Conditions of the Affine Extension of an Incompletely Defined Boolean Function

The paper presents conditions of extension of the weakly defined Boolean functions to their full affine form. The main goal of the analysis is a fast estimation whether a given incompletely defined function can be extended to a full affine form. If it is possible a simple algorithm of the states completion has been proposed. In such a case undefined points are clearly replaced by 0, 1 values. Spectral coefficients of a Boolean function allow to determine whether a partially defined function can be realised as affine

Wybrane metody cyfrowego przetwarzania sygnałów z przykładami programów w Matlabie

The aim of the present monograph is to discuss the theory of digital signal processing and examples of algorithms describing both the theory and practical implementations. The proposed algorithms were implemented in a form of programs written in the Matlab language. The book consists of two parts. Part One presents the theory of spectral analysis of signals used herein, which is next illustrated by examples of spectral analysis and spectral synthesis algorithms. Part Two of the monograph is devoted to the presentation of algorithms utilized in the process of implementing the discussed theory. First, theoretical bases for processing discrete signals are outlined. Then, the readers are provided with de nitions and the mathematical derivations which facilitate the understanding of all the functional algorithms described in the monograph. Part Two contains an overview of various implementations of the previously discussed theory in the areas of image processing and spectral analysis of Boolean functions, by proving the respective theorems. The theorems should facilitate the formulation of corresponding algorithms for image and Boolean functions analysis

An accurate fingerprint reference point determination method based on curvature estimation of separated ridges

This paper presents an effective method for the detection of a fingerprint’s reference point by analyzing fingerprint ridges’ curvatures. The proposed approach is a multi-stage system. The first step extracts the fingerprint ridges from an image and transforms them into chains of discrete points. In the second step, the obtained chains of points are processed by a dedicated algorithm to detect corners and other points of highest curvature on their planar surface. In a series of experiments we demonstrate that the proposed method based on this algorithm allows effective determination of fingerprint reference points. Furthermore, the proposed method is relatively simple and achieves better results when compared with the approaches known from the literature. The reference point detection experiments were conducted using publicly available fingerprint databases FVC2000, FVC2002, FVC2004 and NIST

The k-NN classifier and self-adaptive Hotelling data reduction technique in handwritten signatures recognition

The paper proposes a novel signature verification concept. This new approach uses appropriate similarity coefficients to evaluate the associations between the signature features. This association, called the new composed feature, enables the calculation of a new form of similarity between objects. The most important advantage of the proposed solution is case-by-case matching of similarity coefficients to a signature features, which can be utilized to assess whether a given signature is genuine or forged. The procedure, as described, has been repeated for each person presented in a signatures database. In the verification stage, a two-class classifier recognizes genuine and forged signatures. In this paper, a broad range of classifiers are evaluated. These classifiers all operate on features observed and computed during the data preparation stage. The set of signature composed features of a given person can be reduced what decrease verification error. Such a phenomenon does not occur for the raw features. The approach proposed was tested in a practical environment, with handwritten signatures used as the objects to be compared. The high level of signature recognition obtained confirms that the proposed methodology is efficient and that it can be adapted to accommodate as yet unknown features. The approach proposed can be incorporated into biometric systems

A New Hand-Movement-Based Authentication Method Using Feature Importance Selection with the Hotelling’s Statistic

The growing amount of collected and processed data means that there is a need to control access to these resources. Very often, this type of control is carried out on the basis of biometric analysis. The article proposes a new user authentication method based on a spatial analysis of the movement of the finger’s position. This movement creates a sequence of data that is registered by a motion recording device. The presented approach combines spatial analysis of the position of all fingers at the time. The proposed method is able to use the specific, often different movements of fingers of each user. The experimental results confirm the effectiveness of the method in biometric applications. In this paper, we also introduce an effective method of feature selection, based on the Hotelling T2 statistic. This approach allows selecting the best distinctive features of each object from a set of all objects in the database. It is possible thanks to the appropriate preparation of the input data

Nonlinearity of incomplete Boolean functions: prioritizing spectra calculation

In this paper, a class of linear Boolean functions is analyzed. The Boolean function can be represented as disjoint cubes or in the form of a truth vector. The primary purpose of this analysis is to decide whether an incompletely defined function can be extended to a complete linear form. A simple algorithm for generating all states of this function has been proposed if the Boolean function can have a full representation. The algorithm is beneficial for large functions. The proposed approach can be applied to completely and incompletely defined Boolean functions