Search results for: fingerprint classification

Authors: Jayant V Kulkarni, Jayadevan R, Suresh N Mali, Hemant K Abhyankar, Raghunath S Holambe

Abstract:

The paper describes a new approach for fingerprint classification, based on the distribution of local features (minute details or minutiae) of the fingerprints. The main advantage is that fingerprint classification provides an indexing scheme to facilitate efficient matching in a large fingerprint database. A set of rules based on heuristic approach has been proposed. The area around the core point is treated as the area of interest for extracting the minutiae features as there are substantial variations around the core point as compared to the areas away from the core point. The core point in a fingerprint has been located at a point where there is maximum curvature. The experimental results report an overall average accuracy of 86.57 % in fingerprint classification.

Keywords: Minutiae distribution, Minutiae, Classification, Orientation, Heuristic.

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Authors: Mana Tarjoman, Shaghayegh Zarei

Abstract:

Using efficient classification methods is necessary for automatic fingerprint recognition system. This paper introduces a new structural approach to fingerprint classification by using the directional image of fingerprints to increase the number of subclasses. In this method, the directional image of fingerprints is segmented into regions consisting of pixels with the same direction. Afterwards the relational graph to the segmented image is constructed and according to it, the super graph including prominent information of this graph is formed. Ultimately we apply a matching technique to compare obtained graph with the model graphs in order to classify fingerprints by using cost function. Increasing the number of subclasses with acceptable accuracy in classification and faster processing in fingerprints recognition, makes this system superior.

Keywords: Classification, Directional image, Fingerprint, Graph, Super graph.

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Authors: Mehran Yazdi, Kazem Gheysari

Abstract:

In this paper, we propose an approach for the classification of fingerprint databases. It is based on the fact that a fingerprint image is composed of regular texture regions that can be successfully represented by co-occurrence matrices. So, we first extract the features based on certain characteristics of the cooccurrence matrix and then we use these features to train a neural network for classifying fingerprints into four common classes. The obtained results compared with the existing approaches demonstrate the superior performance of our proposed approach.

Keywords: Biometrics, fingerprint classification, gray level cooccurrence matrix, regular texture representation.

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Authors: W. Y. Leng, S. M. Shamsuddin

Abstract:

Fingerprint based identification system; one of a well known biometric system in the area of pattern recognition and has always been under study through its important role in forensic science that could help government criminal justice community. In this paper, we proposed an identification framework of individuals by means of fingerprint. Different from the most conventional fingerprint identification frameworks the extracted Geometrical element features (GEFs) will go through a Discretization process. The intention of Discretization in this study is to attain individual unique features that could reflect the individual varianceness in order to discriminate one person from another. Previously, Discretization has been shown a particularly efficient identification on English handwriting with accuracy of 99.9% and on discrimination of twins- handwriting with accuracy of 98%. Due to its high discriminative power, this method is adopted into this framework as an independent based method to seek for the accuracy of fingerprint identification. Finally the experimental result shows that the accuracy rate of identification of the proposed system using Discretization is 100% for FVC2000, 93% for FVC2002 and 89.7% for FVC2004 which is much better than the conventional or the existing fingerprint identification system (72% for FVC2000, 26% for FVC2002 and 32.8% for FVC2004). The result indicates that Discretization approach manages to boost up the classification effectively, and therefore prove to be suitable for other biometric features besides handwriting and fingerprint.

Keywords: Discretization, fingerprint identification, geometrical features, pattern recognition

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Authors: Heeseung Choi, Raechoong Kang, Kyungtaek Choi, Jaihie Kim

Abstract:

Fake finger submission attack is a major problem in fingerprint recognition systems. In this paper, we introduce an aliveness detection method based on multiple static features, which derived from a single fingerprint image. The static features are comprised of individual pore spacing, residual noise and several first order statistics. Specifically, correlation filter is adopted to address individual pore spacing. The multiple static features are useful to reflect the physiological and statistical characteristics of live and fake fingerprint. The classification can be made by calculating the liveness scores from each feature and fusing the scores through a classifier. In our dataset, we compare nine classifiers and the best classification rate at 85% is attained by using a Reduced Multivariate Polynomial classifier. Our approach is faster and more convenient for aliveness check for field applications.

Keywords: Aliveness detection, Fingerprint recognition, individual pore spacing, multiple static features, residual noise.

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Authors: Daesung Moon, Woo-Yong Choi, Kiyoung Moon

Abstract:

Fuzzy fingerprint vault is a recently developed cryptographic construct based on the polynomial reconstruction problem to secure critical data with the fingerprint data. However, the previous researches are not applicable to the fingerprint having a few minutiae since they use a fixed degree of the polynomial without considering the number of fingerprint minutiae. To solve this problem, we use an adaptive degree of the polynomial considering the number of minutiae extracted from each user. Also, we apply multiple polynomials to avoid the possible degradation of the security of a simple solution(i.e., using a low-degree polynomial). Based on the experimental results, our method can make the possible attack difficult 2192 times more than using a low-degree polynomial as well as verify the users having a few minutiae.

Keywords: Fuzzy vault, fingerprint recognition multiple polynomials.

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Authors: Mehran Yazdi, Zahra Adelpour, Batoul Bahraini, Yasaman Keshtkar Jahromi

Abstract:

In this paper we use the property of co-occurrence matrix in finding parallel lines in binary pictures for fingerprint identification. In our proposed algorithm, we reduce the noise by filtering the fingerprint images and then transfer the fingerprint images to binary images using a proper threshold. Next, we divide the binary images into some regions having parallel lines in the same direction. The lines in each region have a specific angle that can be used for comparison. This method is simple, performs the comparison step quickly and has a good resistance in the presence of the noise.

Keywords: Parallel lines detection, co-occurrence matrix, fingerprint identification.

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Authors: Rajlaxmi Chouhan, Pritee Khanna

Abstract:

In this manuscript, a wavelet-based blind watermarking scheme has been proposed as a means to provide security to authenticity of a fingerprint. The information used for identification or verification of a fingerprint mainly lies in its minutiae. By robust watermarking of the minutiae in the fingerprint image itself, the useful information can be extracted accurately even if the fingerprint is severely degraded. The minutiae are converted in a binary watermark and embedding these watermarks in the detail regions increases the robustness of watermarking, at little to no additional impact on image quality. It has been experimentally shown that when the minutiae is embedded into wavelet detail coefficients of a fingerprint image in spread spectrum fashion using a pseudorandom sequence, the robustness is observed to have a proportional response while perceptual invisibility has an inversely proportional response to amplification factor “K". The DWT-based technique has been found to be very robust against noises, geometrical distortions filtering and JPEG compression attacks and is also found to give remarkably better performance than DCT-based technique in terms of correlation coefficient and number of erroneous minutiae.

Keywords: Fingerprint watermarking, minutiae, discrete wavelet transform, PN sequence

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Authors: Xu Huang, Jing Fan, Maonian Wu, Yonggen Gu

Abstract:

This paper discusses the design of an indoor mobile robot positioning system. The problem of indoor positioning is solved through Wi-Fi fingerprint positioning to implement a low cost deployment. A wireless fingerprint matching algorithm based on the similarity of unequal length sequences is presented. Candidate sequences selection is defined as a set of mappings, and detection errors caused by wireless hotspot stability and the change of interior pattern can be corrected by transforming the unequal length sequences into equal length sequences. The presented scheme was verified experimentally to achieve the accuracy requirements for an indoor positioning system with low deployment cost.

Keywords: Fingerprint match, indoor positioning, mobile robot positioning system, Wi-Fi, wireless fingerprint.

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Authors: Jayadevan R., Jayant V. Kulkarni, Suresh N. Mali, Hemant K. Abhyankar

Abstract:

An important step in studying the statistics of fingerprint minutia features is to reliably extract minutia features from the fingerprint images. A new reliable method of computation for minutiae feature extraction from fingerprint images is presented. A fingerprint image is treated as a textured image. An orientation flow field of the ridges is computed for the fingerprint image. To accurately locate ridges, a new ridge orientation based computation method is proposed. After ridge segmentation a new method of computation is proposed for smoothing the ridges. The ridge skeleton image is obtained and then smoothed using morphological operators to detect the features. A post processing stage eliminates a large number of false features from the detected set of minutiae features. The detected features are observed to be reliable and accurate.

Keywords: Minutia, orientation field, ridge segmentation, textured image.

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Authors: Jason Zalev, Reza Sedaghat

Abstract:

This paper describes a complex energy signal model that is isomorphic with digital human fingerprint images. By using signal models, the problem of fingerprint matching is transformed into the signal processing problem of finding a correlation between two complex signals that differ by phase-rotation and time-scaling. A technique for minutiae matching that is independent of image translation, rotation and linear-scaling, and is resistant to missing minutiae is proposed. The method was tested using random data points. The results show that for matching prints the scaling and rotation angles are closely estimated and a stronger match will have a higher correlation.

Keywords: Affine Invariant, Fingerprint Recognition, Matching, Minutiae.

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Authors: D. M. S. Bandara, Yunqi Lei, Ye Luo

Abstract:

Fingerprints are suitable as long-term markers of human identity since they provide detailed and unique individual features which are difficult to alter and durable over life time. In this paper, we propose an algorithm to encrypt and decrypt fingerprint images by using a specially designed Elliptic Curve Cryptography (ECC) procedure based on block ciphers. In addition, to increase the confusing effect of fingerprint encryption, we also utilize a chaotic-behaved method called Arnold Cat Map (ACM) for a 2D scrambling of pixel locations in our method. Experimental results are carried out with various types of efficiency and security analyses. As a result, we demonstrate that the proposed fingerprint encryption/decryption algorithm is advantageous in several different aspects including efficiency, security and flexibility. In particular, using this algorithm, we achieve a margin of about 0.1% in the test of Number of Pixel Changing Rate (NPCR) values comparing to the-state-of-the-art performances.

Keywords: Arnold cat map, biometric encryption, block cipher, elliptic curve cryptography, fingerprint encryption, Koblitz’s Encoding.

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Authors: K.Amrithavarshini, S.Chandrachudeswaran

Abstract:

This paper presents an idea to improve the efficiency of security checks in airports through the active tracking and monitoring of passengers and staff using OFDM modulation technique and Finger print authentication. The details of the passenger are multiplexed using OFDM .To authenticate the passenger, the fingerprint along with important identification information is collected. The details of the passenger can be transmitted after necessary modulation, and received using various transceivers placed within the premises of the airport, and checked at the appropriate check points, thereby increasing the efficiency of checking. OFDM has been employed for spectral efficiency.

Keywords: Orthogonal Frequency Division Multiplexing, FFT Algorithm, Fingerprint Authentication, Airport Security

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Authors: V. Praveena, N. Kiruthika

Abstract:

In this paper, we explore a new scheme for filtering spoofed packets (DDOS attack) which is a combination of path fingerprint and client puzzle concepts. In this each IP packet has a unique fingerprint is embedded that represents, the route a packet has traversed. The server maintains a mapping table which contains the client IP address and its corresponding fingerprint. In ingress router, client puzzle is placed. For each request, the puzzle issuer provides a puzzle which the source has to solve. Our design has the following advantages over prior approaches, 1) Reduce the network traffic, as we place a client puzzle at the ingress router. 2) Mapping table at the server is lightweight and moderate.

Keywords: Client puzzle, DDOS attack, Egress, Ingress, IP Spoofing, Spoofed Packet.

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Authors: Hae-Yeoun Lee, In-Koo Kang, Heung-Kyu Lee

Abstract:

This paper addresses an efficient technique to embed and detect digital fingerprint code. Orthogonal modulation method is a straightforward and widely used approach for digital fingerprinting but shows several limitations in computational cost and signal efficiency. Coded modulation method can solve these limitations in theory. However it is difficult to perform well in practice if host signals are not available during tracing colluders, other kinds of attacks are applied, and the size of fingerprint code becomes large. In this paper, we propose a hybrid modulation method, in which the merits of or-thogonal modulation and coded modulation method are combined so that we can achieve low computational cost and high signal efficiency. To analyze the performance, we design a new fingerprint code based on GD-PBIBD theory and modulate this code into images by our method using spread-spectrum watermarking on frequency domain. The results show that the proposed method can efficiently handle large fingerprint code and trace colluders against averaging attacks.

Keywords: Fingerprinting, GD-PBIBD theory, Hybrid modulationtechnique.

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Authors: Hassan Haleh, Zohreh Nasiri, Parisa Farahpour

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During recent years, the traditional learning approaches have undergone fundamental changes due to the emergence of new technologies such as multimedia, hypermedia and telecommunication. E-learning is a modern world phenomenon that has come into existence in the information age and in a knowledgebased society. E-learning has developed significantly within a short period of time. Thus it is of a great significant to secure information, allow a confident access and prevent unauthorized accesses. Making use of individuals- physiologic or behavioral (biometric) properties is a confident method to make the information secure. Among the biometrics, fingerprint is more acceptable and most countries use it as an efficient methods of identification. This article provides a new method to compare the fingerprint comparison by pattern recognition and image processing techniques. To verify fingerprint, the shortest distance method is used together with perceptronic multilayer neural network functioning based on minutiae. This method is highly accurate in the extraction of minutiae and it accelerates comparisons due to elimination of false minutiae and is more reliable compared with methods that merely use directional images.

Keywords: Fingerprint, minutiae, extraction of properties, multilayer neural network

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Authors: Chih-Neng Liang, Huang-Bin Huang, Bo-Chiuan Chen

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Nowadays, keyless entry systems are widely adopted for vehicle immobilizer systems due to both advantages of security and convenience. Keyless entry systems could overcome brute-force key guessing attack, statistics attack and masquerade attack, however, they can't prevent from thieves stealing behavior. In this paper, we proposed a new architecture try to improve the existent flaws. The integration of the keyless entry system and the fingerprint identification technology is more suitable to implement on the portable transponder to achieve higher security needs. We also adopt and modify AES security protocol for life expectancy and security of the portable transponder. In addition, the identification of a driver's fingerprint makes the service of automatic reinstatement of a driver's preferences become possible. Our design can satisfy not only the three kinds of previous illegal attacks, but also the stealing situation. Furthermore, many practical factors, such as costs, life expectancy and performance, have been well considered in the design of portable transponder.

Keywords: Keyless entry-system, fingerprint identification, AES security protocol, vehicle immobilizer system.

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Authors: Sera Syarmila Sameon, Rohaini Ramli

Abstract:

A trustworthy voting process in democratic is important that each vote is recorded with accuracy and impartiality. The accuracy and impartiality are tallied in high rate with biometric system. One of the sign is a fingerprint. Fingerprint recognition is still a challenging problem, because of the distortions among the different impression of the same finger. Because of the trustworthy of biometric voting technologies, it may give a great effect on numbers of voter-s participation and outcomes of the democratic process. Hence in this study, the authors are interested in designing and analyzing the Electronic Voting System and the participation of the users. The system is based on the fingerprint minutiae with the addition of person ID number. This is in order to enhance the accuracy and speed of the voting process. The new design is analyzed by conducting pilot election among a class of students for selecting their representative.

Keywords: Biometric, FAR and FRR, democratic, voting

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Authors: Manal Hassan Abdel Aziz, Fatma Mohamed Magdy Badr El Dine, Nourhan Mohamed Mohamed Saeed

Abstract:

Establishing association between lip print patterns and those of fingerprints as well as blood groups is of fundamental importance in the forensic identification domain. The first aim of the current study was to determine the prevalent types of ABO blood groups, lip prints and fingerprints patterns in both studied populations. Secondly, to analyze any relation found between the different print patterns and the blood groups, which would be valuable in identification purposes. The present study was conducted on 60 healthy volunteers, (30 males and 30 females) from each of the studied population. Lip prints and fingerprints were obtained and classified according to Tsuchihashi's classification and Michael Kuchen’s classification, respectively. The results show that the ulnar loop was the most frequent among both populations. Blood group A was the most frequent among Egyptians, while blood groups O and B were the predominant among Malaysians. Significant relations were observed between lip print patterns and fingerprint (in the second quadrant for Egyptian males and the first one for Malaysian). For Malaysian females, a statistically significant association was proved in the fourth quadrant. Regarding the blood groups, 89.5% of ulnar loops were significantly related to blood group A among Egyptian males. The results proved an association between the fingerprint pattern and the lip prints, as well as between the ABO blood group and the pattern of fingerprints. However, further researches with larger sample sizes need to be directed to approve the current results.

Keywords: ABO, cheiloscopy, dactylography, Egyptians, Malaysians.

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Authors: Sejong Oh

Abstract:

Classification is an important topic in machine learning and bioinformatics. Many datasets have been introduced for classification tasks. A dataset contains multiple features, and the quality of features influences the classification accuracy of the dataset. The power of classification for each feature differs. In this study, we suggest the Classification Influence Index (CII) as an indicator of classification power for each feature. CII enables evaluation of the features in a dataset and improved classification accuracy by transformation of the dataset. By conducting experiments using CII and the k-nearest neighbor classifier to analyze real datasets, we confirmed that the proposed index provided meaningful improvement of the classification accuracy.

Keywords: accuracy, classification, dataset, data preprocessing

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Authors: Shahram Mohammadi, Ali Frajzadeh

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A lot of matching algorithms with different characteristics have been introduced in recent years. For real time systems these algorithms are usually based on minutiae features. In this paper we introduce a novel approach for feature extraction in which the extracted features are independent of shift and rotation of the fingerprint and at the meantime the matching operation is performed much more easily and with higher speed and accuracy. In this new approach first for any fingerprint a reference point and a reference orientation is determined and then based on this information features are converted into polar coordinates. Due to high speed and accuracy of this approach and small volume of extracted features and easily execution of matching operation this approach is the most appropriate for real time applications.

Keywords: Matching, Minutiae, Reference point, Reference orientation

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Authors: Giovanni Luca Masala

Abstract:

Pattern recognition is the research area of Artificial Intelligence that studies the operation and design of systems that recognize patterns in the data. Important application areas are image analysis, character recognition, fingerprint classification, speech analysis, DNA sequence identification, man and machine diagnostics, person identification and industrial inspection. The interest in improving the classification systems of data analysis is independent from the context of applications. In fact, in many studies it is often the case to have to recognize and to distinguish groups of various objects, which requires the need for valid instruments capable to perform this task. The objective of this article is to show several methodologies of Artificial Intelligence for data classification applied to biomedical patterns. In particular, this work deals with the realization of a Computer-Aided Detection system (CADe) that is able to assist the radiologist in identifying types of mammary tumor lesions. As an additional biomedical application of the classification systems, we present a study conducted on blood samples which shows how these methods may help to distinguish between carriers of Thalassemia (or Mediterranean Anaemia) and healthy subjects.

Keywords: Computer Aided Detection, mammary tumor, pattern recognition, dissimilarity

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Authors: Giovanni Luca Masala

Abstract:

Pattern recognition is the research area of Artificial Intelligence that studies the operation and design of systems that recognize patterns in the data. Important application areas are image analysis, character recognition, fingerprint classification, speech analysis, DNA sequence identification, man and machine diagnostics, person identification and industrial inspection. The interest in improving the classification systems of data analysis is independent from the context of applications. In fact, in many studies it is often the case to have to recognize and to distinguish groups of various objects, which requires the need for valid instruments capable to perform this task. The objective of this article is to show several methodologies of Artificial Intelligence for data classification applied to biomedical patterns. In particular, this work deals with the realization of a Computer-Aided Detection system (CADe) that is able to assist the radiologist in identifying types of mammary tumor lesions. As an additional biomedical application of the classification systems, we present a study conducted on blood samples which shows how these methods may help to distinguish between carriers of Thalassemia (or Mediterranean Anaemia) and healthy subjects.

Keywords: Computer Aided Detection, mammary tumor, pattern recognition, thalassemia.

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Authors: Yehjune Heo

Abstract:

Fingerprint Anti-Spoofing approaches have been actively developed and applied in real-world applications. One of the main problems for Fingerprint Anti-Spoofing is not robust to unseen samples, especially in real-world scenarios. A possible solution will be to generate artificial, but realistic fingerprint samples and use them for training in order to achieve good generalization. This paper contains experimental and comparative results with currently popular GAN based methods and uses realistic synthesis of fingerprints in training in order to increase the performance. Among various GAN models, the most popular StyleGAN is used for the experiments. The CNN models were first trained with the dataset that did not contain generated fake images and the accuracy along with the mean average error rate were recorded. Then, the fake generated images (fake images of live fingerprints and fake images of spoof fingerprints) were each combined with the original images (real images of live fingerprints and real images of spoof fingerprints), and various CNN models were trained. The best performances for each CNN model, trained with the dataset of generated fake images and each time the accuracy and the mean average error rate, were recorded. We observe that current GAN based approaches need significant improvements for the Anti-Spoofing performance, although the overall quality of the synthesized fingerprints seems to be reasonable. We include the analysis of this performance degradation, especially with a small number of samples. In addition, we suggest several approaches towards improved generalization with a small number of samples, by focusing on what GAN based approaches should learn and should not learn.

Keywords: Anti-spoofing, CNN, fingerprint recognition, GAN.

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Authors: Suzan Wedyan

Abstract:

Associative classification (AC) is a data mining approach that combines association rule and classification to build classification models (classifiers). AC has attracted a significant attention from several researchers mainly because it derives accurate classifiers that contain simple yet effective rules. In the last decade, a number of associative classification algorithms have been proposed such as Classification based Association (CBA), Classification based on Multiple Association Rules (CMAR), Class based Associative Classification (CACA), and Classification based on Predicted Association Rule (CPAR). This paper surveys major AC algorithms and compares the steps and methods performed in each algorithm including: rule learning, rule sorting, rule pruning, classifier building, and class prediction.

Keywords: Associative Classification, Classification, Data Mining, Learning, Rule Ranking, Rule Pruning, Prediction.

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Authors: Makram Ben Jeddou

Abstract:

ABC classification is widely used by managers for inventory control. The classical ABC classification is based on Pareto principle and according to the criterion of the annual use value only. Single criterion classification is often insufficient for a closely inventory control. Multi-criteria inventory classification models have been proposed by researchers in order to consider other important criteria. From these models, we will consider a specific model in order to make a sensitive analysis on the composite score calculated for each item. In fact, this score, based on a normalized average between a good and a bad optimized index, can affect the ABC-item classification. We will focus on items differently assigned to classes and then propose a classification compromise.

Keywords: ABC classification, Multi criteria inventory classification models, ZF-model.

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Authors: Manvjeet Kaur, Mukhwinder Singh, Akshay Girdhar, Parvinder S. Sandhu

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Most fingerprint recognition techniques are based on minutiae matching and have been well studied. However, this technology still suffers from problems associated with the handling of poor quality impressions. One problem besetting fingerprint matching is distortion. Distortion changes both geometric position and orientation, and leads to difficulties in establishing a match among multiple impressions acquired from the same finger tip. Marking all the minutiae accurately as well as rejecting false minutiae is another issue still under research. Our work has combined many methods to build a minutia extractor and a minutia matcher. The combination of multiple methods comes from a wide investigation into research papers. Also some novel changes like segmentation using Morphological operations, improved thinning, false minutiae removal methods, minutia marking with special considering the triple branch counting, minutia unification by decomposing a branch into three terminations, and matching in the unified x-y coordinate system after a two-step transformation are used in the work.

Keywords: Biometrics, Minutiae, Crossing number, False Accept Rate (FAR), False Reject Rate (FRR).

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Authors: M. Ben Othmen, M. Sayadi, F. Fnaiech

Abstract:

Wavelet transform provides several important characteristics which can be used in a texture analysis and classification. In this work, an efficient texture classification method, which combines concepts from wavelet and co-occurrence matrices, is presented. An Euclidian distance classifier is used to evaluate the various methods of classification. A comparative study is essential to determine the ideal method. Using this conjecture, we developed a novel feature set for texture classification and demonstrate its effectiveness

Keywords: Classification, Wavelet, Co-occurrence, Euclidian Distance, Classifier, Texture.

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Authors: Karim Abouelmehdi, Loubna Dali, Elmoutaoukkil Abdelmajid, Hoda Elsayed Eladnani Fatiha, Benihssane Abderahim

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The security of cloud services is the concern of cloud service providers. In this paper, we will mention different classifications of cloud attacks referred by specialized organizations. Each agency has its classification of well-defined properties. The purpose is to present a high-level classification of current research in cloud computing security. This classification is organized around attack strategies and corresponding defenses.

Keywords: Cloud computing, security, classification, risk.

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Authors: Helyane B. Borges, Julio Cesar Nievola

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Hierarchical classification is a problem with applications in many areas as protein function prediction where the dates are hierarchically structured. Therefore, it is necessary the development of algorithms able to induce hierarchical classification models. This paper presents experimenters using the algorithm for hierarchical classification called Multi-label Hierarchical Classification using a Competitive Neural Network (MHC-CNN). It was tested in ten datasets the Gene Ontology (GO) Cellular Component Domain. The results are compared with the Clus-HMC and Clus-HSC using the hF-Measure.

Keywords: Hierarchical Classification, Competitive Neural Network, Global Classifier.

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