This paper addresses the problem of robust filtering in color images. We propose to improve the bilateral filter by using Ordered Weighted Averaging (OWA) filters. Bilateral filter decreases amount of noise preserving edges when filtering. But the results could be strongly affected by the presence of outliers. In this paper, we define the filtering in the framework of fuzzy logic. If filtering is considered as a weighted averaging, then each filter is associated with a fuzzy set. The membership values of the fuzzy set are the weights of average. In this context, the bilateral filter is a conjunction of two fuzzy sets (i.e. aggregation with AND operator): one in the spatial domain and the other 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 application to color images states the filtering ability for removing noise in presence of outliers.
Philippe Vautrot, Laurent Hussenet, Michel Herbin, "A Robust Filtering Method using OWA filters: Application to Color Images" in Proc. IS&T CGIV 2006 3rd European Conf. on Colour in Graphics, Imaging, and Vision, 2006, pp 24 - 29, https://doi.org/10.2352/CGIV.2006.3.1.art00005