Two-dimensional Navier-Stokes-Voight equation for image inpainting
Mathematics Department, UCSD
Recently, the three-dimensional (3d) Navier-Stokes-Voight (NSV) model ofviscoelastic fluid, was suggested by Cao, et. al. as an inviscid regularization to the 3d Navier-Stokes equations (NSE). The NSV model is shown to be globally well-posed and has a finite-dimensional global attractor making it an attractive sub-grid scale turbulence model for purposes of numericalsimulation.In 2001, Bertalmio, et. al. have built an analogy between the image intensity function for the image inpainting problem and the stream function in two-dimensional (2d) incompressible fluid. The solution to the inpainting problem is obtained by solving the steady state solution of the 2d NSE vorticity transport equation, and simultaneously solving the Poisson problem between the vorticity and stream function, in the region to be inpainted. This elegant analogy enables the solution to the image inpainting problem to be solved using techniques from fluid dynamics.In this talk I will present some of the advantages of using the 2d NSV model as an alternative to 2d NSE when solving the inpainting problem. Our numerical results show that the NSV model, in comparison to NSE, both with the same anisotropic diffusion, yield a more stable solution to the inpainting process. That is, the NSV can be computed at a much larger time-step, reducing the computational expense in the automated inpainting procedure.
Monday, April 7, 2008
11:00AM AP&M 2402
Center for Computational Mathematics9500 Gilman Dr. #0112La Jolla, CA 92093-0112Tel: (858)534-9813