04-05-2011, 04:15 PM
Abstract
A new impulse noise reduction method for colorimages is presented. Color images that are corrupted with impulsenoise are generally filtered by applying a grayscale algorithmon each color component separately or using a vector-based approachwhere each pixel is considered as a single vector. The firstapproach causes artefacts especially on edge and texture pixels.Vector-based methods were successfully introduced to overcomethis problem. Nevertheless, they tend to cluster the noise and toreceive a lower noise reduction performance. In this paper, wediscuss an alternative technique which gives a good noise reductionperformance while much less artefacts are introduced. Themain difference between the proposed method and other classicalnoise reduction methods is that the color information is taken intoaccount to develop 1) a better impulse noise detection method and2) a noise reduction method that filters only the corrupted pixelswhile preserving the color and the edge sharpness. Experimentalresults show that the proposed method provides a significantimprovement on other existing filters.Index Terms—Adaptive filtering, color image denoising, fuzzyfiltering, fuzzy rule-based systems.
I. INTRODUCTION
OVER the last several years, a huge amount of fuzzy-basednoise reduction methods were developed, e.g., the histogramadaptive fuzzy filter (HAF) [1], the fuzzy impulse noisedetection and reduction method (FIDRM) [2], the adaptivefuzzy switching filter (AFSF) [3], the fuzzy similarity-basedfilter (FSB) [4], the fuzzy random impulse noise reductionmethod (FRINRM) [5], and so on. These fuzzy filters aremainly developed for images corrupted with fat-tailed noiselike impulse noise. They outperform rank-order filter schemes(such as the median filter). Although these filters are especiallydeveloped for grayscale images, they can be used to filter colorimages by applying them on each color component separately.This approach generally introduces many color artefacts mainlyon edge and texture elements. To overcome these problems,several nonlinear vector-based approaches were successfully introduced. One of the most important families of nonlinearfilters, which take advantage of the theory of robust statistics[6] is based on the ordering of vectors in a predefined slidingwindow [7], [8]. This ordering is realized by a distance orsimilarity measure where the lowest ranked vector correspondsto that vector which is closest to all the other vectors in apredefined window in terms of the used measure.A huge amount of vector-based impulse noise reductionmethods exist. Most of them are based on the vector medianfilter (VMF) [9], e.g., [8], [10]–[23].The most popular class of nonlinear vector operators is basedon the order statistics, where the output is equal to the vectorassociated with the smallest accumulated distance to all othervectors in the sliding window [8]–[23] or which is most similarto all neighboring pixels [24], [25]. We can distinguish betweenvector filters using the magnitude information (i.e., anEuclidean distance criteria) [8]–[11], using the directional information(i.e., the angular distance criteria) [18] or a combinationof both distance criteria [17], [19].Many of those filters are an improvement of the classicalvector-based filters. These classical vector filters are efficientin removing outliners but also blur image details due to theirpure order statistics approaches. We distinguish between: 1)weighted vector filtering techniques which utilize the local spatialrelationship of the samples inside the supporting window[17], [18], 2) switching schemes so that the filter is only appliedto pixels corrupted with impulse noise [8], [10], [19], [20], [21],[24], [25], and 3) fuzzy-based-approaches in order to distinguishbetween noise and image characteristics [12], [15], [23], [24].Several other vector-based impulse noise reduction methodscan be found in the literature [7], [26]; nevertheless, all of thesemethods have the same major drawbacks, i.e., 1) the higher thenoise level is the lower the noise reduction capability is in comparisonto the component-wise approaches and 2) they tend tocluster the noise into a larger array, which makes it even moredifficult to reduce. The reason for these disadvantages is that thevector-based approaches consider each pixel as a whole unit,while the noise can appear in only one of the three components.In the extreme case where the neighborhood for example containsnine pixels where only one of the three components of eachpixel is corrupted, then the vector-based approaches cannot filterout this noise by using a 3 3 window, while only nine componentsof the 27 components are noisy. Only a small amount ofalternative impulse noise reduction methods for color imagesexist. The fuzzy impulse noise detection and reduction methodfor color images (FIDRMC), studied in [27], is one alternativecolor method which does not use vectors at all.
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