Selman Uguz

Salt and pepper noise filtering with fuzzy-cellular automata

A new image denoising algorithm is proposed to restore digital images corrupted by impulse noise. It is based on two dimensional cellular automata (CA) with the help of fuzzy logic theory. The algorithm describes a local fuzzy transition rule which gives a membership value to the corrupted pixel neighborhood and assigns next state value as a central pixel value. The proposed method removes the noise effectively even at noise level as high as 90%. Extensive simulations show that the proposed algorithm provides better performance than many of the existing filters in terms of noise suppression and detail preservation. Also, qualitative and quantitative measures of the image produce better results on different images compared with the other algorithms.

Structure and reversibility of 2D hexagonal cellular automata

Cellular automata are used to model dynamical phenomena by focusing on their local behavior which depends on the neighboring cells in order to express their global behavior. The geometrical structure of the models suggests the algebraic structure of cellular automata. After modeling the dynamical phenomena, it is sometimes an important problem to be able to move backwards in order to understand it better. This is only possible if cellular automata is reversible. In this paper, 2D finite cellular automata defined by local rules based on hexagonal cell structure are studied. Rule matrix of the hexagonal finite cellular automaton is obtained. The rank of rule matrices representing the 2D hexagonal finite cellular automata via an algorithm is computed. It is a well known fact that determining the reversibility of a 2D cellular automata is a very difficult problem in general. Here, the reversibility problem of this family of 2D hexagonal cellular automata is also resolved completely.

Edge detection with fuzzy cellular automata transition function optimized by PSO

Fig. 2. Proposed method result of different rules for Im 1 ( Δ = 110 , ? = 0.62 ), (a) Original Image, (b) Ground Truth, (c) Rule 47, (d) Rule 170, (e) Rule 367, (f) Rule 510.Display Omitted This study is the application of 2D linear cellular automata (CA) rules with the help of fuzzy membership function to the problems of edge detection.An efficient and simple thresholding technique of edge detection based on CA transition rules optimized by Particle Swarm Optimization method (PSO) is proposed.Results of the proposed to the selected 22 images from the Berkeley Segmentation Dataset (BSDS) are presented.Comparison with some classical Sobel and Canny results is included.Baddeley Delta Metric (BDM) is used for the performance index to compare the results. In this paper we discuss the application of two-dimensional linear cellular automata (CA) rules with the help of fuzzy heuristic membership function to the problems of edge detection in image processing applications. We proposed an efficient and simple thresholding technique of edge detection based on fuzzy cellular automata transition rules optimized by Particle Swarm Optimization method (PSO). Finally, we present some results of the proposed linear rules for edge detection to the selected 22 images from the Berkeley Segmentation Dataset (BSDS) and compare with some classical Sobel and Canny results. Also, Baddeley Delta Metric (BDM) is used for the performance index to compare the results.

REVERSIBILITY ALGORITHMS FOR 3-STATE HEXAGONAL CELLULAR AUTOMATA WITH PERIODIC BOUNDARIES

This paper presents a study of two-dimensional hexagonal cellular automata (CA) with periodic boundary. Although the basic construction of a cellular automaton is a discrete model, its global level behavior at large times and on large spatial scales can be a close approximation to a continuous system. Meanwhile CA is a model of dynamical phenomena that focuses on the local behavior which depends on the neighboring cells in order to express their global behavior. The mathematical structure of the model suggests the importance of the algebraic structure of cellular automata. After modeling the dynamical behaviors, it is sometimes an important problem to be able to move backwards on CAs in order to understand the behaviors better. This is only possible if cellular automaton is a reversible one. In the present paper, we study two-dimensional finite CA defined by hexagonal local rule with periodic boundary over the field ℤ3 (i.e. 3-state). We construct the rule matrix corresponding to the hexagonal periodic cellular automata. For some given coefficients and the number of columns of hexagonal information matrix, we prove that the hexagonal periodic cellular automata are reversible. Moreover, we present general algorithms to determine the reversibility of 2D 3-state cellular automata with periodic boundary. A well known fact is that the determination of the reversibility of a two-dimensional CA is a very difficult problem, in general. In this study, the reversibility problem of two-dimensional hexagonal periodic CA is resolved completely. Since CA are sufficiently simple to allow detailed mathematical analysis, also sufficiently complex to produce chaos in dynamical systems, we believe that our construction will be applied many areas related to these CA using any other transition rules.

Phase diagram and extreme Gibbs measures of the Ising model on a Cayley tree in the presence of competing binary and ternary interactions

One of the main problems of statistical physics is to describe all Gibbs measures corresponding to a given Hamiltonian. It is well known that such measures form a nonempty convex compact subset in the set of all probability measures. The purpose of this article is to investigate phase diagram and extreme Gibbs measures of the Ising model on a Cayley tree in the presence of competing binary and ternary interactions.

Self-Replicating Patterns in 2D Linear Cellular Automata

This paper studies the theoretical aspects of two-dimensional cellular automata (CAs), it classifies this family into subfamilies with respect to their visual behavior and presents an application to pseudo random number generation by hybridization of these subfamilies. Even though the basic construction of a cellular automaton is a discrete model, its macroscopic behavior at large evolution times and on large spatial scales can be a close approximation to a continuous system. Beyond some statistical properties, we consider geometrical and visual aspects of patterns generated by CA evolution. The present work focuses on the theory of two-dimensional CA with respect to uniform periodic, adiabatic and reflexive boundary CA (2D PB, AB and RB) conditions. In total, there are 512 linear rules over the binary field ℤ2 for each boundary condition and the effects of these CA are studied on applications of image processing for self-replicating patterns. After establishing the representation matrices of 2D CA, these linear CA rules are classified into groups of nine and eight types according to their boundary conditions and the number of neighboring cells influencing the cells under consideration. All linear rules have been found to be rendering multiple self-replicating copies of a given image depending on these types. Multiple copies of any arbitrary image corresponding to CA find innumerable applications in real life situation, e.g. textile design, DNA genetics research, statistical physics, molecular self-assembly and artificial life, etc. We conclude by presenting a successful application for generating pseudo numbers to be used in cryptography by hybridization of these 2D CA subfamilies.

On extreme Gibbs measures of the Vannimenus model

One of the main problems of statistical physics is that of describing all Gibbs measures corresponding to a given Hamiltonian. It is well known that such measures form a nonempty convex compact subset in the set of all probability measures. The purpose of this paper is to investigate extreme Gibbs measures of the Vannimenus model.

Structure and Reversibility of 2‐dimensional Hexagonal Cellular Automata

2‐dimensional finite cellular automata defined by local rule based on hexagonal cell structure are studied. Rule matrix of the hexagonal finite cellular automaton is obtained. The rank of rule matrices related to hexagonal finite cellular automata via an algorithm is computed. By using the matrix algebra it is shown that the hexagonal finite cellular automata are reversible, if the number of columns is even and the hexagonal finite cellular automata are not reversible, if the number of the columns is odd.

Uniform Cellular Automata Linear Rules for Edge Detection

In this paper we discuss the application of two-dimensional linear cellular automata rules to the problems of edge detection in monochromatic images. We proposed an efficient and simple method of edge detection based on uniform cellular automata transition matrix representation. We investigate of cellular automata linear rules for edge detection by using matrix representation, in some cases they are strong and some other rules are not in fact useful for practical edge detection. All rules give computationally effective result since the computation mechanism consist only matrix multiplication. Finally, we present some results of the proposed linear rules for edge detection and compare with some classical results.

(3+3+2) warped-like product manifolds with Spin(7) holonomy

Abstract We consider a generalization of eight-dimensional multiply warped product manifolds as a special warped product, by allowing the fiber metric to be non-block diagonal. We define this special warped product as a (3+3+2) warped-like manifold of the form M = F × B , where the base B is a two-dimensional Riemannian manifold, and the fibre F is of the form F = F 1 × F 2 where the F i ( i = 1 , 2 ) are Riemannian 3 -manifolds. We prove that the connection on M is completely determined by the requirement that the Bonan 4-form given in the work of Yasui and Ootsuka [Y. Yasui and T. Ootsuka, Spin ( 7 ) holonomy manifold and superconnection, Class. Quantum Gravity 18 (2001) 807–816] be closed. Assuming that the F i are complete, connected and simply connected, it follows that they are isometric to S 3 with constant curvature k > 0 and the Yasui–Ootsuka solution is unique in the class of (3+3+2) warped-like product metrics admitting a specific Spin ( 7 ) structure.