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Bi-Exponential Edge-Preserving Smoother

P. Thévenaz, D. Sage, M. Unser

IEEE Transactions on Image Processing, vol. 21, no. 9, pp. 3924-3936, September 2012.

Edge-preserving smoothers need not be taxed by a severe computational cost. We present in this paper a lean algorithm that is inspired by the bi-exponential filter and preserves its structure—a pair of one-tap recursions. By a careful but simple local adaptation of the filter weights to the data, we are able to design an edge-preserving smoother that has a very low memory and computational footprint while requiring a trivial coding effort. We demonstrate that our filter (a bi-exponential edge-preserving smoother, or BEEPS) has formal links with the traditional bilateral filter. On a practical side, we observe that the BEEPS also produces images that are similar to those that would result from the bilateral filter, but at a much-reduced computational cost. The cost per pixel is constant and depends neither on the data nor on the filter parameters, not even on the degree of smoothing.

The associated software is available here.

AUTHOR="Th{\'{e}}venaz, P. and Sage, D. and Unser, M.",
TITLE="Bi-Exponential Edge-Preserving Smoother",
JOURNAL="{IEEE} Transactions on Image Processing",

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