Search results for: personal ID images
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1574

Search results for: personal ID images

854 Transportation Mode Choice Analysis for Accessibility of the Mehrabad International Airport by Statistical Models

Authors: N. Mirzaei Varzeghani, M. Saffarzadeh, A. Naderan, A. Taheri

Abstract:

Countries are progressing, and the world's busiest airports see year-on-year increases in travel demand. Passenger acceptability of an airport depends on the airport's appeals, which may include one of these routes between the city and the airport, as well as the facilities to reach them. One of the critical roles of transportation planners is to predict future transportation demand so that an integrated, multi-purpose system can be provided and diverse modes of transportation (rail, air, and land) can be delivered to a destination like an airport. In this study, 356 questionnaires were filled out in person over six days. First, the attraction of business and non-business trips was studied using data and a linear regression model. Lower travel costs, more passengers aged 55 and older using this airport, and other factors are essential for business trips. Non-business travelers, on the other hand, have prioritized using personal vehicles to get to the airport and ensuring convenient access to the airport. Business travelers are also less price-sensitive than non-business travelers regarding airport travel. Furthermore, carrying additional luggage (for example, more than one suitcase per person) undoubtedly decreases the attractiveness of public transit. Afterward, based on the manner and purpose of the trip, the locations with the highest trip generation to the airport were identified. The most famous district in Tehran was District 2, with 23 visits, while the most popular mode of transportation was an online taxi, with 12 trips from that location. Then, significant variables in separation and behavior of travel methods to access the airport were investigated for all systems. In this scenario, the most crucial factor is the time it takes to get to the airport, followed by the method's user-friendliness as a component of passenger preference. It has also been demonstrated that enhancing public transportation trip times reduces private transportation's market share, including taxicabs. Based on the responses of personal and semi-public vehicles, the desire of passengers to approach the airport via public transportation systems was explored to enhance present techniques and develop new strategies for providing the most efficient modes of transportation. Using the binary model, it was clear that business travelers and people who had already driven to the airport were the least likely to change.

Keywords: Multimodal transportation, travel behavior, demand modeling, statistical models.

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853 One Dimensional Object Segmentation and Statistical Features of an Image for Texture Image Recognition System

Authors: Nang Thwe Thwe Oo

Abstract:

Traditional object segmentation methods are time consuming and computationally difficult. In this paper, onedimensional object detection along the secant lines is applied. Statistical features of texture images are computed for the recognition process. Example matrices of these features and formulae for calculation of similarities between two feature patterns are expressed. And experiments are also carried out using these features.

Keywords: 1-D object segmentation, secant lines, objectoccurrence(frequency) matrix, contiguity matrix, statistical features.

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852 The Role of Creative Thinking in Science Education

Authors: Jindriska Svobodova, Jan Novotny

Abstract:

A teacher’s attitude to creativity plays an essential role in the thinking development of his/her students. The purpose of this study is to understand if a science teacher's personal creativity can modify his/her ability to produce various kinds of questions. This research used an education activity based on cosmic sketches and pictures by K.E. Tsiolkovsky, the founder of astronautics, to explore if any relationship between individual creativity and the asking questions skill exists. As a screening instrument, which allows an assessment of the respondent's creative potential, a common test of creative thinking was used. The results of the creativity test and the diversity of the questions are mentioned.

Keywords: Science education, active learning, physics teaching, creativity.

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851 Design and Modeling of Human Middle Ear for Harmonic Response Analysis

Authors: Shende Suraj Balu, A. B. Deoghare, K. M. Pandey

Abstract:

The human middle ear (ME) is a delicate and vital organ. It has a complex structure that performs various functions such as receiving sound pressure and producing vibrations of eardrum and propagating it to inner ear. It consists of Tympanic Membrane (TM), three auditory ossicles, various ligament structures and muscles. Incidents such as traumata, infections, ossification of ossicular structures and other pathologies may damage the ME organs. The conditions can be surgically treated by employing prosthesis. However, the suitability of the prosthesis needs to be examined in advance prior to the surgery. Few decades ago, this issue was addressed and analyzed by developing an equivalent representation either in the form of spring mass system, electrical system using R-L-C circuit or developing an approximated CAD model. But, nowadays a three-dimensional ME model can be constructed using micro X-Ray Computed Tomography (μCT) scan data. Moreover, the concern about patient specific integrity pertaining to the disease can be examined well in advance. The current research work emphasizes to develop the ME model from the stacks of μCT images which are used as input file to MIMICS Research 19.0 (Materialise Interactive Medical Image Control System) software. A stack of CT images is converted into geometrical surface model to build accurate morphology of ME. The work is further extended to understand the dynamic behaviour of Harmonic response of the stapes footplate and umbo for different sound pressure levels applied at lateral side of eardrum using finite element approach. The pathological condition Cholesteatoma of ME is investigated to obtain peak to peak displacement of stapes footplate and umbo. Apart from this condition, other pathologies, mainly, changes in the stiffness of stapedial ligament, TM thickness and ossicular chain separation and fixation are also explored. The developed model of ME for pathologies is validated by comparing the results available in the literatures and also with the results of a normal ME to calculate the percentage loss in hearing capability.

Keywords: Computed tomography, human middle ear, harmonic response, pathologies, tympanic membrane.

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850 Enhancing the Network Security with Gray Code

Authors: Thomas Adi Purnomo Sidhi

Abstract:

Nowadays, network is an essential need in almost every part of human daily activities. People now can seamlessly connect to others through the Internet. With advanced technology, our personal data now can be more easily accessed. One of many components we are concerned for delivering the best network is a security issue. This paper is proposing a method that provides more options for security. This research aims to improve network security by focusing on the physical layer which is the first layer of the OSI model. The layer consists of the basic networking hardware transmission technologies of a network. With the use of observation method, the research produces a schematic design for enhancing the network security through the gray code converter.

Keywords: Network, network security, gray code, physical layer.

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849 Natural Flickering of Methane Diffusion Flames

Authors: K. R. V. Manikantachari, Vasudevan Raghavan, K. Srinivasan

Abstract:

Present study focuses on studying the oscillatory behavior of jet diffusion flames. At a particular jet exit velocity, the flames are seen to exhibit natural flickering. Initially the flickering process is not continuous. In this transition region as well as in the continuous flickering regime, the flickering displays multiple frequency oscillations. The response of the flame to the exit velocity profile of the burner is also studied using three types of burners. The entire range of natural flickering is investigated by capturing high speed digital images and processing them using a MATLAB code.

Keywords: Diffusion flames, Natural flickering, flickering frequency, intermittent flickering

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848 Monte Carlo and Biophysics Analysis in a Criminal Trial

Authors: Luca Indovina, Carmela Coppola, Carlo Altucci, Riccardo Barberi, Rocco Romano

Abstract:

In this paper a real court case, held in Italy at the Court of Nola, in which a correct physical description, conducted with both a Monte Carlo and biophysical analysis, would have been sufficient to arrive at conclusions confirmed by documentary evidence, is considered. This will be an example of how forensic physics can be useful in confirming documentary evidence in order to reach hardly questionable conclusions. This was a libel trial in which the defendant, Mr. DS (Defendant for Slander), had falsely accused one of his neighbors, Mr. OP (Offended Person), of having caused him some damages. The damages would have been caused by an external plaster piece that would have detached from the neighbor’s property and would have hit Mr DS while he was in his garden, much more than a meter far away from the facade of the building from which the plaster piece would have detached. In the trial, Mr. DS claimed to have suffered a scratch on his forehead, but he never showed the plaster that had hit him, nor was able to tell from where the plaster would have arrived. Furthermore, Mr. DS presented a medical certificate with a diagnosis of contusion of the cerebral cortex. On the contrary, the images of Mr. OP’s security cameras do not show any movement in the garden of Mr. DS in a long interval of time (about 2 hours) around the time of the alleged accident, nor do they show any people entering or coming out from the house of Mr. DS in the same interval of time. Biophysical analysis shows that both the diagnosis of the medical certificate and the wound declared by the defendant, already in conflict with each other, are not compatible with the fall of external plaster pieces too small to be found. The wind was at a level 1 of the Beaufort scale, that is, unable to raise even dust (level 4 of the Beaufort scale). Therefore, the motion of the plaster pieces can be described as a projectile motion, whereas collisions with the building cornice can be treated using Newtons law of coefficients of restitution. Numerous numerical Monte Carlo simulations show that the pieces of plaster would not have been able to reach even the garden of Mr. DS, let alone a distance over 1.30 meters. Results agree with the documentary evidence (images of Mr. OP’s security cameras) that Mr. DS could not have been hit by plaster pieces coming from Mr. OP’s property.

Keywords: Biophysical analysis, Monte Carlo simulations, Newton’s law of restitution, projectile motion.

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847 Design of a DCT-based Image Compression with Efficient Enhancement Filter

Authors: Yen-Yu Chen, Pao-Ching Chu, Ya-Ling Tsai

Abstract:

The algorithm represents the DCT coefficients to concentrate signal energy and proposes combination and dictator to eliminate the correlation in the same level subband for encoding the DCT-based images. This work adopts DCT and modifies the SPIHT algorithm to encode DCT coefficients. The proposed algorithm also provides the enhancement function in low bit rate in order to improve the perceptual quality. Experimental results indicate that the proposed technique improves the quality of the reconstructed image in terms of both PSNR and the perceptual results close to JPEG2000 at the same bit rate.

Keywords: JPEG 2000, enhancement filter

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846 People Counting in Transport Vehicles

Authors: Sebastien Harasse, Laurent Bonnaud, Michel Desvignes

Abstract:

Counting people from a video stream in a noisy environment is a challenging task. This project aims at developing a counting system for transport vehicles, integrated in a video surveillance product. This article presents a method for the detection and tracking of multiple faces in a video by using a model of first and second order local moments. An iterative process is used to estimate the position and shape of multiple faces in images, and to track them. the trajectories are then processed to count people entering and leaving the vehicle.

Keywords: face detection, tracking, counting, local statistics

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845 Comparing SVM and Naïve Bayes Classifier for Automatic Microaneurysm Detections

Authors: A. Sopharak, B. Uyyanonvara, S. Barman

Abstract:

Diabetic retinopathy is characterized by the development of retinal microaneurysms. The damage can be prevented if disease is treated in its early stages. In this paper, we are comparing Support Vector Machine (SVM) and Naïve Bayes (NB) classifiers for automatic microaneurysm detection in images acquired through non-dilated pupils. The Nearest Neighbor classifier is used as a baseline for comparison. Detected microaneurysms are validated with expert ophthalmologists’ hand-drawn ground-truths. The sensitivity, specificity, precision and accuracy of each method are also compared.

Keywords: Diabetic retinopathy, microaneurysm, Naïve Bayes classifier, SVM classifier.

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844 Study of Qualitative and Quantitative Metric for Pixel Factor Mapping and Extended Pixel Mapping Method

Authors: Indradip Banerjee, Souvik Bhattacharyya, Gautam Sanyal

Abstract:

In this paper, an approach is presented to investigate the performance of Pixel Factor Mapping (PFM) and Extended PMM (Pixel Mapping Method) through the qualitative and quantitative approach. These methods are tested against a number of well-known image similarity metrics and statistical distribution techniques. The PFM has been performed in spatial domain as well as frequency domain and the Extended PMM has also been performed in spatial domain through large set of images available in the internet.

Keywords: Qualitative, quantitative, PFM, EXTENDED PMM.

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843 Virtualizing Attendance and Reducing Impacts on the Environment with a Mobile Application

Authors: Paulo R. M. de Andrade, Adriano B. Albuquerque, Otávio F. Frota, Robson V. Silveira, Fátima A. da Silva

Abstract:

Information technology has been gaining more and more space whether in industry, commerce or even for personal use, but the misuse of it brings harm to the environment and human health as a result. Contribute to the sustainability of the planet is to compensate the environment, all or part of what withdraws it. The green computing also came to propose practical for use in IT in an environmentally correct way in aid of strategic management and communication. This work focuses on showing how a mobile application can help businesses reduce costs and reduced environmental impacts caused by its processes, through a case study of a public company in Brazil.

Keywords: E-government, green computing, information technology, mobile computing, sustainable development.

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842 Fast Depth Estimation with Filters

Authors: Yiming Nie, Tao Wu, Xiangjing An, Hangen He

Abstract:

Fast depth estimation from binocular vision is often desired for autonomous vehicles, but, most algorithms could not easily be put into practice because of the much time cost. We present an image-processing technique that can fast estimate depth image from binocular vision images. By finding out the lines which present the best matched area in the disparity space image, the depth can be estimated. When detecting these lines, an edge-emphasizing filter is used. The final depth estimation will be presented after the smooth filter. Our method is a compromise between local methods and global optimization.

Keywords: Depth estimation, image filters, stereo match.

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841 Adaptive Skin Segmentation Using Color Distance Map

Authors: Mohammad Shoyaib, M. Abdullah-Al-Wadud, Oksam Chae

Abstract:

In this paper an effective approach for segmenting human skin regions in images taken at different environment is proposed. The proposed method uses a color distance map that is flexible enough to reliably detect the skin regions even if the illumination conditions of the image vary. Local image conditions is also focused, which help the technique to adaptively detect differently illuminated skin regions of an image. Moreover, usage of local information also helps the skin detection process to get rid of picking up much noisy pixels.

Keywords: Color Distance map, Reference skin color, Regiongrowing, Skin segmentation.

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840 Medical Imaging Techniques in Clinical Medicine

Authors: Sharan Badiger, Prema T. Akkasaligar

Abstract:

Medical imaging technology has experienced a dramatic change in the last few years. Medical imaging refers to the techniques and processes used to create images of the human body (or parts thereof) for various clinical purposes such as medical procedures and diagnosis or medical science including the study of normal anatomy and function. With the growth of computers and image technology, medical imaging has greatly influenced the medical field. The diagnosis of a health problem is now highly dependent on the quality and the credibility of the image analysis. This paper deals with the various aspects and types of medical imaging.

Keywords: Computed Tomography, Echocardiography, Medical Imaging, Magnetic Resonance, Ultrasound Imaging.

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839 Liveness Detection for Embedded Face Recognition System

Authors: Hyung-Keun Jee, Sung-Uk Jung, Jang-Hee Yoo

Abstract:

To increase reliability of face recognition system, the system must be able to distinguish real face from a copy of face such as a photograph. In this paper, we propose a fast and memory efficient method of live face detection for embedded face recognition system, based on the analysis of the movement of the eyes. We detect eyes in sequential input images and calculate variation of each eye region to determine whether the input face is a real face or not. Experimental results show that the proposed approach is competitive and promising for live face detection.

Keywords: Liveness Detection, Eye detection, SQI.

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838 Face Recognition Using Eigen face Coefficients and Principal Component Analysis

Authors: Parvinder S. Sandhu, Iqbaldeep Kaur, Amit Verma, Samriti Jindal, Inderpreet Kaur, Shilpi Kumari

Abstract:

Face Recognition is a field of multidimensional applications. A lot of work has been done, extensively on the most of details related to face recognition. This idea of face recognition using PCA is one of them. In this paper the PCA features for Feature extraction are used and matching is done for the face under consideration with the test image using Eigen face coefficients. The crux of the work lies in optimizing Euclidean distance and paving the way to test the same algorithm using Matlab which is an efficient tool having powerful user interface along with simplicity in representing complex images.

Keywords: Eigen Face, Multidimensional, Matching, PCA.

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837 Off-Line Signature Recognition Based On Angle Features and GRNN Neural Networks

Authors: Laila Y. Fannas, Ahmed Y. Ben Sasi

Abstract:

This research presents a handwritten signature recognition based on angle feature vector using Artificial Neural Network (ANN). Each signature image will be represented by an Angle vector. The feature vector will constitute the input to the ANN. The collection of signature images will be divided into two sets. One set will be used for training the ANN in a supervised fashion. The other set which is never seen by the ANN will be used for testing. After training, the ANN will be tested for recognition of the signature. When the signature is classified correctly, it is considered correct recognition otherwise it is a failure.

Keywords: Signature Recognition, Artificial Neural Network, Angle Features.

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836 A Temporal Synchronization Model for Heterogeneous Data in Distributed Systems

Authors: Jorge Estudillo Ramirez, Saul E. Pomares Hernandez

Abstract:

Multimedia distributed systems deal with heterogeneous data, such as texts, images, graphics, video and audio. The specification of temporal relations among different data types and distributed sources is an open research area. This paper proposes a fully distributed synchronization model to be used in multimedia systems. One original aspect of the model is that it avoids the use of a common reference (e.g. wall clock and shared memory). To achieve this, all possible multimedia temporal relations are specified according to their causal dependencies.

Keywords: Multimedia, Distributed Systems, Partial Ordering, Temporal Synchronization

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835 Chinese Tourists’s Behaviors towards Travel and Shopping in Bangkok

Authors: Sasitorn Chetanont

Abstract:

The objectives of this study are to study Chinese tourist’s Behaviors towards travel and shopping in Bangkok. The research methodology was a quantitative research. The sample of this research was 400 Chinese tourists in Bangkok chosen by the accidental sampling and the purposive sampling. Inferential Statistics Analysis by using the Chi-square statistics. As for the results of this study the researcher found that differences between personal, social and cultural information, i.e., gender, age, place of residence, educational level, occupation, income, family, and main objectives of tourism with behaviors of Chinese tourists in Bangkok towards travel and shopping in Bangkok.

Keywords: Tourists’ behavior, Chinese tourists, travelling, expenses in travels.

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834 A System Functions Set-Up through Near Field Communication of a Smartphone

Authors: Jaemyoung Lee

Abstract:

We present a method to set up system functions through a near filed communication (NFC) of a smartphone. The short communication distance of the NFC which is usually less than 4 cm could prevent any interferences from other devices and establish a secure communication channel between a system and the smartphone. The proposed set-up method for system function values is demonstrated for a blacbox system in a car. In demonstration, system functions of a blackbox which is manipulated through NFC of a smartphone are controls of image quality, sound level, shock sensing level to store images, etc. The proposed set-up method for system function values can be used for any devices with NFC.

Keywords: System set-up, near field communication, smartphone, Android.

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833 Independent Encryption Technique for Mobile Voice Calls

Authors: Nael Hirzalla

Abstract:

The legality of some countries or agencies’ acts to spy on personal phone calls of the public became a hot topic to many social groups’ talks. It is believed that this act is considered an invasion to someone’s privacy. Such act may be justified if it is singling out specific cases but to spy without limits is very unacceptable. This paper discusses the needs for not only a simple and light weight technique to secure mobile voice calls but also a technique that is independent from any encryption standard or library. It then presents and tests one encrypting algorithm that is based of Frequency scrambling technique to show fair and delay-free process that can be used to protect phone calls from such spying acts.

Keywords: Frequency Scrambling, Mobile Applications, Real- Time Voice Encryption, Spying on Calls.

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832 Automatic Checkpoint System Using Face and Card Information

Authors: Kriddikorn Kaewwongsri, Nikom Suvonvorn

Abstract:

In the deep south of Thailand, checkpoints for people verification are necessary for the security management of risk zones, such as official buildings in the conflict area. In this paper, we propose an automatic checkpoint system that verifies persons using information from ID cards and facial features. The methods for a person’s information abstraction and verification are introduced based on useful information such as ID number and name, extracted from official cards, and facial images from videos. The proposed system shows promising results and has a real impact on the local society.

Keywords: Face comparison, card recognition, OCR, checkpoint system, authentication.

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831 Thai Halal Products Brand Tips

Authors: Pibool Waijittragum

Abstract:

The purpose of this research is to analyze the marketing strategies of Thai Halal products which related to the way of life for Thai Muslims. The expected benefit is the marketing strategy for brand building process for Halal products in Thailand. 4 elements of marketing strategies which necessary for the brand identity creation is the research framework: consists of Attributes, Benefits, Values and Personality. The research methodology was applied using qualitative and quantitative; 19 marketing experts with dynamic roles in Thai consumer products were interviewed. In addition, a field survey of 122 Thai Muslims selected from 175 Muslim communities in Bangkok was studied. Data analysis will be according to 5 categories of Thai Halal product: 1) Meat 2) Vegetable and Fruits 3) Instant foods and Garnishing ingredient 4) Beverages, Desserts and Snacks 5) Hygienic daily products; such as soap, shampoo and body lotion. The results will explain some suitable representation in the marketing strategies of Thai Halal products as are: 1) Benefit; the characteristics of the product with its benefit. Consumers will purchase this product with the reason of; it is beneficial nutrients product, there are no toxic or chemical residues. Fresh and clean materials 2) Attribute; the exterior images that attract to consumer. Consumers will purchase this product with the reason of; there is a standard proof mark, food and drug secure proof mark and Halal products mark. Packaging and its materials should be draw attention. Use an attractive graphic. Use outstanding images of product, material or ingredients. 3) Value; the value of products that affect to consumers perception; it is healthy products. Accumulate quality of life. It is a product of expertise, manufacturing of research result. Consumers are important. It’s sincere, honest and reliable to all. 4) Personality; reflection of consumers thought. The Personality feedback to them after they were consumes this product; they are health care persons. They are the rational person, moral person, justice person and thoughtful person like a progressive thinking.

Keywords: Marketing strategies, Product identity, Branding, Thai Halal products.

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830 Infrared Face Recognition Using Distance Transforms

Authors: Moulay A. Akhloufi, Abdelhakim Bendada

Abstract:

In this work we present an efficient approach for face recognition in the infrared spectrum. In the proposed approach physiological features are extracted from thermal images in order to build a unique thermal faceprint. Then, a distance transform is used to get an invariant representation for face recognition. The obtained physiological features are related to the distribution of blood vessels under the face skin. This blood network is unique to each individual and can be used in infrared face recognition. The obtained results are promising and show the effectiveness of the proposed scheme.

Keywords: Face recognition, biometrics, infrared imaging.

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829 MovieReco: A Recommendation System

Authors: Dipankaj G Medhi, Juri Dakua

Abstract:

Recommender Systems act as personalized decision guides, aiding users in decisions on matters related to personal taste. Most previous research on Recommender Systems has focused on the statistical accuracy of the algorithms driving the systems, with no emphasis on the trustworthiness of the user. RS depends on information provided by different users to gather its knowledge. We believe, if a large group of users provide wrong information it will not be possible for the RS to arrive in an accurate conclusion. The system described in this paper introduce the concept of Testing the knowledge of user to filter out these “bad users". This paper emphasizes on the mechanism used to provide robust and effective recommendation.

Keywords: Collaborative Filtering, Content Based Filtering, Intelligent Agent, Level of Interest, Recommendation System.

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828 Grid Artifacts Suppression in Computed Radiographic Images

Authors: Igor Belykh

Abstract:

Anti-scatter grids used in radiographic imaging for the contrast enhancement leave specific artifacts. Those artifacts may be visible or may cause Moiré effect when digital image is resized on a diagnostic monitor. In this paper we propose an automated grid artifactsdetection and suppression algorithm which is still an actual problem. Grid artifacts detection is based on statistical approach in spatial domain. Grid artifacts suppression is based on Kaiser bandstop filter transfer function design and application avoiding ringing artifacts. Experimental results are discussed and concluded with description of advantages over existing approaches.

Keywords: Computed radiography, grid artifacts, image filtering.

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827 Identification of Printed Punjabi Words and English Numerals Using Gabor Features

Authors: Rajneesh Rani, Renu Dhir, G. S. Lehal

Abstract:

Script identification is one of the challenging steps in the development of optical character recognition system for bilingual or multilingual documents. In this paper an attempt is made for identification of English numerals at word level from Punjabi documents by using Gabor features. The support vector machine (SVM) classifier with five fold cross validation is used to classify the word images. The results obtained are quite encouraging. Average accuracy with RBF kernel, Polynomial and Linear Kernel functions comes out to be greater than 99%.

Keywords: Script identification, gabor features, support vector machines.

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826 Improved Posterized Color Images based on Color Quantization and Contrast Enhancement

Authors: Oh-Yeol Kwon, Sung-Il Chien

Abstract:

A conventional image posterization method occasionally fails to preserve the shape and color of objects due to the uneffective color reduction. This paper proposes a new image posterizartion method by using modified color quantization for preserving the shape and color of objects and color contrast enhancement for improving lightness contrast and saturation. Experiment results show that our proposed method can provide visually more satisfactory posterization result than that of the conventional method.

Keywords: Color contrast enhancement, color quantization, color segmentation, image posterization

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825 Multiplicative Functional on Upper Triangular Fuzzy Matrices

Authors: Liu Ping

Abstract:

In this paper, for an arbitrary multiplicative functional f from the set of all upper triangular fuzzy matrices to the fuzzy algebra, we prove that there exist a multiplicative functional F and a functional G from the fuzzy algebra to the fuzzy algebra such that the image of an upper triangular fuzzy matrix under f can be represented as the product of all the images of its main diagonal elements under F and other elements under G.

Keywords: Multiplicative functional, triangular fuzzy matrix, fuzzy addition operation, fuzzy multiplication operation.

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