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Top1. Introduction
Digital image processing is a hot long-standing research field including many research topics as image segmentation, images fusion, contrast enhancement, and so on (Gonzalez & Woods, 2018).
Image segmentation is the process of image domain partitioning to image subdomains named segments, satisfying some condition of homogeneity. Several algorithms have been introduced to tackle this problem (Shi and Malik, 2000). They can be classified traditionally into five approaches that are Histogram-based methods, boundary based methods, region-based methods, hybrid based methods, and graph-based methods (Shi and Malik, 2000).
Image fusion is the process of blending or integration of several images that are obtained from various modalities into a single composite and enhanced image. It is divided into three levels: pixel-level integration, feature-level integration, and decision-making level fusion (Pohl and Van Genderen, 1998).
Contrast enhancement increases the overall visual contrast of the image so that the image structures are more clear and distinguishable (Beyerer et al., 2016). It is applied to the images where the contrast between object and background is low (Deng & al., 2016).
Most of digital images have uncertainties associated with the intensity levels of pixels and/or edges. These uncertainties can be traced back to the acquisition chain, to uneven lighting conditions used during imaging or to the noisy environment. For example, it is usually challenging to decide whether a pixel is a noisy pixel or a pixel that belongs to an edge, whether a pixel belongs to the background or the object of the image and therefore introduce a degree of hesitancy associated with the corresponding pixel (Vlachos & Sergiadis, 2007).
On the other hand, the hypergraph theory, which was developed by (Berge, 1989), is a generalization of traditional graph theory giving them a power to model more complex relationships beyond the binary relation. In a hypergraph, an edge can connect more than two vertices. Hypergraphs are highly used by computer science applications especially in optimization, data mining, image processing, clustering, networking and so on. The notion of hypergraphs has been extended in the fuzzy theory and the concept of fuzzy hypergraphs (Mordeson and Nair, 2000) was provided by Kaufmann.
In 1983, Atanassov introduced the concept of intuitionistic fuzzy sets as a generalization of fuzzy sets, where he added a new component, which determines the degree of non-membership of an element in a given set. He also considered a ‘hesitation degree’ while defining the membership function. This hesitation is due to the lack of knowledge in defining the membership function (Atanassov, 1983; 1986). The first definition of intuitionistic fuzzy graphs was proposed by A. Shannon and K. Atanassov (Shannon and Atanassov, 1994).
The research related to Intuitionistic Fuzzy Set theory, which is named IFS, has been of great concern to academics in related fields both at home and abroad. Moreover, IFS has been used in many fields such as decision-making, medical diagnosis, the logic of planning, pattern recognition, machine learning and prediction, and so on. In 2009, (Parvathi and al., 2009) defined the concept of intuitionistic fuzzy hypergraphs (IFHG).
Modeling systems with IFHG finds application in the field of image processing where a digital image can be mathematically modeled as a an IFHG on which many algorithms and operations from the hypergraph theory and intuitionistic fuzzy logic can be applied to achieve some of the image processing goals such as image segmentation, fusion, denoising and quality enhancement. In this context, we will use IFHG as a mathematical tool for digital color image denoising, segmentation and edges detection. First, the input RGB color image is transformed to a HLS image with three components (H, L, S). Each component is then intuitionistically fuzzified using entropy-based technique (Burillo & Bustince, 1996). After that, each fuzzified component is mapped to an IFHG on which some algorithms for denoising, segmentation and edges detection from the hypergraph theory are applied. In order to restore the initial format of the image, we should defuzzify the resulted components and then marge them into one HLS image. At the end, the resulted HLS image is converted to its initial RGB format.