OWA filters: A robust filtering method and its application to color images

Abstract

Bilateral filtering provides a scheme for non-iterative edge-preserving smoothing, but the results could be strongly affected by the presence of outliers. In this paper we develop a robust bilateral filter for color images, and in order to achieve this we propose to improve the bilateral filtering technique [13] by using Ordered Weighted Averaging operators. We adopt a fuzzy logic based approach: if the filtering is considered as a weighted averaging, then each filter is associated with a fuzzy set and the membership values of these fuzzy sets represent the weights. In this context, the bilateral filter is a conjunction of two fuzzy sets in the case of grayscale images: one in the spatial domain and one in a photometric domain. Applied to color images, we propose to extend the conjunction to three fuzzy sets: one in the spatial domain, one in the brightness domain and one in the chromatic domain. Taking into account the robustness of rank filters, we propose to define an OWA filter in order to obtain robust adaptive filters in brightness and chromaticity. The robustness and performance of the filter is illustrated with several experiments, revealing its ability to remove different types of noise in the presence of outliers, while preserving edges. The noise types considered are impulse noise and a combination of Gaussian noise with “salt and pepper” noise types.