Some notes on repeated averaging smoothing
Gaussian smoothing can be accomplished with the Repeated Averaging Smoothing (RAS) method, a technique based on statistical theory. It can also be done with Diffusion Smoothing (DS) method, a technique based on the diffusion equation. The difference between the origins of RAS and DS is great. In this paper, we make explicit the relationship between RAS and DS. These notes show that RAS mask is a special case of diffusion explicit smoothing (DES) scheme, RAS's scale proportion coefficient depends on the diffusion coefficient, etc.. Thus, diffusion implicit smoothing scheme with a changeable time step (DISCT), which is better than DES, will also be better than RAS in terms of both the computational stability and complexity, especially in the scaled space.
Keywordsrepeated averaging Gaussian explict implicit diffusion smoothing cross mask numerical stability and complexity
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