Histogram-based fuzzy colour ﬁlter for image restoration
Abstract-A new impulse noise reduction method for colour images, called histogram-based fuzzy colour ﬁlter (HFC), is presented in this paper. The HFC ﬁlter is particularly eﬀective for reducing high-impulse noise in digital images while preserving edge sharpness. Colour images that are corrupted with noise are generally ﬁltered by applying a greyscale algorithm on each colour component separately. This approach causes artefacts especially on edge or texture pixels. Vector-based ﬁltering methods were successfully introduced to overcome this problem. In this paper, we discuss an alternative technique so that no artefacts are introduced. The main diﬀerence between the new proposed method and the classical vector-based methods is the usage of colour component diﬀerences for the detection of impulse noise and the preservation of the colour component diﬀerences. The construction of the HFC ﬁlter involves three steps: (1) the estimation of the original histogram of the colour component diﬀerences, (2) the construction of suitable fuzzy sets for representing the linguistic values of these diﬀerences and (3) the construction of fuzzy rules that determine the output. Extensive simulation results show that the proposed ﬁlter outperforms many well-known ﬁlters (including vector-based approaches).
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