Fast numerically stable computation of orthogonal Fourier?Mellin moments

An efficient algorithm for the computation of the orthogonal Fourier-Mellin moments (OFMMs) is presented. The proposed method computes the fractional parts of the orthogonal polynomials, which consist of fractional terms, recursively, by eliminating the number of factorial calculations. The recursive computation of the fractional terms makes the overall computation of the OFMMs a very fast procedure in comparison with the conventional direct method. Actually, the computational complexity of the proposed method is linear O(p) in multiplications, with p being the moment order, while the corresponding complexity of the direct method is O(p²). Moreover, this recursive algorithm has better numerical behaviour, as it arrives at an overflow situation much later than the original one and does not introduce any finite precision errors. These are the two major advantages of the algorithm introduced in the current work, establishing the computation of the OFMMs to a very high order as a quite easy and achievable task. Appropriate simulations on images of different sizes justify the superiority of the proposed algorithm over the conventional algorithm currently used     

A New Neuro-FDS Definition for Indirect Adaptive Control of Unknown Nonlinear Systems Using a Method of Parameter Hopping

The indirect adaptive regulation of unknown nonlinear dynamical systems is considered in this paper. The method is based on a new neuro-fuzzy dynamical system (neuro-FDS) definition, which uses the concept of adaptive fuzzy systems (AFSs) operating in conjunction with high-order neural network functions (FHONNFs). Since the plant is considered unknown, we first propose its approximation by a special form of an FDS and then the fuzzy rules are approximated by appropriate HONNFs. Thus, the identification scheme leads up to a recurrent high-order neural network (RHONN), which however takes into account the fuzzy output partitions of the initial FDS. The proposed scheme does not require a priori experts' information on the number and type of input variable membership functions making it less vulnerable to initial design assumptions. Once the system is identified around an operation point, it is regulated to zero adaptively. Weight updating laws for the involved HONNFs are provided, which guarantee that both the identification error and the system states reach zero exponentially fast, while keeping all signals in the closed loop bounded. The existence of the control signal is always assured by introducing a novel method of parameter hopping, which is incorporated in the weight updating law. Simulations illustrate the potency of the method and comparisons with conventional approaches on benchmarking systems are given. Also, the applicability of the method is tested on a direct current (dc) motor system where it is shown that by following the proposed procedure one can obtain asymptotic regulation.     

Parameterized real-time moment computation on gray images using block techniques

Moments constitute a well-known tool in the field of image analysis and pattern recognition, but they suffer from the drawback of high computational cost. Efforts for the reduction of the required computational complexity have been reported, mainly focused on binary images, but recently some approaches for gray images have been also presented. In this study, we propose a simple but effective approach for the computation of gray image moments. The gray image is decomposed in a set of binary images. Some of these binary images are substituted by an ideal image, which is called “half-intensity” image. The remaining binary images are represented using the image block representation concept and their moments are computed fast using block techniques. The proposed method computes approximated moment values with an error of 2–3% from the exact values and operates in real time (i.e., video rate). The procedure is parameterized by the number m of “half-intensity” images used, which controls the approximation error and the speed gain of the method. The computational complexity is O(kL ²), where k is the number of blocks and L is the moment order.     

Bi-linear adaptive estimation of Fuzzy Cognitive Networks

Fuzzy Cognitive Networks (FCNs) have been introduced by the authors as an operational extension of Fuzzy Cognitive Maps (FCMs), initially introduced by Kosko to model complex behavioral systems in various scientific areas. FCNs rely on the admission that the underlying cognitive graph reaches a certain equilibrium point after an initial perturbation. Weight conditions for reaching equilibrium points have been recently derived in [54] along with an algorithm for weight estimation. In this paper, the conditions are extended to take into account not only the weights of the map but also the inclination parameters of the involved sigmoid functions, increasing the structural flexibility of the network. This in turn gives rise to the development of a new adaptive bilinear weight and sigmoid parameter estimation algorithm, which employs appropriate weight projection criteria to assure that the equilibrium is always achieved.     

New maximum power point tracker for PV arrays using fuzzy controller in close cooperation with fuzzy cognitive networks

The studies on the photovoltaic (PV) generation are extensively increasing, since it is considered as an essentially inexhaustible and broadly available energy resource. However, the output power induced in the photovoltaic modules depends on solar radiation and temperature of the solar cells. Therefore, to maximize the efficiency of the renewable energy system, it is necessary to track the maximum power point of the PV array. In this paper, a maximum power point tracker using fuzzy set theory is presented to improve energy conversion efficiency. A new method is proposed, by using a fuzzy cognitive network, which is in close cooperation with the presented fuzzy controller. The new method gives a very good maximum power operation of any PV array under different conditions such as changing insolation and temperature. The simulation studies show the effectiveness of the proposed algorithm.     

Efficient computation of Zernike and Pseudo-Zernike moments for pattern classification applications

Two novel algorithms for the fast computation of the Zernike and Pseudo-Zernike moments are presented in this paper. The proposed algorithms are very useful, particularly in the case of using the computed moments, as discriminative features in pattern classification applications, where the computation of single moments of several orders is required. The derivation of the algorithms is based on the elimination of the factorial computations, by computing recursively the fractional terms of the orthogonal polynomials being used. The newly introduced algorithms are compared to the direct methods, which are the only methods that permit the computation of single moments of any order. The computational complexity of the proposed method is O(p ²) in multiplications, with p being the moment order, while the corresponding complexity of the direct method is O(p ³). Appropriate experiments justify the superiority of the proposed recursive algorithms over the direct ones, establishing them as alternative to the original algorithms, for the fast computation of the Zernike and Pseudo-Zernike moments.