A GPU Laplacian Solver for Diffusion Curves and Poisson Image Editing

Information

• Publication Type: Journal Paper with Conference Talk
• Workgroup(s)/Project(s):
  • Detailed Surfaces for Interactive Rendering
• Date: December 2009
• Journal: Transaction on Graphics (Siggraph Asia 2009)
• Volume: 28
• Number: 5
• Location: Yokohama, Japan
• Lecturer: Stefan Jeschke
• ISSN: 0730-0301
• Event: Siggraph Asia
• Booktitle: Transactions on Graphics (Siggraph Asia 2009)
• Organization: ACM
• Publisher: ACM Press
• Conference date: 16. December 2009 – 19. December 2009
• Pages: 1 – 8
• Keywords: Poisson equation, Line and Curve rendering , Diffusion

Abstract

We present a new Laplacian solver for minimal surfaces—surfaces having a mean curvature of zero everywhere except at some fixed (Dirichlet) boundary conditions. Our solution has two main contributions: First, we provide a robust rasterization technique to transform continuous boundary values (diffusion curves) to a discrete domain. Second, we define a variable stencil size diffusion solver that solves the minimal surface problem. We prove that the solver converges to the right solution, and demonstrate that it is at least as fast as commonly proposed multigrid solvers, but much simpler to implement. It also works for arbitrary image resolutions, as well as 8 bit data. We show examples of robust diffusion curve rendering where our curve rasterization and diffusion solver eliminate the strobing artifacts present in previous methods. We also show results for real-time seamless cloning and stitching of large image panoramas.

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BibTeX

@article{jeschke-09-solver,
  title =      "A GPU Laplacian Solver for Diffusion Curves and Poisson
               Image Editing",
  author =     "Stefan Jeschke and David Cline and Peter Wonka",
  year =       "2009",
  abstract =   "We present a new Laplacian solver for minimal
               surfaces—surfaces having a mean curvature of zero
               everywhere except at some fixed (Dirichlet) boundary
               conditions. Our solution has two main contributions: First,
               we provide a robust rasterization technique to transform
               continuous boundary values (diffusion curves) to a discrete
               domain. Second, we define a variable stencil size diffusion
               solver that solves the minimal surface problem. We prove
               that the solver converges to the right solution, and
               demonstrate that it is at least as fast as commonly proposed
               multigrid solvers, but much simpler to implement. It also
               works for arbitrary image resolutions, as well as 8 bit
               data. We show examples of robust diffusion curve rendering
               where our curve rasterization and diffusion solver eliminate
               the strobing artifacts present in previous methods. We also
               show results for real-time seamless cloning and stitching of
               large image panoramas.",
  month =      dec,
  journal =    "Transaction on Graphics (Siggraph Asia 2009)",
  volume =     "28",
  number =     "5",
  issn =       "0730-0301",
  booktitle =  "Transactions on Graphics (Siggraph Asia 2009)",
  organization = "ACM",
  publisher =  "ACM Press",
  pages =      "1--8",
  keywords =   "Poisson equation, Line and Curve rendering , Diffusion",
  URL =        "https://www.cg.tuwien.ac.at/research/publications/2009/jeschke-09-solver/",
}