(600.657)

This seminar will survey a variety of applications of the Poisson in the domain of computer graphics. The course will begin by reviewing the Poisson equation and several numerical methods for solving the associated linear system. Next, we will consider applications of the Poisson equation to challenges in image editing, including HDR compression, inpainting, and texture synthesis. Finally, we will consider generalizations of the system to 3D shapes, including applications such as mesh deformation and surface reconstruction.

This course will be broken up into two general areas. We will begin by considering applications of the Laplacian to problems in image processing and then we will consider applications to mesh editing.

- Images
- Shapes
- Mesh Optimization
- Editing and Deformation
- Differential Coordinates for Local Mesh Morphing and Deformation
- Differential Coordinates for Interactive Mesh Editing
- Laplacian Surface Editing
- Mesh Editing with Poisson-Based Gradient Field Manipulation
- Large Mesh Deformation Using the Volumetric Graph Laplacian
- Mesh Editing Based on Discrete Laplace and Poisson Models
- Harmonic Coordinates for Character Animation
- Mesh Editing in ROI with Dual Laplacian

- Reconstruction
- Representation and Matching

Students will be regularly assigned papers to read, and two students each week will present papers to the seminar. Additionally, there will be a final project that students will be expected to submit by the end of the semester (to be done in groups of two). Students will submit a written proposal for the project by the middle of the semester

Date | Subject | Presenter | Required Reading | Notes |
---|---|---|---|---|

9/10/07 | Introduction | Kazhdan | Notes | |

9/12/07 | The Poisson Equation | Kazhdan | Notes | |

9/17/07 | Solving (Large/Sparse/Symmetric/Etc.) Linear Systems | Kazhdan | Notes | |

9/19/07 | Image HDR Compression | Matt Moses | Fattal et al., SIGGRAPH 2002 | Notes Presentation |

9/24/07 | Image Matting | Robert Jacques | Sun et al., SIGGRAPH 2004 | Notes Presentation |

9/26/07 | Image Editing | Charles Robertson | Perez et al., SIGGRAPH 2003 | Presentation |

10/01/07 | Pin Wu | Levin et al., ECCV 2004 | Presentation | |

10/03/07 | Gagan Bansal | Agarwala et al., SIGGRAPH 2004 | Presentation | |

10/08/07 | Bhaskar Kishore | Jia et al., SIGGRAPH 2006 | Presentation | |

10/10/07 | Ioannis Atsonios | Agarwala, SIGGRAPH 2007 | Presentation | |

10/15/07 | Fall Break |
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10/17/07 | Project Proposals Due |
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Surface Reconstruction | Kazhdan | Kazhdan et al., SGP 2006 | Notes | |

10/22/07 | Cotangent Weight Laplacian | Kazhdan | Tutte, LMS 1963 Wardetzky et al., Eurographics 2007 |
Notes |

10/24/07 | Reconstruction | Dan Abretske | Agrawala et al., ICCV 2005 | Presentation |

10/29/07 | Poisson Matching | Raphael Sznitman | Gorelick et al., PAMI 2006 | Presentation |

10/31/07 | Harmonic Coordinates | Dustin Franklin | Joshi et al., SIGGRAPH 2007 | Presentation |

11/05/07 | Mesh Editing/Deformation | Ming Chuang | Nealen et al., Graphite 2006 | Presentation |

11/07/07 | Gagan Bansal | Yu et al., SIGGRAPH 2004 | Presentation | |

11/12/07 | Barry Shih | Alexa, SIGGRAPH 2006 (Courses) | Presentation | |

11/14/07 | Shape Embedding | Dan Abretske | Rustamov, Eurographics 2007 | Presentation |

11/19/07 | Mesh Editing/Deformation | Ioannis Atsonios | Alexa, The Visual Computer 2003 | Presentation |

11/21/07 | Bhaskar Kishore | Zhou et al., SIGGRAPH 2005 | Presentation | |

11/26/07 | Dustin Franklin | Sorkine et al., SGP 2004 | ||

11/28/07 | Surface Fairing | Charles Robertson | Taubin, 1995 | Presentation |

12/03/07 | Isometry Invariant Mesh Representation | Robert Jaques | Reuter et al., 2005 |
Presentation |

12/05/07 | Bhaskar and Barry | |||

Dan and Robert | ||||

12/10/07 | Charles and Matthew | |||

Ioannis and Gagan | ||||

Ming and Pin |

- Introduction to Scale-Space Theory: Multiscale Geometric Image Analysis
- An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
- Geometric Signal Processing on Polygonal Meshes
- Discrete Combinatorial Laplacian Operators for Digital Geometry Processing
- Digital Bas-Relief from 3D Scenes