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In this paper we study the bilateral filter proposed by Tomasi and Manduchi and show that it can be viewed 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...
In this paper we present methods for downsampling datasets defined on graphs (i.e., graph-signals) by extending downsampling results for traditional N-dimensional signals. In particular, we study the spectral properties of k-regular bipartite graphs (K-RBG) and prove that downsampling in these graphs is governed by a Nyquist-like criteria. The results are useful for designing critically sampled filter-banks...
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