Background a famous psychologists show that the second order variations extracted by the Laplacian operator are the most significant perceptually (Land and McCann 1971) a scalar function on a bounded domain is uniquely defined by its values on the boundary and its Laplacian in the interior The Poisson equation has a unique solution vcc可视计算研究中心
• A famous psychologists show that the secondorder variations extracted by the Laplacian operator are the most significant perceptually (Land and McCann 1971) • A scalar function on a bounded domain is uniquely defined by its values on the boundary and its Laplacian in the interior. • The Poisson equation has a unique solution. Background 6
Related work- poisson equation Fattalet al. 2002 Entire images Lewis 2001 harmonic interpolation Our method Local images Our method Guided Interpolation cc可视计算研究中心 Visual Computing Research Center
Related work– poisson equation 7 Fattal et al. 2002 Entire images Our method Local images Lewis 2001 harmonic interpolation Our method Guided Interpolation
Related work--multiresolution images blending Burt and Adelson 1983 long range (larger gradient) mixing Poisson seamless cloning small gradient source/destination color transfer monochrome transfer cc可视计算研究中心 Visual Computing Research Center
• Burt and Adelson1983 long range(larger gradient) mixing • Poisson seamless cloning small gradient Related work—multiresolution images blending 8
Related work- seamless cloning VAL inpainting techniques-PDE. more complex EXample-based interpolation methods than poisson equation( Bertalmio et al handle large holes and textured boundaries 2000) Barret and Cheney 2002) a guided interpolation framework, with the guidance being selected by the user and this framework is not limited in seamless Cloning cc可视计算研究中心 Visual Computing Research Center
inpainting techniques-PDE . more complex than poisson equation ( Bertalmio et al. 2000 ) Related work– seamless cloning 9 a guided interpolation framework , with the guidance being selected by the user ,and this framework is not limited in seamless cloning Example-based interpolation methods ; handle large holes and textured boundaries ( Barret and Cheney 2002)
Interpolation Problem S S: a closed subset of r2 Q2: a closed subset of S, with boundary aQ fr known scalar function over sio ·f: unknown scalar function overΩ cc可视计算研究中心
• S: a closed subset of R2 • Ω: a closed subset of S, with boundary ∂Ω • f*: known scalar function over S\Ω • f: unknown scalar function over Ω Interpolation Problem 10