Fast marching inpainting
Following the idea that known image information has to be propagated from the contour of the area to inpaint towards its innermost parts, Alexander Telea's inpainting algorithm uses Sethian's fast marching method (FFM) to construct and maintain a list of the pixels forming the contour. The area delimited by this band is progressively shrunk while pixels are processed until none remain to be inpainted.
FFM only helps with the order in which pixels are processed, but does not determine how each pixel is going to be actually inpainted. Telea performs a weighted average of all pixels in the neighborhood of the inpainted pixel. The neighborhood is determined by a radius, which value should be close to the thickness of the area to inpainted. The weight function depends on the following factors:
- the distance between a pixel and it neighbors, ie closers neighbors contribute more;
- the level set distance to the original contour, ie neighbors on the same level set (or iso line) contribute more;
- the collinearity of the vector from a pixel to its neighbors and the FFM direction of propagation. This factor will have the effect of extending isophotes (ie lines) reaching the area to inpaint, by giving more weight to neighbors when they are in the axis going from the inpainting pixel in the direction of propagation of the FFM.
Our implementation borrows from several sources, including the OpenCV C++ implementation and Telea's implementation itself. As advised in the original paper, we first run a FFM in order to compute distances between pixels outside of the mask and the initial mask contour, before running the main FFM that performs the actual inpainting.
Despite closely following the same algorithm, our Python version is considerably slower than the mentioned implementations. Indeed FFM inpainting is not a vectorized algorithm but rather an iterative one, and therefore doesn't fully benefit from using NumPy. In order to keep the processing time under a reasonable amount, we have chosen to only compute the weighted average previously described, dropping the average gradient that is also mentioned in the article and applied in most implementations. This allows for a x6 speed gain while maintaining "good-enough" results, albeit not as smooth.
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Samples images from https://homepages.cae.wisc.edu/~ece533/images/
The Telea algorithm gives satisfying results for narrow masks. One of its niceties is that it can be directly applied to masks containing non-contiguous regions, without any additional code. When used with larger masks or on textured or patterned images, its half-blurring half-stretching effect will however become apparent.