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Poisson Image Editing
Patric Perez, Michel Gangnet, and Andrew Black (SIGGRAPH 2003)
Seminar Talk by
Tim Weyrich
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Overview
• Guided Image Interpolation• Discretized Solution• Editing Operations• Discussion
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Interpolation Problem
• f *: known image values• f : unknown values over region Ω• Assuming scalar image values
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Simple Interpolation
• Maximize smoothness
• Boundary constraints
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Simple Interpolation
• Solution: Laplace Equation with Dirichletboundary conditions
• Membrane solution• Unsatisfactory due to over-blurring
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Guided Interpolation
• v: guided field• v may be gradient of a function g
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Guided Interpolation
• Minimize differenceof gradient fields
• Solution: Poisson Equationwith Dirichlet boundary conditions
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Discrete Poisson Solver• Discretize directly by
for neighbors p and q with
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Discrete Poisson Solver• Minimum satisfies linear system of equations
If neighborhood overlaps boundary:
For interior points:
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Discrete Poisson Solver
• Linear system of equations– sparse (banded)– symmetric– positive-definite
• Irregular shape of boundary requires general solver, such as– Gauss-Seidel iteration– Multi-grid
• System can be solved at interactive rates
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Seamless Cloning
• Importing Gradients froma Source Image g
• Discretize
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Seamless Cloning Results
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Mixing Gradients• Two Variants
– v averaged from source and destination gradients transparency
– Select stronger one from source and destination gradients:
Discretization:
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Mixing Gradients Results
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Mixing Gradients Results
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Mixing Gradients Results
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Texture Flattening
• Preserve only salient gradients
with masking function so that
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Texture Flattening
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Local Illumination Changes
• Approximate tone mapping transformation after Fattal et al. 2002:
• Attenuating large gradients
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Local Color Changes
• Mix two differently colored version of original image– One provides f * outside– One provides g inside
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Local Color Changes
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Seamless Tiling• Select original image as g• Boundary condition:
– f *north = f *south = 0.5 (gnorth + gsouth)– Similarly for the east and west
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Discussion
Pros• Very general framework• No parameter tuning required• Method does not require precise selection• Versatile method
– Seamless cloning, mixing gradients– Texture flatening– Local changes of illumination and color– Seamless tiling
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Discussion
Cons• Cloning requires either of the images to be
smooth• No refined selection is returned• Minimization only adapts low-frequency
content– Potential color shift / re-coloring difficult to control– Dissatisfactory tiling– Cloning requires careful placement of prominent
features
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Outlook
• More image editing operators– Combinations (insert while flattening)– Other non-linear operations on gradients– More than one source images
• Poisson editing of triangle meshes– Feature transfer– Detail preserving deformations
• Other editing domains possible?
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Thanks
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Seamless Tiling
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Mixing Gradients Results
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