |

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