Search results for: differential images

Authors: Nadia M. G. AL-Sa'idi, Muhammad Rushdan Md. Sd., Adil M. Ahmed

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The IFS is a scheme for describing and manipulating complex fractal attractors using simple mathematical models. More precisely, the most popular “fractal –based" algorithms for both representation and compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces. In this paper a new generalized space called Multi-Fuzzy Fractal Space was constructed. On these spases a distance function is defined, and its completeness is proved. The completeness property of this space ensures the existence of a fixed-point theorem for the family of continuous mappings. This theorem is the fundamental result on which the IFS methods are based and the fractals are built. The defined mappings are proved to satisfy some generalizations of the contraction condition.

Keywords: Fuzzy metric space, Fuzzy fractal space, Multi fuzzy fractal space.

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Authors: Khaled Harrar, Rachid Jennane

Abstract:

The purpose of this study is the discrimination of 28 postmenopausal with osteoporotic femoral fractures from an agematched control group of 28 women using texture analysis based on fractals. Two pre-processing approaches are applied on radiographic images; these techniques are compared to highlight the choice of the pre-processing method. Furthermore, the values of the fractal dimension are compared to those of the fractal signature in terms of the classification of the two populations. In a second analysis, the BMD measure at proximal femur was compared to the fractal analysis, the latter, which is a non-invasive technique, allowed a better discrimination; the results confirm that the fractal analysis of texture on calcaneus radiographs is able to discriminate osteoporotic patients with femoral fracture from controls. This discrimination was efficient compared to that obtained by BMD alone. It was also present in comparing subgroups with overlapping values of BMD.

Keywords: Osteoporosis, fractal dimension, fractal signature, bone mineral density.

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Authors: J. Ierache, N. A. Mangiarua, S. A. Bevacqua, N. N. Verdicchio, M. E. Becerra, D. R. Sanz, M. E. Sena, F. M. Ortiz, N. D. Duarte, S. Igarza

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Augmented Reality is a technology that involves the overlay of virtual content, which is context or environment sensitive, on images of the physical world in real time. This paper presents the development of a catalog system that facilitates and allows the creation, publishing, management and exploitation of augmented multimedia contents and Augmented Reality applications, creating an own space for anyone that wants to provide information to real objects in order to edit and share it then online with others. These spaces would be built for different domains without the initial need of expert users. Its operation focuses on the context of Web 2.0 or Social Web, with its various applications, developing contents to enrich the real context in which human beings act permitting the evolution of catalog’s contents in an emerging way.

Keywords: Augmented Reality, Catalog System, Computer Graphics, Mobile Application.

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Authors: B.W. Field

Abstract:

For a variety of safety and economic reasons, engineering undergraduates in Australia have experienced diminishing access to the real hardware that is typically the embodiment of their theoretical studies. This trend will delay the development of practical competence, decrease the ability to model and design, and suppress motivation. The author has attempted to address this concern by creating a software tool that contains both photographic images of real machinery, and sets of graphical modeling 'tools'. Academics from a range of disciplines can use the software to set tutorial tasks, and incorporate feedback comments for a range of student responses. An evaluation of the software demonstrated that students who had solved modeling problems with the aid of the electronic tutor performed significantly better in formal examinations with similar problems. The 2-D graphical diagnostic routines in the Tutor have the potential to be used in a wider range of problem-solving tasks.

Keywords: CAL, graphics, modeling, structural distillation, tutoring.

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Authors: Houda Bdiri Gabbouj, Néjib Hassen, Kamel Besbes

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This paper presents a low-voltage low-power differential linear transconductor with near rail-to-rail input swing. Based on the current-mirror OTA topology, the proposed transconductor combines the Flipped Voltage Follower (FVF) technique to linearize the transconductor behavior that leads to class- AB linear operation and the virtual transistor technique to lower the effective threshold voltages of the transistors which offers an advantage in terms of low supply requirement. Design of the OTA has been discussed. It operates at supply voltages of about ±0.8V. Simulation results for 0.18μm TSMC CMOS technology show a good input range of 1Vpp with a high DC gain of 81.53dB and a total harmonic distortion of -40dB at 1MHz for an input of 1Vpp. The main aim of this paper is to present and compare new OTA design with high transconductance, which has a potential to be used in low voltage applications.

Keywords: Amplifier class AB, current mirror, flipped voltage follower, low voltage.

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Authors: Hafizuddin W. Yussof, Syamsutajri S. Bahri, Adam P. Harvey

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Strong anion exchange resins with QN+OH-, have the potential to be developed and employed as heterogeneous catalyst for transesterification, as they are chemically stable to leaching of the functional group. Nine different SIERs (SIER1-9) with QN+OH-were prepared by suspension polymerization of vinylbenzyl chloridedivinylbenzene (VBC-DVB) copolymers in the presence of n-heptane (pore-forming agent). The amine group was successfully grafted into the polymeric resin beads through functionalization with trimethylamine. These SIERs are then used as a catalyst for the transesterification of triacetin with methanol. A set of differential equations that represents the Langmuir-Hinshelwood-Hougen- Watson (LHHW) and Eley-Rideal (ER) models for the transesterification reaction were developed. These kinetic models of LHHW and ER were fitted to the experimental data. Overall, the synthesized ion exchange resin-catalyzed reaction were welldescribed by the Eley-Rideal model compared to LHHW models, with sum of square error (SSE) of 0.742 and 0.996, respectively.

Keywords: Anion exchange resin, Eley-Rideal, Langmuir-Hinshelwood-Hougen-Watson, transesterification.

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Authors: Bhatti A., Nahavandi S., Hossny M.

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Current advancements in nanotechnology are dependent on the capabilities that can enable nano-scientists to extend their eyes and hands into the nano-world. For this purpose, a haptics (devices capable of recreating tactile or force sensations) based system for AFM (Atomic Force Microscope) is proposed. The system enables the nano-scientists to touch and feel the sample surfaces, viewed through AFM, in order to provide them with better understanding of the physical properties of the surface, such as roughness, stiffness and shape of molecular architecture. At this stage, the proposed work uses of ine images produced using AFM and perform image analysis to create virtual surfaces suitable for haptics force analysis. The research work is in the process of extension from of ine to online process where interaction will be done directly on the material surface for realistic analysis.

Keywords: Haptics, AFM, force feedback, image analysis.

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Authors: B. Bagheri Nakhjavanlo, T. J. Ellis, P. Raoofi, J. Dehmeshki

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This paper presents a customized deformable model for the segmentation of abdominal and thoracic aortic aneurysms in CTA datasets. An important challenge in reliably detecting aortic aneurysm is the need to overcome problems associated with intensity inhomogeneities and image noise. Level sets are part of an important class of methods that utilize partial differential equations (PDEs) and have been extensively applied in image segmentation. A Gaussian kernel function in the level set formulation, which extracts the local intensity information, aids the suppression of noise in the extracted regions of interest and then guides the motion of the evolving contour for the detection of weak boundaries. The speed of curve evolution has been significantly improved with a resulting decrease in segmentation time compared with previous implementations of level sets. The results indicate the method is more effective than other approaches in coping with intensity inhomogeneities.

Keywords: Abdominal and thoracic aortic aneurysms, intensityinhomogeneity, level sets, local fitting binary.

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Authors: P. C. Tewari, Parveen Kumar

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The paper describes the availability analysis of milling system of a rice milling plant using probabilistic approach. The subsystems under study are special purpose machines. The availability analysis of the system is carried out to determine the effect of failure and repair rates of each subsystem on overall performance (i.e. steady state availability) of system concerned. Further, on the basis of effect of repair rates on the system availability, maintenance repair priorities have been suggested. The problem is formulated using Markov Birth-Death process taking exponential distribution for probable failures and repair rates. The first order differential equations associated with transition diagram are developed by using mnemonic rule. These equations are solved using normalizing conditions and recursive method to drive out the steady state availability expression of the system. The findings of the paper are presented and discussed with the plant personnel to adopt a suitable maintenance policy to increase the productivity of the rice milling plant.

Keywords: Markov process, milling system, availability modeling, rice milling plant.

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Authors: Fahmi Kammoun, Mohamed Salim Bouhlel

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In the framework of the image compression by Wavelet Transforms, we propose a perceptual method by incorporating Human Visual System (HVS) characteristics in the quantization stage. Indeed, human eyes haven-t an equal sensitivity across the frequency bandwidth. Therefore, the clarity of the reconstructed images can be improved by weighting the quantization according to the Contrast Sensitivity Function (CSF). The visual artifact at low bit rate is minimized. To evaluate our method, we use the Peak Signal to Noise Ratio (PSNR) and a new evaluating criteria witch takes into account visual criteria. The experimental results illustrate that our technique shows improvement on image quality at the same compression ratio.

Keywords: Contrast Sensitivity Function, Human Visual System, Image compression, Wavelet transforms.

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Authors: Khalid Salhi, El Miloud Jaara, Mohammed Talibi Alaoui

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In this paper, we present a neural approach for unsupervised natural color-texture image segmentation, which is based on both Kohonen maps and mathematical morphology, using a combination of the texture and the image color information of the image, namely, the fractal features based on fractal dimension are selected to present the information texture, and the color features presented in RGB color space. These features are then used to train the network Kohonen, which will be represented by the underlying probability density function, the segmentation of this map is made by morphological watershed transformation. The performance of our color-texture segmentation approach is compared first, to color-based methods or texture-based methods only, and then to k-means method.

Keywords: Segmentation, color-texture, neural networks, fractal, watershed.

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Authors: Tan Wee Choon, Abdul Saad Salleh, Saifulnizan Jamian, Mohd. Imran Ghazali

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Phase transformation temperature is one of the most important parameters for the shape memory alloys (SMAs). The most popular method to determine these phase transformation temperatures is the Differential Scanning Calorimeter (DSC), but due to the limitation of the DSC testing itself, it made it difficult for the finished product which is not in the powder form. A novel method which uses the Universal Testing Machine has been conducted to determine the phase transformation temperatures. The Flexinol wire was applied with force and maintained throughout the experiment and at the same time it was heated up slowly until a temperature of approximately 1000C with direct current. The direct current was then slowly decreased to cool down the temperature of the Flexinol wire. All the phase transformation temperatures for Flexinol wire were obtained. The austenite start at 52.540C and austenite finish at 60.900C, while martensite start at 44.780C and martensite finish at 32.840C.

Keywords: Phase transformation temperature, Robotic, Shapememory alloy, Universal Testing Machine.

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Authors: Ronit Chakraborty, Sugata Banerji

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There has been a marked increase in the reported prevalence of Autism Spectrum Disorder (ASD) among children in the US over the past two decades. This research has analyzed the growth in state-level ASD prevalence against 45 different potentially explanatory factors including socio-economic, demographic, healthcare, public policy and political factors. The goal was to understand if these factors have adequate predictive power in modeling the differential growth in ASD prevalence across various states, and, if they do, which factors are the most influential. The key findings of this study include (1) there is a confirmation that the chosen feature set has considerable power in predicting the growth in ASD prevalence, (2) the most influential predictive factors are identified, (3) given the nature of the most influential predictive variables, an indication that a considerable portion of the reported ASD prevalence differentials across states could be attributable to over and under diagnosis, and (4) Florida is identified as a key outlier state pointing to a potential under-diagnosis of ASD.

Keywords: Autism Spectrum Disorder, ASD, clustering, Machine Learning, predictive modeling.

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Authors: Milorad Pavlovic, Anna Manzato, Antonella Cecchi

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Cultural heritage conservation is a challenge for contemporary society. In recent decades, significant resources have been allocated for the conservation and restoration of architectural heritage. Historical buildings were restored, protected and reinforced with the intent to limit the risks of degradation or loss, due to phenomena of structural damage and to external factors such as differential settlements, earthquake effects, etc. The wide diffusion of historic masonry constructions in Italy, Europe and the Mediterranean area requires reliable tools for the evaluation of their structural safety. In this paper is presented a free modal analysis performed on a minor historical architecture located in the village of Bagno Grande, near the city of L’Aquila in Italy. The location is characterized by a complex urban context, seriously damaged by the earthquake of 2009. The aim of this work is to check the structural behavior of a masonry building characterized by several boundary conditions imposed by adjacent buildings and infrastructural facilities.

Keywords: FEM, masonry, minor historical architecture, modal analysis.

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Authors: Moung Young Lee, Chul Gyu Song

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Photoacoustic imaging is the imaging technology that combines the optical imaging and ultrasound. This provides the high contrast and resolution due to optical imaging and ultrasound imaging, respectively. We developed the real-time photoacoustic tomography (PAT) system using linear-ultrasound transducer and digital acquisition (DAQ) board. There are two types of algorithm for reconstructing the photoacoustic signal. One is back-projection algorithm, the other is FFT algorithm. Especially, we used the non-uniform FFT algorithm. To evaluate the performance of our system and algorithms, we monitored two wires that stands at interval of 2.89 mm and 0.87 mm. Then, we compared the images reconstructed by algorithms. Finally, we monitored the two hairs crossed and compared between these algorithms.

Keywords: Back-projection, image comparison, non-uniform FFT, photoacoustic tomography.

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Authors: Mercan Efe Güney, Barış Parlatangiller, Melik Ayer

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In Turkey, while urban area boundaries are enlarged by making decisions on investment areas in cities, development plans are made according to government decisions, rather than scientific criteria. Even environment protection laws state that “if public interest is at stake”, areas under mandatory protection can be transformed into investment areas. This leads to destruction of valuable agricultural lands. Paper demonstrates loss of agricultural lands by superimposing plans, Suitability of the Lands for Agricultural Use and Google Earth Images in an exemplary settlement, and expresses that urban area boundaries should be included in legislation as an official boundary for all settlements.

Keywords: Agriculture, boundary, city planning, development plan, legislation.

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Authors: A. C. Sarmah

Abstract:

The Al-MoO3-P-CdTe-Al MOS sandwich structures were fabricated by vacuum deposition method on cleaned glass substrates. Capacitance versus voltage measurements were performed at different frequencies and sweep rates of applied voltages for oxide and semiconductor films of different thicknesses. In the negative voltage region of the C-V curve a high differential capacitance of the semiconductor was observed and at high frequencies (<10 kHz) the transition from accumulation to depletion and further to deep depletion was observed as the voltage was swept from negative to positive. A study have been undertaken to determine the value of acceptor density and some depletion layer parameters such as depletion layer capacitance, depletion width, impurity concentration, flat band voltage, Debye length, flat band capacitance, diffusion or built-in-potential, space charge per unit area etc. These were determined from C-V measurements for different oxide and semiconductor thicknesses.

Keywords: Debye length, Depletion width, flat band capacitance, impurity concentration.

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Authors: Bogdan Il. Bogdanov, Plamen S. Pashev, Yancho H. Hristov, Dimitar P.Georgiev, Irena G. Markovska

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The crystallization kinetics and phase transformation of SiO2.Al2O3.0,56P2O5.1,8CaO.0,56CaF2 glass have been investigated using differential thermal analysis (DTA), x-ray diffraction (XRD), and scanning electron microscopy (SEM). Glass samples were obtained by melting the glass mixture at 14500С/120 min. in platinum crucibles. The mixture were prepared from chemically pure reagents: SiO2, Al(OH)3, H3PO4, CaCO3 and CaF2. The non-isothermal kinetics of crystallization was studied by applying the DTA measurements carried out at various heating rates. The activation energies of crystallization and viscous flow were measured as 348,4 kJ.mol–1 and 479,7 kJ.mol–1 respectively. Value of Avrami parameter n ≈ 3 correspond to a three dimensional of crystal growth mechanism. The major crystalline phase determined by XRD analysis was fluorapatite (Ca(PO4)3F) and as the minor phases – fluormargarite (CaAl2(Al2SiO2)10F2) and vitlokite (Ca9P6O24). The resulting glass-ceramic has a homogeneous microstructure, composed of prismatic crystals, evenly distributed in glass phase.

Keywords: glass-ceramic, crystallization, non-isothermalkinetics, Avrami parameter

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Authors: So-Jeong Youn, Kyung-Whan Oh

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The human friendly interaction is the key function of a human-centered system. Over the years, it has received much attention to develop the convenient interaction through intention recognition. Intention recognition processes multimodal inputs including speech, face images, and body gestures. In this paper, we suggest a novel approach of intention recognition using a graph representation called Intention Graph. A concept of valid intention is proposed, as a target of intention recognition. Our approach has two phases: goal recognition phase and intention recognition phase. In the goal recognition phase, we generate an action graph based on the observed actions, and then the candidate goals and their plans are recognized. In the intention recognition phase, the intention is recognized with relevant goals and user profile. We show that the algorithm has polynomial time complexity. The intention graph is applied to a simple briefcase domain to test our model.

Keywords: Intention recognition, intention, graph, HCI.

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Authors: P. Phokharatkul, S. Chaisriya, S. Somkuarnpanit, S. Phaiboon, C. Kimpan

Abstract:

This paper proposes a new method for image searches and image indexing in databases with a color temperature histogram. The color temperature histogram can be used for performance improvement of content–based image retrieval by using a combination of color temperature and histogram. The color temperature histogram can be represented by a range of 46 colors. That is more than the color histogram and the dominant color temperature. Moreover, with our method the colors that have the same color temperature can be separated while the dominant color temperature can not. The results showed that the color temperature histogram retrieved an accurate image more often than the dominant color temperature method or color histogram method. This also took less time so the color temperature can be used for indexing and searching for images.

Keywords: Color temperature histogram, color temperature, animage retrieval and content-based image retrieval.

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Authors: Salim Istyaq, Mohammad Sarosh Umar

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Today, the mankind is in the stage of development, every day comes with new proposal of technology, in order to secure these types of technology, we also prepare high yielding security modules to conserve these resources. The capacity of human brain to recognize anything is far more than any species; this is all due to our developing cycle of curiosity. In this paper, we proposed a scheme based on graphical password using QR Code which provides more security to the recent online system. It also contains a supportive sound signature. In this system, authentication is done using sequence of images in QR code form. Users select one click-point per image with the help of QR scanner or recognizer. The encoded phrase in a QR code emphasizes the minimum probability of attacking via shoulder surfing or other attacks.

Keywords: Graphical password, QR code, sound signature, image authentication, cued click point.

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Authors: Yanyan Xu, Lizhi Xiong, Zhengquan Xu, Li Jiang

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In order to protect data privacy, image with sensitive or private information needs to be encrypted before being outsourced to the cloud. However, this causes difficulties in image retrieval and data management. A secure image retrieval method based on orthogonal decomposition is proposed in the paper. The image is divided into two different components, for which encryption and feature extraction are executed separately. As a result, cloud server can extract features from an encrypted image directly and compare them with the features of the queried images, so that the user can thus obtain the image. Different from other methods, the proposed method has no special requirements to encryption algorithms. Experimental results prove that the proposed method can achieve better security and better retrieval precision.

Keywords: Secure image retrieval, secure search, orthogonal decomposition, secure cloud computing.

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Authors: P. Meesuk, T. Kulworawanichpong, P. Pao-la-or

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This paper proposes a set of quasi-static mathematical model of magnetic fields caused by high voltage conductors of distribution transformer by using a set of second-order partial differential equation. The modification for complex magnetic field analysis and time-harmonic simulation are also utilized. In this research, transformers were study in both balanced and unbalanced loading conditions. Computer-based simulation utilizing the threedimensional finite element method (3-D FEM) is exploited as a tool for visualizing magnetic fields distribution volume a distribution transformer. Finite Element Method (FEM) is one among popular numerical methods that is able to handle problem complexity in various forms. At present, the FEM has been widely applied in most engineering fields. Even for problems of magnetic field distribution, the FEM is able to estimate solutions of Maxwell-s equations governing the power transmission systems. The computer simulation based on the use of the FEM has been developed in MATLAB programming environment.

Keywords: Distribution Transformer, Magnetic Field, Load Unbalance, 3-D Finite Element Method (3-D FEM)

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Authors: Barenten Suciu

Abstract:

In this paper, a theoretical study on the forced vibration of one degree of freedom system equipped with inerter, working under load-type or displacement-type excitation, is presented. Differential equations of movement are solved under cosinusoidal excitation, and explicit relations for the magnitude, resonant magnitude, phase angle, resonant frequency, and critical frequency are obtained. Influence of the inertance and damping on these dynamic characteristics is clarified. From the obtained results, one concludes that the inerter increases the magnitude of vibration and the phase angle of the damped mechanical system. Moreover, the magnitude ratio and difference of phase angles are not depending on the actual type of excitation. Consequently, such kind of similitude allows for the comparison of various theoretical and experimental results, which can be broadly found in the literature.

Keywords: One degree of freedom vibration, inerter, parallel connection, load-type excitation, displacement-type excitation.

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Authors: Nikhat Nawaz, S. Srinivasulu, P. Kesava Rao

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Feature extraction plays an important role in many remote sensing applications. Automatic extraction of water bodies is of great significance in many remote sensing applications like change detection, image retrieval etc. This paper presents a procedure for automatic extraction of water information from remote sensing images. The algorithm uses the relative location of R color component of the chromaticity diagram. This method is then integrated with the effectiveness of the spatial scale transformation of whole method. The whole method is based on water index fitted from spectral library. Experimental results demonstrate the improved accuracy and effectiveness of the integrated method for automatic extraction of water bodies.

Keywords: Chromaticity, Feature Extraction, Remote Sensing, Spectral library, Water Index.

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Authors: Sang Hoon Lee, Jong Sue Bae, Taewan Kim, Jin Mo Song, Jong Ju Kim

Abstract:

Image target detection and tracking methods based on target information such as intensity, shape model, histogram and target dynamics have been proven to be robust to target model variations and background clutters as shown by recent researches. However, no definitive answer has been given to occluded target by counter measure or limited field of view(FOV). In this paper, we will present a novel tracking method using filtering and computational geometry. This paper has two central goals: 1) to deal with vulnerable target measurements; and 2) to maintain target tracking out of FOV using non-target-originated information. The experimental results, obtained with airborne images, show a robust tracking ability with respect to the existing approaches. In exploring the questions of target tracking, this paper will be limited to consideration of airborne image.

Keywords: Tracking, Computational geometry, Homography, Filter

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Authors: Hatam H. Ali, Mohd Shahrizal Sunar, Hoshang Kolivand, Mohd Azhar Bin M. Arsad

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Rendering light shafts is one of the important topics in computer gaming and interactive applications. The methods and models that are used to generate light shafts play crucial role to make a scene more realistic in computer graphics. This article discusses the image-based shadows and geometric-based shadows that contribute in generating volumetric shadows and light shafts, depending on ray tracing, radiosity, and ray marching technique. The main aim of this study is to provide researchers with background on a progress of light scattering methods so as to make it available for them to determine the technique best suited to their goals. It is also hoped that our classification helps researchers find solutions to the shortcomings of each method.

Keywords: Shaft of lights, realistic images, image-based, and geometric-based.

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Authors: Doraid Dalalah

Abstract:

A topologically oriented neural network is very efficient for real-time path planning for a mobile robot in changing environments. When using a recurrent neural network for this purpose and with the combination of the partial differential equation of heat transfer and the distributed potential concept of the network, the problem of obstacle avoidance of trajectory planning for a moving robot can be efficiently solved. The related dimensional network represents the state variables and the topology of the robot's working space. In this paper two approaches to problem solution are proposed. The first approach relies on the potential distribution of attraction distributed around the moving target, acting as a unique local extreme in the net, with the gradient of the state variables directing the current flow toward the source of the potential heat. The second approach considers two attractive and repulsive potential sources to decrease the time of potential distribution. Computer simulations have been carried out to interrogate the performance of the proposed approaches.

Keywords: Mobile robot, Path Planning, Mesh, Potential field.

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Authors: Ping Yuan, Mu-Sheng Chiang, Syu-Fang Liu, Shih-Bin Wang, Ming-Jun Kuo

Abstract:

This study investigates the electrical performance of a planar solid oxide fuel cell unit with cross-flow configuration when the fuel utilization gets higher and the fuel inlet flow are non-uniform. A software package in this study solves two-dimensional, simultaneous, partial differential equations of mass, energy, and electro-chemistry, without considering stack direction variation. The results show that the fuel utilization increases with a decrease in the molar flow rate, and the average current density decreases when the molar flow rate drops. In addition, non-uniform Pattern A will induce more severe happening of non-reaction area in the corner of the fuel exit and the air inlet. This non-reaction area deteriorates the average current density and then deteriorates the electrical performance to –7%.

Keywords: Performance, Solid oxide fuel cell, non-uniform, fuelutilization

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Authors: F.Ebrahimi, A.Rastgo

Abstract:

Analytical investigation of the free vibration behavior of circular functionally graded (FG) plates integrated with two uniformly distributed actuator layers made of piezoelectric (PZT4) material on the top and bottom surfaces of the circular FG plate based on the classical plate theory (CPT) is presented in this paper. The material properties of the functionally graded substrate plate are assumed to be graded in the thickness direction according to the power-law distribution in terms of the volume fractions of the constituents and the distribution of electric potential field along the thickness direction of piezoelectric layers is simulated by a quadratic function. The differential equations of motion are solved analytically for clamped edge boundary condition of the plate. The detailed mathematical derivations are presented and Numerical investigations are performed for FG plates with two surface-bonded piezoelectric layers. Emphasis is placed on investigating the effect of varying the gradient index of FG plate on the free vibration characteristics of the structure. The results are verified by those obtained from threedimensional finite element analyses.

Keywords: Circular plate, CPT, Functionally graded, Piezoelectric.

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