Abstract
The bilateral filter and the non-local means (NL-means) filter are known as very powerful nonlinear filters. The first contribution of this paper is to give a general framework which involves the bilateral filter and the NL-means filter. The general framework is derived based on Bayesian inference. Our analysis reveals that the range weight in the bilateral filter and the similarity measure in the NL-means filter are associated with a noise model or a likelihood distribution. The second contribution is to extend the bilateral filter and the NL-means filter for a general noise model. We also provide a filter classification. The filter classification framework clarifies the differences among existing filters and helps us to develop new filters. As example of future directions, we extend the bilateral filter and the NL-means filter for a general noise model. Both extended filters are theoretically and experimentally justified.
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