Bilateral Filter: Graph Spectral Interpretation and Extensions
This work provides a theoretical foundation for image processing practitioners to design adaptive filters, but it is incremental as it builds on existing bilateral filter concepts.
The authors tackled the problem of interpreting and extending the bilateral filter by modeling it as a spectral domain transform on a weighted graph, where edge weights adapt to image data, and they generalized it to propose more flexible, application-specific spectral filters that can be implemented efficiently without expensive matrix diagonalization.
In this paper we study the bilateral filter proposed by Tomasi and Manduchi, as a spectral domain transform defined on a weighted graph. The nodes of this graph represent the pixels in the image and a graph signal defined on the nodes represents the intensity values. Edge weights in the graph correspond to the bilateral filter coefficients and hence are data adaptive. Spectrum of a graph is defined in terms of the eigenvalues and eigenvectors of the graph Laplacian matrix. We use this spectral interpretation to generalize the bilateral filter and propose more flexible and application specific spectral designs of bilateral-like filters. We show that these spectral filters can be implemented with k-iterative bilateral filtering operations and do not require expensive diagonalization of the Laplacian matrix.