Search results for: visual error concealment.
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1788

Search results for: visual error concealment.

918 Effect of Different BER Performance Comparison of MAP and ML Detection

Authors: Naveed Ur Rehman, Rehan Jamil, Irfan Jamil

Abstract:

In this paper, we regard as a coded transmission over a frequency-selective channel. We plan to study analytically the convergence of the turbo-detector using a maximum a posteriori (MAP) equalizer and a MAP decoder. We demonstrate that the densities of the maximum likelihood (ML) exchanged during the iterations are e-symmetric and output-symmetric. Under the Gaussian approximation, this property allows to execute a one-dimensional scrutiny of the turbo-detector. By deriving the analytical terminology of the ML distributions under the Gaussian approximation, we confirm that the bit error rate (BER) performance of the turbo-detector converges to the BER performance of the coded additive white Gaussian noise (AWGN) channel at high signal to noise ratio (SNR), for any frequency selective channel.

Keywords: MAP, ML, SNR, Decoder, BER, Coded transmission.

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917 Using Data Mining Techniques for Estimating Minimum, Maximum and Average Daily Temperature Values

Authors: S. Kotsiantis, A. Kostoulas, S. Lykoudis, A. Argiriou, K. Menagias

Abstract:

Estimates of temperature values at a specific time of day, from daytime and daily profiles, are needed for a number of environmental, ecological, agricultural and technical applications, ranging from natural hazards assessments, crop growth forecasting to design of solar energy systems. The scope of this research is to investigate the efficiency of data mining techniques in estimating minimum, maximum and mean temperature values. For this reason, a number of experiments have been conducted with well-known regression algorithms using temperature data from the city of Patras in Greece. The performance of these algorithms has been evaluated using standard statistical indicators, such as Correlation Coefficient, Root Mean Squared Error, etc.

Keywords: regression algorithms, supervised machine learning.

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916 Time Synchronization between the eNBs in E-UTRAN under the Asymmetric IP Network

Authors: M. Kollar, A. Zieba

Abstract:

In this paper, we present a method for a time synchronization between the two eNodeBs (eNBs) in E-UTRAN (Evolved Universal Terrestrial Radio Access) network. The two eNBs are cooperating in so-called inter eNB CA (Carrier Aggregation) case and connected via asymmetrical IP network. We solve the problem by using broadcasting signals generated in E-UTRAN as synchronization signals. The results show that the time synchronization with the proposed method is possible with the error significantly less than 1 ms which is sufficient considering the time transmission interval is 1 ms in E-UTRAN. This makes this method (with low complexity) more suitable than Network Time Protocol (NTP) in the mobile applications with generated broadcasting signals where time synchronization in asymmetrical network is required.

Keywords: E-UTRAN, IP scheduled throughput, initial burst delay, synchronization, NTP, delay, asymmetric network.

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915 An Iterative Algorithm for Inverse Kinematics of 5-DOF Manipulator with Offset Wrist

Authors: Juyi Park, Jung-Min Kim, Hee-Hwan Park, Jin-Wook Kim, Gye-Hyung Kang, Soo-Ho Kim

Abstract:

This paper presents an iterative algorithm to find a inverse kinematic solution of 5-DOF robot. The algorithm is to minimize the iteration number. Since the 5-DOF robot cannot give full orientation of tool. Only z-direction of tool is satisfied while rotation of tool is determined by kinematic constraint. This work therefore described how to specify the tool direction and let the tool rotation free. The simulation results show that this algorithm effectively worked. Using the proposed iteration algorithm, error due to inverse kinematics converged to zero rapidly in 5 iterations. This algorithm was applied in real welding robot and verified through various practical works.

Keywords: 5-DOF manipulator, Inverse kinematics, Iterative algorithm, Wrist offset.

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914 Image Sensor Matrix High Speed Simulation

Authors: Z. Feng, V. Viswanathan, D. Navarro, I. O'Connor

Abstract:

This paper presents a new high speed simulation methodology to solve the long simulation time problem of CMOS image sensor matrix. Generally, for integrating the pixel matrix in SOC and simulating the system performance, designers try to model the pixel in various modeling languages such as VHDL-AMS, SystemC or Matlab. We introduce a new alternative method based on spice model in cadence design platform to achieve accuracy and reduce simulation time. The simulation results indicate that the pixel output voltage maximum error is at 0.7812% and time consumption reduces from 2.2 days to 13 minutes achieving about 240X speed-up for the 256x256 pixel matrix.

Keywords: CMOS image sensor, high speed simulation, image sensor matrix simulation.

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913 On the Impact of Reference Node Placement in Wireless Indoor Positioning Systems

Authors: Supattra Aomumpai, Chutima Prommak

Abstract:

This paper presents a studyof the impact of reference node locations on the accuracy of the indoor positioning systems. In particular, we analyze the localization accuracy of the RSSI database mapping techniques, deploying on the IEEE 802.15.4 wireless networks. The results show that the locations of the reference nodes used in the positioning systems affect the signal propagation characteristics in the service area. Thisin turn affects the accuracy of the wireless indoor positioning system. We found that suitable location of reference nodes could reduce the positioning error upto 35 %.

Keywords: Indoor positioning systems, IEEE 802.15.4 wireless networks, Signal propagation characteristics

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912 Ontology for a Voice Transcription of OpenStreetMap Data: The Case of Space Apprehension by Visually Impaired Persons

Authors: Said Boularouk, Didier Josselin, Eitan Altman

Abstract:

In this paper, we present a vocal ontology of OpenStreetMap data for the apprehension of space by visually impaired people. Indeed, the platform based on produsage gives a freedom to data producers to choose the descriptors of geocoded locations. Unfortunately, this freedom, called also folksonomy leads to complicate subsequent searches of data. We try to solve this issue in a simple but usable method to extract data from OSM databases in order to send them to visually impaired people using Text To Speech technology. We focus on how to help people suffering from visual disability to plan their itinerary, to comprehend a map by querying computer and getting information about surrounding environment in a mono-modal human-computer dialogue.

Keywords: Ontology, OpenStreetMap, visually impaired people, TTS, taxonomy.

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911 Watermarking Scheme for Color Images using Wavelet Transform based Texture Properties and Secret Sharing

Authors: Nagaraj V. Dharwadkar, B.B.Amberker

Abstract:

In this paper, a new secure watermarking scheme for color image is proposed. It splits the watermark into two shares using (2, 2)- threshold Visual Cryptography Scheme (V CS) with Adaptive Order Dithering technique and embeds one share into high textured subband of Luminance channel of the color image. The other share is used as the key and is available only with the super-user or the author of the image. In this scheme only the super-user can reveal the original watermark. The proposed scheme is dynamic in the sense that to maintain the perceptual similarity between the original and the watermarked image the selected subband coefficients are modified by varying the watermark scaling factor. The experimental results demonstrate the effectiveness of the proposed scheme. Further, the proposed scheme is able to resist all common attacks even with strong amplitude.

Keywords: VCS, Dithering, HVS, DWT.

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910 Analysis of Testing and Operational Software Reliability in SRGM based on NHPP

Authors: S. Thirumurugan, D. R. Prince Williams

Abstract:

Software Reliability is one of the key factors in the software development process. Software Reliability is estimated using reliability models based on Non Homogenous Poisson Process. In most of the literature the Software Reliability is predicted only in testing phase. So it leads to wrong decision-making concept. In this paper, two Software Reliability concepts, testing and operational phase are studied in detail. Using S-Shaped Software Reliability Growth Model (SRGM) and Exponential SRGM, the testing and operational reliability values are obtained. Finally two reliability values are compared and optimal release time is investigated.

Keywords: Error Detection Rate, Estimation of Parameters, Instantaneous Failure Rate, Mean Value Function, Non Homogenous Poisson Process (NHPP), Software Reliability.

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909 An Improved Lattice Reduction Aided Detection Scheme for MIMO-OFDM System

Authors: Jang-Kyun Ahn, Seung-Jun Yu, Eui-Young Lee, Hyoung-Kyu Song

Abstract:

This paper proposes an efficient lattice-reduction-aided detection (LRD) scheme to improve the detection performance of MIMO-OFDM system. In this proposed scheme, V candidate symbols are considered at the first layer, and V probable streams are detected with LRD scheme according to the first detected V candidate symbols. Then, the most probable stream is selected through a ML test. Since the proposed scheme can more accurately detect initial symbol and can reduce transmission of error to rest symbols, the proposed scheme shows more improved performance than conventional LRD with very low complexity.

Keywords: Lattice reduction aided detection, MIMO-OFDM, QRD-M, V-BLAST.

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908 Modelling of Induction Motor Including Skew Effect Using MWFA for Performance Improvement

Authors: M. Harir, A. Bendiabdellah, A. Chaouch, N. Benouzza

Abstract:

This paper deals with the modelling and simulation of the squirrel cage induction motor by taking into account all space harmonic components as well as the introduction of the bars skew in the calculation of the linear evolution of the magnetomotive force (MMF) between the slots extremities. The model used is based on multiple coupled circuits and the modified winding function approach (MWFA). The effect of skewing is included in the calculation of motors inductances with an axial asymmetry in the rotor. The simulation results in both time and spectral domains show the effectiveness and merits of the model and the error that may be caused if the skew of the bars are neglected.

Keywords: Modelling, MWFA, Skew effect, Squirrel cage induction motor, Spectral domain.

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907 Virtual Gesture Screen System Based on 3D Visual Information and Multi-Layer Perceptron

Authors: Yang-Keun Ahn, Min-Wook Kim, Young-Choong Park, Kwang-Soon Choi, Woo-Chool Park, Hae-Moon Seo, Kwang-Mo Jung

Abstract:

Active research is underway on virtual touch screens that complement the physical limitations of conventional touch screens. This paper discusses a virtual touch screen that uses a multi-layer perceptron to recognize and control three-dimensional (3D) depth information from a time of flight (TOF) camera. This system extracts an object-s area from the image input and compares it with the trajectory of the object, which is learned in advance, to recognize gestures. The system enables the maneuvering of content in virtual space by utilizing human actions.

Keywords: Gesture Recognition, Depth Sensor, Virtual Touch Screen

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906 Why do Clawback Provisions Affect Financial Reporting Quality? - An Analysis of Trigger Effects

Authors: Yu-Chun Lin

Abstract:

We identify clawback triggers from firms- proxy statements (Form DEF 14A) and use the likelihood of restatements to proxy for financial reporting quality. Based on a sample of 578 U.S. firms that voluntarily adopt clawback provisions during 2003-2009, when restatement-based triggers could be decomposed into two types: fraud and unintentional error, and we do observe the evidence that using fraud triggers is associated with high financial reporting quality. The findings support that fraud triggers can enhance deterrent effect of clawback provision by establishing a viable disincentive against fraud, misconduct, and otherwise harmful acts. These results are robust to controlling for the compensation components, to different sample specifications and to a number of sensitivity.

Keywords: Accruals quality, Clawback provisions, Compensation, Restatements.

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905 Analysis of Sonogram Images of Thyroid Gland Based on Wavelet Transform

Authors: M. Bastanfard, B. Jalaeian, S. Jafari

Abstract:

Sonogram images of normal and lymphocyte thyroid tissues have considerable overlap which makes it difficult to interpret and distinguish. Classification from sonogram images of thyroid gland is tackled in semiautomatic way. While making manual diagnosis from images, some relevant information need not to be recognized by human visual system. Quantitative image analysis could be helpful to manual diagnostic process so far done by physician. Two classes are considered: normal tissue and chronic lymphocyte thyroid (Hashimoto's Thyroid). Data structure is analyzed using K-nearest-neighbors classification. This paper is mentioned that unlike the wavelet sub bands' energy, histograms and Haralick features are not appropriate to distinguish between normal tissue and Hashimoto's thyroid.

Keywords: Sonogram, thyroid, Haralick feature, wavelet.

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904 Adaptive Impedance Control for Unknown Non-Flat Environment

Authors: Norsinnira Zainul Azlan, Hiroshi Yamaura

Abstract:

This paper presents a new adaptive impedance control strategy, based on Function Approximation Technique (FAT) to compensate for unknown non-flat environment shape or time-varying environment location. The target impedance in the force controllable direction is modified by incorporating adaptive compensators and the uncertainties are represented by FAT, allowing the update law to be derived easily. The force error feedback is utilized in the estimation and the accurate knowledge of the environment parameters are not required by the algorithm. It is shown mathematically that the stability of the controller is guaranteed based on Lyapunov theory. Simulation results presented to demonstrate the validity of the proposed controller.

Keywords: Adaptive impedance control, Function Approximation Technique (FAT), impedance control, unknown environment position.

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903 Influence of Vortex Generator on Flow Behavior of Air Stream

Authors: Chakkapong Supasri, Tanongkiat Kiatsiriroat, Atipoang Nuntaphan

Abstract:

 

This research studied the influence of delta wing and delta winglet vortex generators on air flow characteristic. Normally, the vortex generator has been used for enhancing the heat transfer performance by promote the helical flow of air stream. The vortex generator was setup in the wind tunnel and the flow pattern of air stream passing the vortex generator was observed by using smoke generator. The Reynolds number of air stream was between 30,000 and 80,000. It is found that the delta winglet having 20mm fin height and 30 degree of air stream contact angle generates the maximum helical flow of air stream.

Keywords: Vortex generator, Flow behavior, Visual study, Delta wing, Delta winglet, Smoke generator.

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902 Detection of Bias in GPS satellites- Measurements for Enhanced Measurement Integrity

Authors: Mamoun F. Abdel-Hafez

Abstract:

In this paper, the detection of a fault in the Global Positioning System (GPS) measurement is addressed. The class of faults considered is a bias in the GPS pseudorange measurements. This bias is modeled as an unknown constant. The fault could be the result of a receiver fault or signal fault such as multipath error. A bias bank is constructed based on set of possible fault hypotheses. Initially, there is equal probability of occurrence for any of the biases in the bank. Subsequently, as the measurements are processed, the probability of occurrence for each of the biases is sequentially updated. The fault with a probability approaching unity will be declared as the current fault in the GPS measurement. The residual formed from the GPS and Inertial Measurement Unit (IMU) measurements is used to update the probability of each fault. Results will be presented to show the performance of the presented algorithm.

Keywords: Estimation and filtering, Statistical data analysis, Faultdetection and identification.

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901 Spline Collocation for Solving System of Fredholm and Volterra Integral Equations

Authors: N. Ebrahimi, J. Rashidinia

Abstract:

In this paper, numerical solution of system of Fredholm and Volterra integral equations by means of the Spline collocation method is considered. This approximation reduces the system of integral equations to an explicit system of algebraic equations. The solution is collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. The error analysis of proposed numerical method is studied theoretically. The results are compared with the results obtained by other methods to illustrate the accuracy and the implementation of our method.

Keywords: Convergence analysis, Cubic B-spline, Newton- Cotes formula, System of Fredholm and Volterra integral equations.

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900 Calibration of Parallel Multi-View Cameras

Authors: M. Ali-Bey, N. Manamanni, S. Moughamir

Abstract:

This paper focuses on the calibration problem of a multi-view shooting system designed for the production of 3D content for auto-stereoscopic visualization. The considered multiview camera is characterized by coplanar and decentered image sensors regarding to the corresponding optical axis. Based on the Faugéras and Toscani-s calibration approach, a calibration method is herein proposed for the case of multi-view camera with parallel and decentered image sensors. At first, the geometrical model of the shooting system is recalled and some industrial prototypes with some shooting simulations are presented. Next, the development of the proposed calibration method is detailed. Finally, some simulation results are presented before ending with some conclusions about this work.

Keywords: Auto-stereoscopic display, camera calibration, multi-view cameras, visual servoing

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899 Exponential Particle Swarm Optimization Approach for Improving Data Clustering

Authors: Neveen I. Ghali, Nahed El-Dessouki, Mervat A. N., Lamiaa Bakrawi

Abstract:

In this paper we use exponential particle swarm optimization (EPSO) to cluster data. Then we compare between (EPSO) clustering algorithm which depends on exponential variation for the inertia weight and particle swarm optimization (PSO) clustering algorithm which depends on linear inertia weight. This comparison is evaluated on five data sets. The experimental results show that EPSO clustering algorithm increases the possibility to find the optimal positions as it decrease the number of failure. Also show that (EPSO) clustering algorithm has a smaller quantization error than (PSO) clustering algorithm, i.e. (EPSO) clustering algorithm more accurate than (PSO) clustering algorithm.

Keywords: Particle swarm optimization, data clustering, exponential PSO.

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898 Particle Swarm Optimisation of a Terminal Synergetic Controllers for a DC-DC Converter

Authors: H. Abderrezek, M. N. Harmas

Abstract:

DC-DC converters are widely used as reliable power source for many industrial and military applications, computers and electronic devices. Several control methods were developed for DC-DC converters control mostly with asymptotic convergence. Synergetic control (SC) is a proven robust control approach and will be used here in a so called terminal scheme to achieve finite time convergence. Lyapounov synthesis is adopted to assure controlled system stability. Furthermore particle swarm optimization (PSO) algorithm, based on an integral time absolute of error (ITAE) criterion will be used to optimize controller parameters. Simulation of terminal synergetic control of a DC-DC converter is carried out for different operating conditions and results are compared to classic synergetic control performance, that which demonstrate the effectiveness and feasibility of the proposed control method.

Keywords: DC-DC converter, PSO, finite time, terminal, synergetic control.

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897 Adaptive Kernel Filtering Used in Video Processing

Authors: Rasmus Engholm, Eva B. Vedel Jensen, Henrik Karstoft

Abstract:

In this paper we present a noise reduction filter for video processing. It is based on the recently proposed two dimensional steering kernel, extended to three dimensions and further augmented to suit the spatial-temporal domain of video processing. Two alternative filters are proposed - the time symmetric kernel and the time asymmetric kernel. The first reduces the noise on single sequences, but to handle the problems at scene shift the asymmetric kernel is introduced. The performance of both are tested on simulated data and on a real video sequence together with the existing steering kernel. The proposed kernels improves the Rooted Mean Squared Error (RMSE) compared to the original steering kernel method on video material.

Keywords: Adaptive image filtering, noise reduction, kernel methods, video processing.

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896 Software Improvements of the Accuracy in the Air-Electronic Measurement Systems for Geometrical Dimensions

Authors: Miroslav H. Hristov, Velizar A. Vassilev, Georgi K. Dukendjiev

Abstract:

Due to the constant development of measurement systems and the aim for computerization, unavoidable improvements are made for the main disadvantages of air gauges. With the appearance of the air-electronic measuring devices, some of their disadvantages are solved. The output electrical signal allows them to be included in the modern systems for measuring information processing and process management. Producer efforts are aimed at reducing the influence of supply pressure and measurement system setup errors. Increased accuracy requirements and preventive error measures are due to the main uses of air electronic systems - measurement of geometric dimensions in the automotive industry where they are applied as modules in measuring systems to measure geometric parameters, form, orientation and location of the elements.

Keywords: Air-electronic, geometrical parameters, improvement, measurement systems.

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895 Performance Evaluation of Distributed and Co-Located MIMO LTE Physical Layer Using Wireless Open-Access Research Platform

Authors: Ishak Suleiman, Ahmad Kamsani Samingan, Yeoh Chun Yeow, Abdul Aziz Bin Abdul Rahman

Abstract:

In this paper, we evaluate the benefits of distributed 4x4 MIMO LTE downlink systems compared to that of the co-located 4x4 MIMO LTE downlink system. The performance evaluation was carried out experimentally by using Wireless Open-Access Research Platform (WARP), where the comparison between the 4x4 MIMO LTE transmission downlink system in distributed and co-located techniques was examined. The measured Error Vector Magnitude (EVM) results showed that the distributed technique achieved better system performance compared to the co-located arrangement.

Keywords: Multiple-input-multiple-output, MIMO, distributed MIMO, co-located MIMO, LTE.

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894 Qualitative Modelling for Ferromagnetic Hysteresis Cycle

Authors: M. Mordjaoui, B. Boudjema, M. Chabane, R. Daira

Abstract:

In determining the electromagnetic properties of magnetic materials, hysteresis modeling is of high importance. Many models are available to investigate those characteristics but they tend to be complex and difficult to implement. In this paper a new qualitative hysteresis model for ferromagnetic core is presented, based on the function approximation capabilities of adaptive neuro fuzzy inference system (ANFIS). The proposed ANFIS model combined the neural network adaptive capabilities and the fuzzy logic qualitative approach can restored the hysteresis curve with a little RMS error. The model accuracy is good and can be easily adapted to the requirements of the application by extending or reducing the network training set and thus the required amount of measurement data.

Keywords: ANFIS modeling technique, magnetic hysteresis, Jiles-Atherton model, ferromagnetic core.

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893 Orthogonal Regression for Nonparametric Estimation of Errors-in-Variables Models

Authors: Anastasiia Yu. Timofeeva

Abstract:

Two new algorithms for nonparametric estimation of errors-in-variables models are proposed. The first algorithm is based on penalized regression spline. The spline is represented as a piecewise-linear function and for each linear portion orthogonal regression is estimated. This algorithm is iterative. The second algorithm involves locally weighted regression estimation. When the independent variable is measured with error such estimation is a complex nonlinear optimization problem. The simulation results have shown the advantage of the second algorithm under the assumption that true smoothing parameters values are known. Nevertheless the use of some indexes of fit to smoothing parameters selection gives the similar results and has an oversmoothing effect.

Keywords: Grade point average, orthogonal regression, penalized regression spline, locally weighted regression.

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892 A Fiber Optic Interferometric Sensor for Dynamic Measurement

Authors: N. Sathitanon, S. Pullteap

Abstract:

An optical fiber Fabry-Perot interferometer (FFPI) is proposed and demonstrated for dynamic measurements in a mechanical vibrating target. A polishing metal with a low reflectance value adhered to a mechanical vibrator was excited via a function generator at various excitation frequencies. Output interference fringes were generated by modulating the reference and sensing signal at the output arm. A fringe-counting technique was used for interpreting the displacement information on the dedicated computer. The fiber interferometer has been found the capability of the displacement measurements of 1.28 μm – 96.01 μm. A commercial displacement sensor was employed as a reference sensor for investigating the measurement errors from the fiber sensor. A maximum percentage measurement error of approximately 1.59 % was obtained.

Keywords: Optical fiber sensors, dynamic displacement, fringe counting, reference displacement sensor.

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891 A Novel Metric for Performance Evaluation of Image Fusion Algorithms

Authors: Nedeljko Cvejic, Artur Łoza, David Bull, Nishan Canagarajah

Abstract:

In this paper, we present a novel objective nonreference performance assessment algorithm for image fusion. It takes into account local measurements to estimate how well the important information in the source images is represented by the fused image. The metric is based on the Universal Image Quality Index and uses the similarity between blocks of pixels in the input images and the fused image as the weighting factors for the metrics. Experimental results confirm that the values of the proposed metrics correlate well with the subjective quality of the fused images, giving a significant improvement over standard measures based on mean squared error and mutual information.

Keywords: Fusion performance measures, image fusion, non-reference quality measures, objective quality measures.

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890 Performance Analysis of a Hybrid DF-AF Hybrid RF/FSO System under Gamma Gamma Atmospheric Turbulence Channel Using MPPM Modulation

Authors: Hechmi Saidi, Noureddine Hamdi

Abstract:

The performance of hybrid amplify and forward - decode and forward (AF-DF) hybrid radio frequency/free space optical (RF/FSO) communication system, that adopts M-ary pulse position modulation (MPPM) techniques, is analyzed. Both exact and approximate symbol-error rates (SERs) are derived. The random variations of the received optical irradiance, produced by the atmospheric turbulence, is modeled by the gamma-gamma (GG) statistical distribution. A closed-form expression for the probability density function (PDF) is derived for the whole above system is obtained. Thanks to the use of hybrid AF-DF hybrid RF/FSO configuration and MPPM, the effects of atmospheric turbulence is mitigated; hence the capacity of combating atmospheric turbulence and the transmissitted signal quality are improved.

Keywords: FSO, RF, hybrid, AF, DF, SER, SNR, GG channel.

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889 Stabilization of the Bernoulli-Euler Plate Equation: Numerical Analysis

Authors: Carla E. O. de Moraes, Gladson O. Antunes, Mauro A. Rincon

Abstract:

The aim of this paper is to study the internal stabilization of the Bernoulli-Euler equation numerically. For this, we consider a square plate subjected to a feedback/damping force distributed only in a subdomain. An algorithm for obtaining an approximate solution to this problem was proposed and implemented. The numerical method used was the Finite Difference Method. Numerical simulations were performed and showed the behavior of the solution, confirming the theoretical results that have already been proved in the literature. In addition, we studied the validation of the numerical scheme proposed, followed by an analysis of the numerical error; and we conducted a study on the decay of the energy associated.

Keywords: Bernoulli-Euler Plate Equation, Numerical Simulations, Stability, Energy Decay, Finite Difference Method.

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