A simple spectral clustering algorithm that can be implemented using a few lines of Matlab is presented, and tools from matrix perturbation theory are used to analyze the algorithm, and give conditions under which it can be expected to do well.Expand

The problem of finding a best code for a given dataset is closely related to the problem of graph partitioning and can be shown to be NP hard and a spectral method is obtained whose solutions are simply a subset of thresholded eigenvectors of the graph Laplacian.Expand

A generic framework which allows for whole image restoration using any patch based prior for which a MAP (or approximate MAP) estimate can be calculated is proposed and a generic, surprisingly simple Gaussian Mixture prior is presented, learned from a set of natural images.Expand

This work explains how to obtain region-based free energy approximations that improve the Bethe approximation, and corresponding generalized belief propagation (GBP) algorithms, and describes empirical results showing that GBP can significantly outperform BP.Expand

A closed-form solution to natural image matting that allows us to find the globally optimal alpha matte by solving a sparse linear system of equations and predicts the properties of the solution by analyzing the eigenvectors of a sparse matrix, closely related to matrices used in spectral image segmentation algorithms.Expand

This paper presents a simple colorization method that requires neither precise image segmentation, nor accurate region tracking, and demonstrates that high quality colorizations of stills and movie clips may be obtained from a relatively modest amount of user input.Expand

It is shown that BP can only converge to a fixed point that is also a stationary point of the Bethe approximation to the free energy, which enables connections to be made with variational approaches to approximate inference.Expand

This paper compares the marginals computed using loopy propagation to the exact ones in four Bayesian network architectures, including two real-world networks: ALARM and QMR, and finds that the loopy beliefs often converge and when they do, they give a good approximation to the correct marginals.Expand

IEEE Transactions on Pattern Analysis and Machine…

17 June 2006

TLDR

A closed-form solution to natural image matting that allows us to find the globally optimal alpha matte by solving a sparse linear system of equations and predicts the properties of the solution by analyzing the eigenvectors of a sparse matrix, closely related to matrices used in spectral image segmentation algorithms.Expand

It is shown that BP can only converge to a stationary point of an approximate free energy, known as the Bethe free energy in statistical physics, and generalized belief propagation (GBP) versions of these Kikuchi approximations are derived.Expand