Interval-valued and intuitionistic fuzzy mathematical morphologies as special cases of L-fuzzy mathematical morphology

Mathematical morphology (MM) offers a wide range of tools for image processing and computer vision. MM was originally conceived for the processing of binary images and later extended to gray-scale morphology. Extensions of classical binary morphology to gray-scale morphology include approaches based on fuzzy set theory that give rise to fuzzy mathematical morphology (FMM). From a mathematical point of view, FMM relies on the fact that the class of all fuzzy sets over a certain universe forms a complete lattice. Recall that complete lattices provide for the most general framework in which MM can be conducted. The concept of L-fuzzy set generalizes not only the concept of fuzzy set but also the concepts of interval-valued fuzzy set and Atanassov’s intuitionistic fuzzy set. In addition, the class of L-fuzzy sets forms a complete lattice whenever the underlying set L constitutes a complete lattice. Based on these observations, we develop a general approach towards L-fuzzy mathematical morphology in this paper. Our focus is in particular on the construction of connectives for interval-valued and intuitionistic fuzzy mathematical morphologies that arise as special, isomorphic cases of L-fuzzy MM. As an application of these ideas, we generate a combination of some well-known medical image reconstruction techniques in terms of interval-valued fuzzy image processing

Ultrafuzziness Optimization Based on Type II Fuzzy Sets for Image Thresholding

Image thresholding is one of the processing techniques to provide high quality preprocessed image. Image vagueness and bad illumination are common obstacles yielding in a poor image thresholding output. By assuming image as fuzzy sets, several different fuzzy thresholding techniques have been proposed to remove these obstacles during threshold selection. In this paper, we proposed an algorithm for thresholding image using ultrafuzziness optimization to decrease uncertainty in fuzzy system by common fuzzy sets like type II fuzzy sets. Optimization was conducted by involving ultrafuzziness measurement for background and object fuzzy sets separately. Experimental results demonstrated that the proposed image thresholding method had good performances for images with high vagueness, low level contrast, and grayscale ambiguity

A construction method of Atanassov’s intuitionistic fuzzy sets for image processing

In this work we introduce a new construction method of Atanassov\u27s intuitionistic fuzzy sets (A-IFSs) from fuzzy sets. We use A-IFSs in image processing. We propose a new image magnification algorithm using A-IFSs. This algorithm is characterized by its simplicity and its efficiency

Delaunay triangulation based image enhancement for echocardiography images

A novel image enhancement approach for automatic echocardiography image processing is proposed. The main steps include undecimated wavelet based speckle noise reduction, edge detection, followed by a regional enhancement process that employs Delaunay triangulation based thresholding. The edge detection is performed using a fuzzy logic based center point detection and a subsequent radial search based fuzzy multiscale edge detection. The edges obtained are used as the vertices for Delaunay triangulation for enhancement purposes. This method enhances the heart wall region in the echo image. This technique is applied to both synthetic and real image sets that were obtained from a local hospital

SOME TRIGONOMETRIC SIMILARITY MEASURES OF COMPLEX FUZZY SETS WITH APPLICATION

Similarity measures of fuzzy sets are applied to compare the closeness among fuzzy sets. These measures have numerous applications in pattern recognition, image processing, texture synthesis, medical diagnosis, etc. However, in many cases of pattern recognition, digital image processing, signal processing, and so forth, the similarity measures of the fuzzy sets are not appropriate due to the presence of dual information of an object, such as amplitude term and phase term. In these cases, similarity measures of complex fuzzy sets are the most suitable for measuring proximity between objects with two-dimensional information. In the present paper, we propose some trigonometric similarity measures of the complex fuzzy sets involving similarity measures based on the sine, tangent, cosine, and cotangent functions. Furthermore, in many situations in real life, the weight of an attribute plays an important role in making the right decisions using similarity measures. So in this paper, we also consider the weighted trigonometric similarity measures of the complex fuzzy sets, namely, the weighted similarity measures based on the sine, tangent, cosine, and cotangent functions. Some properties of the similarity measures and the weighted similarity measures are discussed. We also apply our proposed methods to the pattern recognition problem and compare them with existing methods to show the validity and effectiveness of our proposed methods

Fuzzy logic applications to expert systems and control

A considerable amount of work on the development of fuzzy logic algorithms and application to space related control problems has been done at the Johnson Space Center (JSC) over the past few years. Particularly, guidance control systems for space vehicles during proximity operations, learning systems utilizing neural networks, control of data processing during rendezvous navigation, collision avoidance algorithms, camera tracking controllers, and tether controllers have been developed utilizing fuzzy logic technology. Several other areas in which fuzzy sets and related concepts are being considered at JSC are diagnostic systems, control of robot arms, pattern recognition, and image processing. It has become evident, based on the commercial applications of fuzzy technology in Japan and China during the last few years, that this technology should be exploited by the government as well as private industry for energy savings

Edge Detection in Remote Sensing Images Based on Fuzzy Image Representation

Edge detection is an important task in image processing. There are a lot of approaches in this area: Sobel, Canny operators and others. One of the perspective techniques in image processing is the use of fuzzy logic and fuzzy sets theory. They allow us to increase processing quality by representing information in its fuzzy form. Most of the existing fuzzy image processing methods switch to fuzzy sets on very late stages, so this leads to some useful information loss. In this paper a novel method of edge detection based on fuzzy image representation and fuzzy pixels is proposed. With this approach we convert the image to fuzzy form on the first step. Different approaches to this conversion are described. Several membership functions for fuzzy pixel description and requirements for their form and view are given. A novel approach to edge detection based on Sobel operator and fuzzy image representation is proposed. Experimental testing of developed method was performed on remote sensing images. Comparison of result with Sobel, Prewitt, Roberts and Canny operators is presented. Developed method selected more details (edges) rather then Sobel, Prewitt and Roberts operators, but less than Canny operator. This is because the selected convolution kernel (Sobel) has size 3x3. There are also used only simple functions of estimating the real intensities of pixels. Later, to increase quality it is necessary to use more complex masks of size 5x5 and 7x7 or median filters. Developed approach showed its workability in solving imagep rocessing problems. The proposed fuzzy model in the future can be extended to use higher level fuzzy sets (Type-2FS and others)