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Problem
Input image with some area (the hole) which should be filled with data from the rest of the image.

Idea
Repeatedly shrink the hole by:
Selecting an area which overlaps both the hole and a part of the image around it.
Finding a region (fragment) in the image which is similar to .
Copying over the pixels from the fragment into the hole.

Finding
We search for an optimal pixel offset such that


The first term is constant w.r.t. .
The third term can be computed in with some precomputations.
What remains is the middle term which corresponds to a convolution. We can compute this by transforming both the input image as well as the region into the frequency domain and then doing the multiplication there. We then transform back to the pixel domain and find the maximum intensity pixel.

Compositing
After we have found the best source fragment, we compute an ideal seam for the fragment we copy over. This can be computed by a min-flow graph cut.

Color Correction
Additionally, we adjust the color of the copied-over pixels such that they match the hole boundary. We do this by prescribing that the color corrected pixels should have the same color gradients as the source pixels

while on the boundary, there should be no color difference

By applying the divergence on both sides, we turn this into a Poisson Equation



Perspective Correction
Sometimes, we want to reconstruct pixels from parts of the image which are viewed at an angle. Let the user define piecewise homographies by painting in the vertices of square patches. Flatten the image by applying the homographies and use this flattened image for the image completion.