Graph spectral image smoothing using the heat kernel

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The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains (2012, methodology): “This method is a variant of the graph-based anisotropic diffusion image smoothing method of [11].”
Accelerated filtering on graphs using Lanczos method (2015, background): “For instance, many applications in image processing beneﬁt from the use of graphs that describe connections between local patches in the image (e.g. [ 13, 22] and references therein).”
GSPBOX: A toolbox for signal processing on graphs (2014, background): “Parameters allow the resulting graph to vary between local and non-local and to use different distance functions [12, 4].”
Image denoising with nonlocal spectral graph wavelets (2010, methodology): “Zhang and Hancock studied image smoothing using the heat kernel corresponding to the graph Laplacian, using a graph whose edge weights depended on the difference of local neighboring windows [10].”