Integrate a gradient
field subject to the constraint of matching a
reference image
field as closely as possible.
Integrate a gradient
field subject to the constraint of matching a
reference image
field as closely as possible. Since this is
impossible in general, there is a tradeoff term, lambda
, which allows
one to balance fidelity to the reference image
(larger lambda
) and
the gradient
(smaller lambda).
The "periodized" FFT of the reference image field which we want to match as best we can. See the paper "Periodic plus Smooth Image Decomposition," Journal of Mathematical Imaging and Vision, vol 39:2, pp. 161-179, 2011, for a description of the periodic FFT.
The desired gradient field to be integrated.
Tradeoff between fidelity to image
(larger value) and
integrated gradient
(smaller value).
Fourier transform of image which best satisfies the given constraints.
Solves the screened Poisson equation in the Fourier domain. See the paper "Fourier analysis of the 2D screened Poisson equation for gradient domain problems," by Bhat, Curless, Cohen and Zitnick, 2008.