The Poisson Equation in Image & Shape Processing

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.

General Breakdown
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.

Student Responsibilities
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 (October 17th) and will present the results of their projects to the class in the last two lectures (December 5th and 10th).

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
10/17/07 Project Proposals Due
Surface Reconstruction Kazhdan Kazhdan et al., SGP 2006 Notes
10/22/07 Cotangent Weight Laplacian Kazhdan Tutte, LMS 1963
Wardetzky et al., Eurographics 2007
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

More Papers: