Search results for: Object motion detection

Authors: Ahmad H. Abdelgwad, Ahmed A. Nashat

Abstract:

Landmine detection is an important and yet challenging problem remains to be solved. Ground Penetrating Radar (GPR) is a powerful and rapidly maturing technology for subsurface threat identification. The detection methodology of GPR depends mainly on the contrast of the dielectric properties of the searched target and its surrounding soil. This contrast produces a partial reflection of the electromagnetic pulses that are being transmitted into the soil and then being collected by the GPR.  One of the most critical hardware components for the performance of GPR is the antenna system. The current paper explores the design and simulation of a pyramidal horn antenna operating at L-band frequencies (1- 2 GHz) to detect a landmine. A prototype model of the GPR system setup is developed to simulate full wave analysis of the electromagnetic fields in different soil types. The contrast in the dielectric permittivity of the landmine and the sandy soil is the most important parameter to be considered for detecting the presence of landmine. L-band horn antenna is proved to be well-versed in the investigation of landmine detection.

Keywords: Full wave analysis, ground penetrating radar, horn antenna design, landmine detection.

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Authors: N. Ghatwary, A. Ahmed, H. Jalab

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In this paper, an approach for the liver tumor detection in computed tomography (CT) images is represented. The detection process is based on classifying the features of target liver cell to either tumor or non-tumor. Fractional differential (FD) is applied for enhancement of Liver CT images, with the aim of enhancing texture and edge features. Later on, a fusion method is applied to merge between the various enhanced images and produce a variety of feature improvement, which will increase the accuracy of classification. Each image is divided into NxN non-overlapping blocks, to extract the desired features. Support vector machines (SVM) classifier is trained later on a supplied dataset different from the tested one. Finally, the block cells are identified whether they are classified as tumor or not. Our approach is validated on a group of patients’ CT liver tumor datasets. The experiment results demonstrated the efficiency of detection in the proposed technique.

Keywords: Fractional differential (FD), Computed Tomography (CT), fusion.

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Authors: P. Sanzo

Abstract:

Ten percent of the population will develop plantar fasciitis (PF) during their lifetime. Two million people are treated yearly accounting for 11-15% of visits to medical professionals. Treatment ranges from conservative to surgical intervention. The purpose of this study was to assess the effects of extracorporeal shockwave therapy (ECSWT) on heel pain, function, range of motion (ROM), and strength in patients with PF. One hundred subjects were treated with ECSWT and measures were taken before and three months after treatment. There was significant differences in visual analog scale scores for pain at rest (p=0.0001); after activity (p= 0.0001) and; overall improvement (p=0.0001). There was also significant improvement in Lower Extremity Functional Scale scores (p=0.0001); ankle plantarflexion (p=0.0001), dorsiflexion (p=0.001), and eversion (p=0.017),and first metatarsophalangeal joint flexion (p=0.002) and extension (p=0.003) ROM. ECSWT is an effective treatment improving heel pain, function and ROM in patients with PF.

Keywords: Extracorporeal shockwave therapy, shockwave therapy, plantar fasciitis, heel pain, function, range of motion, strength.

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Authors: Lenka Krulikovská, Jaroslav Polec

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In this paper we present a modification to existed model of threshold for shot cut detection, which is able to adapt itself to the sequence statistics and operate in real time, because it use for calculation only previously evaluated frames. The efficiency of proposed modified adaptive threshold scheme was verified through extensive test experiment with several similarity metrics and achieved results were compared to the results reached by the original model. According to results proposed threshold scheme reached higher accuracy than existed original model.

Keywords: Abrupt cut, shot cut detection, adaptive threshold.

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Authors: Nor Fazlina Iryani Abdul Hamid, Mohamad Khatim Hasan

Abstract:

Numbers of software quality measurement system have been implemented over the past few years, but none of them focuses on telecommunication industry. Software quality measurement system for telecommunication industry was a system that could calculate the quality value of the measured software that totally focused in telecommunication industry. Before designing a system, quality factors, quality attributes and quality metrics were identified based on literature review and survey. Then, using the identified quality factors, quality attributes and quality metrics, quality model for telecommunication industry was constructed. Each identified quality metrics had its own formula. Quality value for the system was measured based on the quality metrics and aggregated by referring to the quality model. It would classify the quality level of the software based on Net Satisfaction Index (NSI). The system was designed using object-oriented approach in web-based environment. Thus, existing of software quality measurement system was important to both developers and users in order to produce high quality software product for telecommunication industry.

Keywords: Software Quality, Quality Measurement, Object-oriented Approach, Net satisfaction Index.

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Authors: Yu Ren Lin, Yu Hong Li

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Vision-based intelligent vehicle applications often require large amounts of memory to handle video streaming and image processing, which in turn increases complexity of hardware and software. This paper presents an FPGA implement of a vision-based blind spot warning system. Using video frames, the information of the blind spot area turns into one-dimensional information. Analysis of the estimated entropy of image allows the detection of an object in time. This idea has been implemented in the XtremeDSP video starter kit. The blind spot warning system uses only 13% of its logic resources and 95k bits block memory, and its frame rate is over 30 frames per sec (fps).

Keywords: blind-spot area, image, FPGA

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Authors: Xie Kai, Laith K. Abbas, Chen Dongyang, Yang Fufeng, Rui Xiaoting

Abstract:

Effect of plunging motion on the pitch oscillating NACA0012 airfoil is investigated using computational fluid dynamics (CFD). A simulation model based on overset grid technology and k - ω shear stress transport (SST) turbulence model is established, and the numerical simulation results are compared with available experimental data and other simulations. Two cases of phase angle φ = 0, μ which represents the phase difference between the pitching and plunging motions of an airfoil are performed. Airfoil vortex generation, moving, and shedding are discussed in detail. Good agreements have been achieved with the available literature. The upward plunging motion made the equivalent angle of attack less than the actual one during pitching analysis. It is observed that the formation of the stall vortex is suppressed, resulting in a decrease in the lift coefficient and a delay of the stall angle. However, the downward plunging motion made the equivalent angle of attack higher the actual one.

Keywords: Dynamic stall, pitching-plunging, computational fluid dynamics, helicopter blade rotor, airfoil.

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Authors: Mahmoud E. Mohamed, Ahmed F. Shalash, Hanan A. Kamal

Abstract:

In communication systems, frequency jump is a serious problem caused by the oscillators used. Kalman filters are used to detect that jump, despite the tradeoff between the noise level and the speed of the detection. In this paper, an improvement is introduced in the Kalman filter, through a nonlinear change in the bandwidth of the filter. Simulation results show a considerable improvement in the filter speed with a very low noise level. Additionally, the effect on the response to false alarms is also presented and false alarm rate show improvement.

Keywords: Kalman Filter, Innovation, False Detection.

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Authors: Abdessamad Essaouabi, Ibnelhaj Elhassane

Abstract:

Efficient storage, transmission and use of video information are key requirements in many multimedia applications currently being addressed by MPEG-4. To fulfill these requirements, a new approach for representing video information which relies on an object-based representation, has been adopted. Therefore, objectbased watermarking schemes are needed for copyright protection. This paper proposes a novel blind object watermarking scheme for images and video using the in place lifting shape adaptive-discrete wavelet transform (SA-DWT). In order to make the watermark robust and transparent, the watermark is embedded in the average of wavelet blocks using the visual model based on the human visual system. Wavelet coefficients n least significant bits (LSBs) are adjusted in concert with the average. Simulation results shows that the proposed watermarking scheme is perceptually invisible and robust against many attacks such as lossy image/video compression (e.g. JPEG, JPEG2000 and MPEG-4), scaling, adding noise, filtering, etc.

Keywords: Watermark, visual model, robustness, in place lifting shape adaptive-discrete wavelet transform.

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Authors: Kedit J.

Abstract:

This paper is the tomographic images reconstruction simulation for defects detection in specimen. The specimen is the thin cylindrical steel contained with low density materials. The defects in material are simulated in three shapes.The specimen image function will be transformed to projection data. Radon transform and its inverse provide the mathematical for reconstructing tomographic images from projection data. The result of the simulation show that the reconstruction images is complete for defect detection.

Keywords: Tomography, Tomography Reconstruction, Radon Transform

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Authors: Jheng-Long Wu, Pei-Chann Chang, Hsuan-Ming Chen

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This research focus on the intrusion detection system (IDS) development which using artificial immune system (AIS) with population based incremental learning (PBIL). AIS have powerful distinguished capability to extirpate antigen when the antigen intrude into human body. The PBIL is based on past learning experience to adjust new learning. Therefore we propose an intrusion detection system call PBIL-AIS which combine two approaches of PBIL and AIS to evolution computing. In AIS part we design three mechanisms such as clonal selection, negative selection and antibody level to intensify AIS performance. In experimental result, our PBIL-AIS IDS can capture high accuracy when an intrusion connection attacks.

Keywords: Artificial immune system, intrusion detection, population-based incremental learning, evolution computing.

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Authors: Blessing Ojeme, Frederick Quinn, Russell Karls, Shannon Quinn

Abstract:

The detection and segmentation of mitochondria from fluorescence microscopy is crucial for understanding the complex structure of the nervous system. However, the constant fission and fusion of mitochondria and image distortion in the background make the task of detection and segmentation challenging. Although there exists a number of open-source software tools and artificial intelligence (AI) methods designed for analyzing mitochondrial images, the availability of only a few combined expertise in the medical field and AI required to utilize these tools poses a challenge to its full adoption and use in clinical settings. Motivated by the advantages of automated methods in terms of good performance, minimum detection time, ease of implementation, and cross-platform compactibility, this study proposes a fully automated framework for the detection and segmentation of mitochondria using both image shape information and descriptive statistics. Using the low-cost, open-source Python and OpenCV library, the algorithms are implemented in three stages: pre-processing; image binarization; and coarse-to-fine segmentation. The proposed model is validated using the fluorescence mitochondrial dataset. Ground truth labels generated using Labkit were also used to evaluate the performance of our detection and segmentation model using precision, recall and rand index. The study produces good detection and segmentation results and reports the challenges encountered during the image analysis of mitochondrial morphology from the fluorescence mitochondrial dataset. A discussion on the methods and future perspectives of fully automated frameworks concludes the paper.

Keywords: 2D, Binarization, CLAHE, detection, fluorescence microscopy, mitochondria, segmentation.

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Authors: Seungyeong Choi, Namkyu Lee, Dong Il Shim, Young Mun Lee, Yong-Ki Park, Hyung Hee Cho

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Effect of the cross-sectional geometry on heat transfer and particle motion of circulating fluidized bed riser for CO₂ capture was investigated. Numerical simulation using Eulerian-eulerian method with kinetic theory of granular flow was adopted to analyze gas-solid flow consisting in circulating fluidized bed riser. Circular, square, and rectangular cross-sectional geometry cases of the same area were carried out. Rectangular cross-sectional geometries were analyzed having aspect ratios of 1: 2, 1: 4, 1: 8, and 1:16. The cross-sectional geometry significantly influenced the particle motion and heat transfer. The downward flow pattern of solid particles near the wall was changed. The gas-solid mixing degree of the riser with the rectangular cross section of the high aspect ratio was the lowest. There were differences in bed-to-wall heat transfer coefficient according to rectangular geometry with different aspect ratios.

Keywords: Bed geometry, computational fluid dynamics, circulating fluidized bed riser, heat transfer.

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Authors: Ali Ben Abbes, ImedRiadh Farah, Vincent Barra

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Remotely sensed data are a significant source for monitoring and updating databases for land use/cover. Nowadays, changes detection of urban area has been a subject of intensive researches. Timely and accurate data on spatio-temporal changes of urban areas are therefore required. The data extracted from multi-temporal satellite images are usually non-stationary. In fact, the changes evolve in time and space. This paper is an attempt to propose a methodology for changes detection in urban area by combining a non-stationary decomposition method and stochastic modeling. We consider as input of our methodology a sequence of satellite images I₁, I₂, … I_n at different periods (t = 1, 2, ..., n). Firstly, a preprocessing of multi-temporal satellite images is applied. (e.g. radiometric, atmospheric and geometric). The systematic study of global urban expansion in our methodology can be approached in two ways: The first considers the urban area as one same object as opposed to non-urban areas (e.g. vegetation, bare soil and water). The objective is to extract the urban mask. The second one aims to obtain a more knowledge of urban area, distinguishing different types of tissue within the urban area. In order to validate our approach, we used a database of Tres Cantos-Madrid in Spain, which is derived from Landsat for a period (from January 2004 to July 2013) by collecting two frames per year at a spatial resolution of 25 meters. The obtained results show the effectiveness of our method.

Keywords: Multi-temporal satellite image, urban growth, Non-stationarity, stochastic modeling.

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Authors: Kamaljit Kaur, Kirti Minhas, Neha Mehan, Namita Kakkar

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Software complexity metrics are used to predict critical information about reliability and maintainability of software systems. Object oriented software development requires a different approach to software complexity metrics. Object Oriented Software Metrics can be broadly classified into static and dynamic metrics. Static Metrics give information at the code level whereas dynamic metrics provide information on the actual runtime. In this paper we will discuss the various complexity metrics, and the comparison between static and dynamic complexity.

Keywords: Static Complexity, Dynamic Complexity, Halstead Metric, Mc Cabe's Metric.

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Authors: Somkiat Lerkvaranyu, Yoshikazu Miyanaga

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In this paper, a new technique of signal detection has been proposed for detecting the orthogonal frequency-division multiplexing (OFDM) signal in the presence of nonlinear distortion.There are several advantages of OFDM communications system.However, one of the existing problems is remain considered as the nonlinear distortion generated by high-power-amplifier at the transmitter end due to the large dynamic range of an OFDM signal. The proposed method is the maximum likelihood detection with the symbol estimation. When the training data are available, the neural network has been used to learn the characteristic of received signal and to estimate the new positions of the transmitted symbol which are provided to the maximum likelihood detector. Resulting in the system performance, the nonlinear distortions of a traveling wave tube amplifier with OFDM signal are considered in this paper.Simulation results of the bit-error-rate performance are obtained with 16-QAM OFDM systems.

Keywords: OFDM, TWTA, nonlinear distortion, detection.

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Authors: Edikan E. Akpanibah, Ogunmodimu Dupe Catherine

Abstract:

The relevance of geometric Brownian motion (GBM) in modelling the behaviour of stock market prices (SMP) cannot be over emphasized taking into consideration the volatility of the SMP. Consequently, there is need to investigate how GBM models are being estimated and used in financial market to predict SMP. To achieve this, the GBM estimation and its application to the SMP of some selected companies are studied. The normal and log-normal distributions were used to determine the expected value, variance and co-variance. Furthermore, the GBM model was used to predict the SMP of some selected companies over a period of time and the mean absolute percentage error (MAPE) were calculated and used to determine the accuracy of the GBM model in predicting the SMP of the four companies under consideration. It was observed that for all the four companies, their MAPE values were within the region of acceptance. Also, the MAPE values of our data were compared to an existing literature to test the accuracy of our prediction with respect to time of investment. Finally, some numerical simulations of the graphs of the SMP, expectations and variance of the four companies over a period of time were presented using MATLAB programming software.

Keywords: Stock Market, Geometric Brownian Motion, normal and log-normal distribution, mean absolute percentage error.

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Authors: Antonio Di Leva, Roberto Berchi, Gianpiero Pescarmona, Michele Sonnessa

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The aim of a biological model is to understand the integrated structure and behavior of complex biological systems as a function of the underlying molecular networks to achieve simulation and forecast of their operation. Although several approaches have been introduced to take into account structural and environment related features, relatively little attention has been given to represent the behavior of biological systems. The Abstract Biological Process (ABP) model illustrated in this paper is an object-oriented model based on UML (the standard object-oriented language). Its main objective is to bring into focus the functional aspects of the biological system under analysis.

Keywords: Biological processes, system dynamics, systemmodeling, UML.

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Authors: Hussin K. Ragb, Vijayan K. Asari

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In this paper, we present a pedestrian detection descriptor called Fused Structure and Texture (FST) features based on the combination of the local phase information with the texture features. Since the phase of the signal conveys more structural information than the magnitude, the phase congruency concept is used to capture the structural features. On the other hand, the Center-Symmetric Local Binary Pattern (CSLBP) approach is used to capture the texture information of the image. The dimension less quantity of the phase congruency and the robustness of the CSLBP operator on the flat images, as well as the blur and illumination changes, lead the proposed descriptor to be more robust and less sensitive to the light variations. The proposed descriptor can be formed by extracting the phase congruency and the CSLBP values of each pixel of the image with respect to its neighborhood. The histogram of the oriented phase and the histogram of the CSLBP values for the local regions in the image are computed and concatenated to construct the FST descriptor. Several experiments were conducted on INRIA and the low resolution DaimlerChrysler datasets to evaluate the detection performance of the pedestrian detection system that is based on the FST descriptor. A linear Support Vector Machine (SVM) is used to train the pedestrian classifier. These experiments showed that the proposed FST descriptor has better detection performance over a set of state of the art feature extraction methodologies.

Keywords: Pedestrian detection, phase congruency, local phase, LBP features, CSLBP features, FST descriptor.

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Authors: Piercarlo Dondi, Luca Lombardi, Marco Porta

Abstract:

In the last years numerous applications of Human- Computer Interaction have exploited the capabilities of Time-of- Flight cameras for achieving more and more comfortable and precise interactions. In particular, gesture recognition is one of the most active fields. This work presents a new method for interacting with a virtual object in a 3D space. Our approach is based on the fusion of depth data, supplied by a ToF camera, with color information, supplied by a HD webcam. The hand detection procedure does not require any learning phase and is able to concurrently manage gestures of two hands. The system is robust to the presence in the scene of other objects or people, thanks to the use of the Kalman filter for maintaining the tracking of the hands.

Keywords: Gesture recognition, human-computer interaction, Time-of-Flight camera.

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Authors: Peng Shen Ong, Yoong Choon Chang, Chee Pun Ooi, Ettikan K. Karuppiah, Shahirina Mohd Tahir

Abstract:

Falling has been one of the major concerns and threats to the independence of the elderly in their daily lives. With the worldwide significant growth of the aging population, it is essential to have a promising solution of fall detection which is able to operate at high accuracy in real-time and supports large scale implementation using multiple cameras. Field Programmable Gate Array (FPGA) is a highly promising tool to be used as a hardware accelerator in many emerging embedded vision based system. Thus, it is the main objective of this paper to present an FPGA-based solution of visual based fall detection to meet stringent real-time requirements with high accuracy. The hardware architecture of visual based fall detection which utilizes the pixel locality to reduce memory accesses is proposed. By exploiting the parallel and pipeline architecture of FPGA, our hardware implementation of visual based fall detection using FGPA is able to achieve a performance of 60fps for a series of video analytical functions at VGA resolutions (640x480). The results of this work show that FPGA has great potentials and impacts in enabling large scale vision system in the future healthcare industry due to its flexibility and scalability.

Keywords: Fall detection, FPGA, hardware implementation.

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Authors: Hanaa M. Abdelgawad, Mona Safar, Ayman M. Wahba

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Real time image and video processing is a demand in many computer vision applications, e.g. video surveillance, traffic management and medical imaging. The processing of those video applications requires high computational power. Thus, the optimal solution is the collaboration of CPU and hardware accelerators. In this paper, a Canny edge detection hardware accelerator is proposed. Edge detection is one of the basic building blocks of video and image processing applications. It is a common block in the pre-processing phase of image and video processing pipeline. Our presented approach targets offloading the Canny edge detection algorithm from processing system (PS) to programmable logic (PL) taking the advantage of High Level Synthesis (HLS) tool flow to accelerate the implementation on Zynq platform. The resulting implementation enables up to a 100x performance improvement through hardware acceleration. The CPU utilization drops down and the frame rate jumps to 60 fps of 1080p full HD input video stream.

Keywords: High Level Synthesis, Canny edge detection, Hardware accelerators, and Computer Vision.

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Authors: Olesya Bolkhovskaya, Alexey Davydov, Alexander Maltsev

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In this paper two approaches to joint signal detection, time of arrival (ToA) and angle of arrival (AoA) estimation in multi-element antenna array are investigated. Two scenarios were considered: first one, when the waveform of the useful signal is known a priori and, second one, when the waveform of the desired signal is unknown. For first scenario, the antenna array signal processing based on multi-element matched filtering (MF) with the following non-coherent detection scheme and maximum likelihood (ML) parameter estimation blocks is exploited. For second scenario, the signal processing based on the antenna array elements covariance matrix estimation with the following eigenvector analysis and ML parameter estimation blocks is applied. The performance characteristics of both signal processing schemes are thoroughly investigated and compared for different useful signals and noise parameters.

Keywords: Antenna array, signal detection, ToA, AoA estimation.

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Authors: Hongbin Gu, Dongsu Wu, Hui Liu

Abstract:

A novel low-cost flight simulator with the development goals cost effectiveness and high performance has been realized for meeting the huge pilot training needs of airlines. The simulator consists of an aircraft dynamics model, a sophisticated designed low-profile electrical driven motion system with a subsided cabin, a mixed reality based semi-virtual cockpit system, a control loading system and some other subsystems. It shows its advantages over traditional flight simulator by its features achieved with open architecture, software solutions and low-cost hardware.

Keywords: Flight simulator, mixed reality, motion system, control loading system.

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Authors: Vitalice K. Oduol, C. Ardil

Abstract:

The paper presents frame and burst acquisition in a satellite communication network based on time division multiple access (TDMA) in which the transmissions may be carried on different transponders. A unique word pattern is used for the acquisition process. The search for the frame is aided by soft-decision of QPSK modulated signals in an additive white Gaussian channel. Results show that when the false alarm rate is low the probability of detection is also low, and the acquisition time is long. Conversely when the false alarm rate is high, the probability of detection is also high and the acquisition time is short. Thus the system operators can trade high false alarm rates for high detection probabilities and shorter acquisition times.

Keywords: burst acquisition, burst time plan, frame acquisition, satellite access, satellite TDMA, unique word detection

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Authors: Jindong Gu, Matthias Schubert, Volker Tresp

Abstract:

In many outlier detection tasks, only training data belonging to one class, i.e., the positive class, is available. The task is then to predict a new data point as belonging either to the positive class or to the negative class, in which case the data point is considered an outlier. For this task, we propose a novel corrupted Generative Adversarial Network (CorGAN). In the adversarial process of training CorGAN, the Generator generates outlier samples for the negative class, and the Discriminator is trained to distinguish the positive training data from the generated negative data. The proposed framework is evaluated using an image dataset and a real-world network intrusion dataset. Our outlier-detection method achieves state-of-the-art performance on both tasks.

Keywords: Outlier detection, generative adversary networks, semi-supervised learning.

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Authors: Jan Flusser

Abstract:

This paper aims to present a survey of object recognition/classification methods based on image moments. We review various types of moments (geometric moments, complex moments) and moment-based invariants with respect to various image degradations and distortions (rotation, scaling, affine transform, image blurring, etc.) which can be used as shape descriptors for classification. We explain a general theory how to construct these invariants and show also a few of them in explicit forms. We review efficient numerical algorithms that can be used for moment computation and demonstrate practical examples of using moment invariants in real applications.

Keywords: Object recognition, degraded images, moments, moment invariants, geometric invariants, invariants to convolution, moment computation.

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Authors: B. B. M. Moasheri, S. Azadinia

Abstract:

Wavelets have provided the researchers with significant positive results, by entering the texture defect detection domain. The weak point of wavelets is that they are one-dimensional by nature so they are not efficient enough to describe and analyze two-dimensional functions. In this paper we present a new method to detect the defect of texture images by using curvelet transform. Simulation results of the proposed method on a set of standard texture images confirm its correctness. Comparing the obtained results indicates the ability of curvelet transform in describing discontinuity in two-dimensional functions compared to wavelet transform

Keywords: Curvelet, Defect detection, Wavelet.

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Authors: Zoltán Szabó, Blanka Štorková

Abstract:

We analyze hand dexterity in Parkinson-s disease patients (PD) and control subjects using a natural manual transport task (moving an object from one place to another). Eight PD patients and ten control subjects performed the task repeatedly at maximum speed both in OFF and ON medicated status. The movement parameters and the grip and load forces were recorded by a single optoelectronic camera and force transducers built in the especially designed object. Using the force and velocity signals, ten subsequent phases of the transport movement were defined and their durations were measured. The outline of 3D optical measurement is presented to obtain more precise movement trajectory.

Keywords: Manual transport, movement phases, Parkinson's disease.

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Authors: Shun-Chang Chang

Abstract:

In this paper, different nonlinear dynamics analysis techniques are employed to unveil the rich nonlinear phenomena of the electromagnetic system. In particular, bifurcation diagrams, time responses, phase portraits, Poincare maps, power spectrum analysis, and the construction of basins of attraction are all powerful and effective tools for nonlinear dynamics problems. We also employ the method of Lyapunov exponents to show the occurrence of chaotic motion and to verify those numerical simulation results. Finally, two cases of a chaotic electromagnetic system being effectively controlled by a reference signal or being synchronized to another nonlinear electromagnetic system are presented.

Keywords: bifurcation, Poincare map, Lyapunov exponent, chaotic motion.

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