http://www.vision.huji.ac.il/SpectralMatting/

A very influential paper that does matting almost automatically. I was very excited on seeing this paper as I am tired of excusing bad algorithms with unneccessary user-interactions…

The contribution of the paper is only in combining matting Laplacian with spectral clustering theory. The former came in the author’s eariler paper, while the latter is almost a small area in machine learning(?). But the assumptions behind these two components are both interesting. For the matting Laplacian, the author was actually shows that local linear models could be very powerful models to describe edges and boundaries, even if they’re of some very complicated shape. For spectral clustering, it’s interesting to see how eigenvectors specify the affinity of samples. My favorite way of seeing this is from the stochastic process aspect: Imagine a particle wandering over the image, and it has preference to traveling between similar pixels. The alpha value is then just, given its starting point(s), the probability it will end up with staying at a specific pixel, and it’s a linear combination to the eigen-vectors.

One may dislike this paper because the actual algorithm is slow, but I bet it can be accelerated with some multiscale techniques. And I like this paper because it provides an in-depth discussion about spectral matting. Although it might not be detailed enough in comparison to relevant papers from theoretical machine learning side, it is a better introduction for vision students than the spectral segmentation paper I think.