Sparse inverse bilateral filters for image processing
The bilateral filter (BF) is a prominent tool for adaptive, structure-preserving image filtering. It can be interpreted as a graph-based filter, where the nodes of the graph correspond to image pixels and link weights correspond to filter coefficients. Graphs associated to BFs of typical sizes used in practice are very dense. In this paper, we propose an efficient method for constructing a sparse graph for adaptive filtering of an image. The Laplacian matrix of the proposed sparse graph approximates the inverse of a dense BF kernel matrix. This is analogous to the idea of finding a sparse inverse covariance of a Gaussian Markov random field (GMRF) with a dense covariance matrix. The eigenvectors of the proposed graph Laplacian are approximately equal to the eigenvectors of the BF graph and allow for low frequency representation of the image similar to the BF eigenvectors. Filters in the form of polynomials of this sparse Laplacian offer a more flexible and less computationally complex alternative to a dense BF, with similar performance.