Fourier Analysis of the 2D Screened Poisson Equation for Gradient Domain Problems
Abstract
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. Further analysis reveals the structure of the spatial filters that solve the 2D screened Poisson equation and shows gradient scaling to be a well-defined sharpen filter that generalizes Laplacian sharpening, which itself can be mapped to gradient domain filtering. Results using a DCT-based screened Poisson solver are demonstrated on several applications including image blending for panoramas, image sharpening, and de-blocking of compressed images.
Cite
Text
Bhat et al. "Fourier Analysis of the 2D Screened Poisson Equation for Gradient Domain Problems." European Conference on Computer Vision, 2008. doi:10.1007/978-3-540-88688-4_9Markdown
[Bhat et al. "Fourier Analysis of the 2D Screened Poisson Equation for Gradient Domain Problems." European Conference on Computer Vision, 2008.](https://mlanthology.org/eccv/2008/bhat2008eccv-fourier/) doi:10.1007/978-3-540-88688-4_9BibTeX
@inproceedings{bhat2008eccv-fourier,
title = {{Fourier Analysis of the 2D Screened Poisson Equation for Gradient Domain Problems}},
author = {Bhat, Pravin and Curless, Brian and Cohen, Michael F. and Zitnick, C. Lawrence},
booktitle = {European Conference on Computer Vision},
year = {2008},
pages = {114-128},
doi = {10.1007/978-3-540-88688-4_9},
url = {https://mlanthology.org/eccv/2008/bhat2008eccv-fourier/}
}