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.
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Bhat, P., Curless, B., Cohen, M., Zitnick, C.L. (2008). Fourier Analysis of the 2D Screened Poisson Equation for Gradient Domain Problems. In: Forsyth, D., Torr, P., Zisserman, A. (eds) Computer Vision – ECCV 2008. ECCV 2008. Lecture Notes in Computer Science, vol 5303. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88688-4_9
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DOI: https://doi.org/10.1007/978-3-540-88688-4_9
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