Samuel Morillas

A fast impulsive noise color image filter using fuzzy metrics

In this paper, the problem of impulsive noise reduction in multichannel images is addressed. A new filter is proposed on the basis of a recently introduced family of computationally attractive filters with a good detail-preserving ability (FSVF). FSVF is based on privileging the central pixel in each filtering window in order to replace it only when it is really noisy and preserve the original undistorted image structures. The new filter is based on a novel fuzzy metric and it is created by combining the mentioned scheme and the fuzzy metric. The use of the fuzzy metric makes the filter computationally simpler and it allows to adjust the privilege of the central pixel giving the filter an adaptive nature. Moreover, it is shown that the new filter outperforms the classical-order statistics filtering techniques and its performance is similar to FSVF, outperforming it in some cases.

Fuzzy Peer Groups for Reducing Mixed Gaussian-Impulse Noise From Color Images

The <i>peer</i> <i>group</i> of an image pixel is a pixel similarity-based concept which has been successfully used to devise image denoising methods. However, since it is difficult to define the pixel similarity in a crisp way, we propose to represent this similarity in fuzzy terms. In this paper, we introduce the <i>fuzzy</i> <i>peer</i> <i>group</i> concept, which extends the <i>peer</i> <i>group</i> concept in the fuzzy setting. A <i>fuzzy</i> <i>peer</i> <i>group</i> will be defined as a fuzzy set that takes a <i>peer</i> <i>group</i> as support set and where the membership degree of each <i>peer</i> <i>group</i> member will be given by its fuzzy similarity with respect to the pixel under processing. The <i>fuzzy</i> <i>peer</i> <i>group</i> of each image pixel will be determined by means of a novel fuzzy logic-based procedure. We use the <i>fuzzy</i> <i>peer</i> <i>group</i> concept to design a two-step color image filter cascading a fuzzy rule-based switching impulse noise filter by a fuzzy average filtering over the <i>fuzzy</i> <i>peer</i> <i>group</i>. Both steps use the same <i>fuzzy</i> <i>peer</i> <i>group</i>, which leads to computational savings. The proposed filter is able to efficiently suppress both Gaussian noise and impulse noise, as well as mixed Gaussian-impulse noise. Experimental results are provided to show that the proposed filter achieves a promising performance.

A New Fuzzy Color Correlated Impulse Noise Reduction Method

A new impulse noise reduction method for color images is presented. Color images that are corrupted with impulse noise are generally filtered by applying a grayscale algorithm on each color component separately or using a vector-based approach where each pixel is considered as a single vector. The first approach causes artefacts especially on edge and texture pixels. Vector-based methods were successfully introduced to overcome this problem. Nevertheless, they tend to cluster the noise and to receive a lower noise reduction performance. In this paper, we discuss an alternative technique which gives a good noise reduction performance while much less artefacts are introduced. The main difference between the proposed method and other classical noise reduction methods is that the color information is taken into account to develop (1) a better impulse noise detection method and (2) a noise reduction method that filters only the corrupted pixels while preserving the color and the edge sharpness. Experimental results show that the proposed method provides a significant improvement on other existing filters.

Examples of fuzzy metrics and applications

In this paper we present new examples of fuzzy metrics in the sense of George and Veeramani. The examples have been classified attending to their construction and most of the well-known fuzzy metrics are particular cases of those given here. In particular, novel fuzzy metrics, by means of fuzzy and classical metrics and certain special types of functions, are introduced. We also give an extension theorem for two fuzzy metrics that agree in its nonempty intersection. Finally, we give an application of this type of fuzzy metrics to color image processing. We propose a fuzzy metric that simultaneously takes into account two different distance criteria between color image pixels and we use this fuzzy metric to filter noisy images, obtaining promising results. This application is also illustrative of how fuzzy metrics can be used in other engineering problems.

Fast detection and removal of impulsive noise using peer groups and fuzzy metrics

A novel approach to impulsive noise detection in color images is introduced. In the paper, the peer group concept is redefined by means of a certain fuzzy metric. This concept is employed for the fast detection of noisy pixels by taking advantage of the fuzzy metric properties. On the basis of the noisy pixel detection a switching filter between the arithmetic mean filter (AMF) and the identity operation is proposed. The proposed switching filter achieves a trade-off between noise suppression and signal-detail preservation and is faster than recently introduced switching filters based on the peer group concept.

Local self-adaptive fuzzy filter for impulsive noise removal in color images

This paper describes a new filter for impulsive noise reduction in color images based on a recently introduced family of vector filters with a good ability for preserving details. These filters use a reduced ordering of color vectors in order to detect and replace impulses. The proposed filter uses local statistics to adapt itself to simultaneously remove impulses and preserve image edges and details. The proposed filtering technique is robust and achieves a good balance between noise attenuation and detail reservation. In addition, it outperforms well-known vector filtering solutions and produces visually pleasing filtered color images.

Isolating impulsive noise pixels in color images by peer group techniques

A new method for removing impulsive noise in color images is presented. The fuzzy metric peer group concept is used to build novel switching vector filters. In the proposed filtering procedure, a set of noise-free pixels of high reliability is determined by applying a highly restrictive condition based on the peer group concept. Afterwards, an iterative detection process is used to refine the initial findings by detecting additional noise-free pixels. Finally, noisy pixels are filtered by maximizing the employed fuzzy distance criterion between the pixels inside the filter window. Comparisons are provided to show that our approach suppresses impulsive noise, while preserving image details. In addition, the method is analyzed in order to justify the necessity of the iterative process and demonstrate the computational efficiency of the proposed approach.

On a class of completable fuzzy metric spaces

In this paper we study some properties of a class of fuzzy metric spaces, in the sense of George and Veeramani, called strong. This class includes the class of stationary fuzzy metrics, and in particular, when the fuzzy metric is principal, we obtain a family of metrics which are compatible with the topology induced by the fuzzy metric. Also, we study some aspects of the completion of strong fuzzy metrics and we find a class of completable stationary fuzzy metrics which includes the class of stationary fuzzy ultrametrics.

New adaptive vector filter using fuzzy metrics

Classical nonlinear vector median-based filters are well-known methods for impulsive noise suppression in color images, but mostly they lack good detail-preserving ability. We use a class of fuzzy metrics to introduce a vector filter aimed at improving the detail-preserving ability of classical vector filters while effectively removing impulsive noise. The output of the proposed method is the pixel inside the filter window which maximizes the similarity in color and spatial closeness. The use of fuzzy metrics allows us to handle both criteria simultaneously. The filter is designed so that the importance of the spatial criterion can be adjusted. We show that the filter can adapt to the density of the contaminating noise by adjusting the spatial criterion importance. Classical and recent filters are used to assess the proposed filtering. The experimental results show that the proposed technique performs competitively.

Fuzzy bilateral filtering for color images

Bilateral filtering is a well-known technique for smoothing gray-scale and color images while preserving edges and image details by means of an appropriate nonlinear combination of the color vectors in a neighborhood. The pixel colors are combined based on their spatial closeness and photometric similarity. In this paper, a particular class of fuzzy metrics is used to represent the spatial and photometric relations between the color pixels adapting the classical bilateral filtering. It is shown that the use of these fuzzy metrics is more appropriate than the classical measures used.