Fourier Analysis of the 2D Screened Poisson Equation for Gradient Domain Problems
نویسندگان
چکیده
Applications We analyze the problem of reconstructing a 2D function that approximates a set of desired gradients and a data term. The combined data and gradient terms enable operations like modifying the gradients of an image while staying close to the original image. Starting with a variational formulation, we arrive at the “screened Poisson equation” known in physics. Analysis of this equation in the Fourier domain leads to a direct, exact, and efficient solution to the problem. Results using a DCT-based screened Poisson solver are demonstrated on several applications including painterly rendering, image re-lighting, image sharpening, and de-blocking of compressed images. 1 1 1,2 2 University of Washington Microsoft Research 1 2
منابع مشابه
Fast Direct Solver for Poisson Equation in a 2D Elliptical Domain
In this article, we extend our previous work (M.-C. Lai and W.-C. Wang, Numer Methods Partial Differential Eq 18:56–68, 2002) for developing some fast Poisson solvers on 2D polar and spherical geometries to an elliptical domain. Instead of solving the equation in an irregular Cartesian geometry, we formulate the equation in elliptical coordinates. The solver relies on representing the solution ...
متن کاملA truly meshless method formulation for analysis of non-Fourier heat conduction in solids
The non-Fourier effect in heat conduction is important in strong thermal environments and thermal shock problems. Generally, commercial FE codes are not available for analysis of non-Fourier heat conduction. In this study, a meshless formulation is presented for the analysis of the non-Fourier heat conduction in the materials. The formulation is based on the symmetric local weak form of the sec...
متن کاملNon-Fourier heat conduction equation in a sphere; comparison of variational method and inverse Laplace transformation with exact solution
Small scale thermal devices, such as micro heater, have led researchers to consider more accurate models of heat in thermal systems. Moreover, biological applications of heat transfer such as simulation of temperature field in laser surgery is another pathway which urges us to re-examine thermal systems with modern ones. Non-Fourier heat transfer overcomes some shortcomings of Fourier heat tran...
متن کاملParallel Implementation of a Data-Transpose Technique for the Solution of Poisson's Equation in Cylindrical Coordinates
We present a parallel nite-diierence algorithm for the solution of the 3D cylindrical Poisson equation. The algorithm is based on a data-transpose technique, in which all computations are performed independently on each node, and all communications are restricted to global 3D data-transposition between nodes. The data-transpose technique aids us in implementing two sequential algorithms for the...
متن کامل2D Analytical Modeling of Magnetic Vector Potential in Surface Mounted and Surface Inset Permanent Magnet Machines
A 2D analytical method for magnetic vector potential calculation in inner rotor surface mounted and surface inset permanent magnet machines considering slotting effects, magnetization orientation and winding layout has been proposed in this paper. The analytical method is based on the resolution of Laplace and Poisson equations as well as Maxwell equation in quasi- Cartesian coordinate by using...
متن کامل