Search results for: Gabor Filters

Authors: Yasunori Sugita, Toshinori Yoshikawa

Abstract:

The design problem of Infinite Impulse Response (IIR) digital filters is usually expressed as the minimization problem of the complex magnitude error that includes both the magnitude and phase information. However, the group delay of the filter obtained by solving such design problem may be far from the desired group delay. In this paper, we propose a design method of stable IIR digital filters with prespecified maximum group delay errors. In the proposed method, the approximation problems of the magnitude-phase and group delay are separately defined, and these two approximation problems are alternately solved using successive projections. As a result, the proposed method can design the IIR filters that satisfy the prespecified allowable errors for not only the complex magnitude but also the group delay by alternately executing the coefficient update for the magnitude-phase and the group delay approximation. The usefulness of the proposed method is verified through some examples.

Keywords: Filter design, Group delay approximation, Stable IIRfilters, Successive projection method.

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Authors: Praseeda Lekshmi.V, Dr.M.Sasikumar

Abstract:

Facial recognition and expression analysis is rapidly becoming an area of intense interest in computer science and humancomputer interaction design communities. The most expressive way humans display emotions is through facial expressions. In this paper skin and non-skin pixels were separated. Face regions were extracted from the detected skin regions. Facial expressions are analyzed from facial images by applying Gabor wavelet transform (GWT) and Discrete Cosine Transform (DCT) on face images. Radial Basis Function (RBF) Network is used to identify the person and to classify the facial expressions. Our method reliably works even with faces, which carry heavy expressions.

Keywords: Face Recognition, Radial Basis Function, Gabor Wavelet Transform, Discrete Cosine Transform

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Authors: Sanghoon Park, Ki-Jin Kim, Kwang-Ho Ahn, Hyeon-Woo Lee

Abstract:

It is very effective way to utilize a very wide tunable filter in co-existing multi-standards wireless communications environment. Especially, as the long term evolution (LTE) communication era has come, the multi-band coverage is one of the important features required for the RF components. In this paper, we present the frequency conversion technique, and so generate two types of RF filters which are specially designed for the superb tunable ability to support multiple wireless communication standards. With the help of a complex mixing structure, the inherent image signal is suppressed. The RF band-pass filter (BPF) and notch filter achieve 1.8dB and 1.6dB insertion losses and 18 dB and 17 dB attenuations, respectively. The quality factor show greater than 30.

Keywords: RF filters, interference, wideband, tunable, channel selection, complex mixing, balanced mixer.

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Authors: M. Challal, F. Labu, M. Dehmas, A. Azrar

Abstract:

In this paper, three types of defected ground structure (DGS) units which are triangular-head (TH), rectangular-head (RH) and U-shape (US) are investigated. They are further used to low-pass and band-pass filters designs (LPF and BPF) and the obtained performances are examined. The LPF employing RH-DGS geometry presents the advantages of compact size, low-insertion loss and wide stopband compared to the other filters. It provides cutoff frequency of 2.5 GHz, largest rejection band width of 20 dB from 2.98 to 8.76 GHz, smallest transition region and smallest sharpness of the cutoff frequency. The BPF based on RH-DGS has the highest bandwidth (BW) of about 0.74 GHz and the lowest center frequency of 3.24 GHz, whereas the other BPFs have BWs less than 0.7 GHz.

Keywords: Defected ground structure (DGS), triangular-head(TH) DGS, rectangular-head (RH) DGS, U-shape (US) DGS, lowpassfilter (LPF) and band-pass filter (BPF).

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Authors: Praseeda Lekshmi.V, Dr.M.Sasikumar

Abstract:

Facial expression analysis is rapidly becoming an area of intense interest in computer science and human-computer interaction design communities. The most expressive way humans display emotions is through facial expressions. In this paper we present a method to analyze facial expression from images by applying Gabor wavelet transform (GWT) and Discrete Cosine Transform (DCT) on face images. Radial Basis Function (RBF) Network is used to classify the facial expressions. As a second stage, the images are preprocessed to enhance the edge details and non uniform down sampling is done to reduce the computational complexity and processing time. Our method reliably works even with faces, which carry heavy expressions.

Keywords: Face Expression, Radial Basis Function, GaborWavelet Transform, Human Computer Interaction.

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Authors: C. S. Sastry, Saurabh Jain, Ashish Mishra

Abstract:

Image retrieval is a topic where scientific interest is currently high. The important steps associated with image retrieval system are the extraction of discriminative features and a feasible similarity metric for retrieving the database images that are similar in content with the search image. Gabor filtering is a widely adopted technique for feature extraction from the texture images. The recently proposed sparsity promoting l1-norm minimization technique finds the sparsest solution of an under-determined system of linear equations. In the present paper, the l1-norm minimization technique as a similarity metric is used in image retrieval. It is demonstrated through simulation results that the l1-norm minimization technique provides a promising alternative to existing similarity metrics. In particular, the cases where the l1-norm minimization technique works better than the Euclidean distance metric are singled out.

Keywords: l1-norm minimization, content based retrieval, modified Gabor function.

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Authors: Faten A. Dawood, Rahmita W. Rahmat, Suhaini B. Kadiman, Lili N. Abdullah, Mohd D. Zamrin

Abstract:

Echocardiography imaging is one of the most common diagnostic tests that are widely used for assessing the abnormalities of the regional heart ventricle function. The main goal of the image enhancement task in 2D-echocardiography (2DE) is to solve two major anatomical structure problems; speckle noise and low quality. Therefore, speckle noise reduction is one of the important steps that used as a pre-processing to reduce the distortion effects in 2DE image segmentation. In this paper, we present the common filters that based on some form of low-pass spatial smoothing filters such as Mean, Gaussian, and Median. The Laplacian filter was used as a high-pass sharpening filter. A comparative analysis was presented to test the effectiveness of these filters after being applied to original 2DE images of 4-chamber and 2-chamber views. Three statistical quantity measures: root mean square error (RMSE), peak signal-to-ratio (PSNR) and signal-tonoise ratio (SNR) are used to evaluate the filter performance quantitatively on the output enhanced image.

Keywords: Gaussian operator, median filter, speckle texture, peak signal-to-ratio

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Authors: Christian Mayr, Holger Eisenreich, Stephan Henker, René Schüffny

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Image convolution similar to the receptive fields found in mammalian visual pathways has long been used in conventional image processing in the form of Gabor masks. However, no VLSI implementation of parallel, multi-layered pulsed processing has been brought forward which would emulate this property. We present a technical realization of such a pulsed image processing scheme. The discussed IC also serves as a general testbed for VLSI-based pulsed information processing, which is of interest especially with regard to the robustness of representing an analog signal in the phase or duration of a pulsed, quasi-digital signal, as well as the possibility of direct digital manipulation of such an analog signal. The network connectivity and processing properties are reconfigurable so as to allow adaptation to various processing tasks.

Keywords: Neural image processing, pulse computation application, pulsed Gabor convolution, VLSI pulse routing.

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Authors: A. Biran, P. Sobhe Bidari, A. Almazroe V. Lakshminarayanan, K. Raahemifar

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Diabetic Retinopathy (DR) is a severe retinal disease which is caused by diabetes mellitus. It leads to blindness when it progress to proliferative level. Early indications of DR are the appearance of microaneurysms, hemorrhages and hard exudates. In this paper, an automatic algorithm for detection of DR has been proposed. The algorithm is based on combination of several image processing techniques including Circular Hough Transform (CHT), Contrast Limited Adaptive Histogram Equalization (CLAHE), Gabor filter and thresholding. Also, Support Vector Machine (SVM) Classifier is used to classify retinal images to normal or abnormal cases including non-proliferative or proliferative DR. The proposed method has been tested on images selected from Structured Analysis of the Retinal (STARE) database using MATLAB code. The method is perfectly able to detect DR. The sensitivity specificity and accuracy of this approach are 90%, 87.5%, and 91.4% respectively.

Keywords: Diabetic retinopathy, fundus images, STARE, Gabor filter, SVM.

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Authors: Jun Gil Ahn, Jong Kang Park, Jong Tae Kim

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In this paper, we analyze major components of activity recognition (AR) in wearable device with 9-axis sensors and sensor fusion filters. 9-axis sensors commonly include 3-axis accelerometer, 3-axis gyroscope and 3-axis magnetometer. We chose sensor fusion filters as Kalman filter and Direction Cosine Matrix (DCM) filter. We also construct sensor fusion data from each activity sensor data and perform classification by accuracy of AR using Naïve Bayes and SVM. According to the classification results, we observed that the DCM filter and the specific combination of the sensing axes are more effective for AR in wearable devices while classifying walking, running, ascending and descending.

Keywords: Accelerometer, activity recognition, directional cosine matrix filter, gyroscope, Kalman filter, magnetometer.

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Authors: A. Diet, M. Villegas, G. Baudoin

Abstract:

This work concerns the measurements of a Bulk Acoustic Waves (BAW) emission filter S parameters and compare with prototypes simulated types. Thanks to HP-ADS, a co-simulation of filters- characteristics in a digital radio-communication chain is performed. Four cases of modulation schemes are studied in order to illustrate the impact of the spectral occupation of the modulated signal. Results of simulations and co-simulation are given in terms of Error Vector Measurements to be useful for a general sensibility analysis of 4th/3rd Generation (G.) emitters (wideband QAM and OFDM signals)

Keywords: RF architectures, BAW filters.

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Authors: Krzysztof Walczak

Abstract:

Fractional delay FIR filters design method based on the differential evolution algorithm is presented. Differential evolution is an evolutionary algorithm for solving a global optimization problems in the continuous search space. In the proposed approach, an evolutionary algorithm is used to determine the coefficients of a fractional delay FIR filter based on the Farrow structure. Basic differential evolution is enhanced with a restricted mating technique, which improves the algorithm performance in terms of convergence speed and obtained solution. Evolutionary optimization is carried out by minimizing an objective function which is based on the amplitude response and phase delay errors. Experimental results show that the proposed algorithm leads to a reduction in the amplitude response and phase delay errors relative to those achieved with the Least-Squares method.

Keywords: Fractional Delay Filters, Farrow Structure, Evolutionary Computation, Differential Evolution

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Authors: Suman Senapati, Goutam Saha

Abstract:

Real world Speaker Identification (SI) application differs from ideal or laboratory conditions causing perturbations that leads to a mismatch between the training and testing environment and degrade the performance drastically. Many strategies have been adopted to cope with acoustical degradation; wavelet based Bayesian marginal model is one of them. But Bayesian marginal models cannot model the inter-scale statistical dependencies of different wavelet scales. Simple nonlinear estimators for wavelet based denoising assume that the wavelet coefficients in different scales are independent in nature. However wavelet coefficients have significant inter-scale dependency. This paper enhances this inter-scale dependency property by a Circularly Symmetric Probability Density Function (CS-PDF) related to the family of Spherically Invariant Random Processes (SIRPs) in Log Gabor Wavelet (LGW) domain and corresponding joint shrinkage estimator is derived by Maximum a Posteriori (MAP) estimator. A framework is proposed based on these to denoise speech signal for automatic speaker identification problems. The robustness of the proposed framework is tested for Text Independent Speaker Identification application on 100 speakers of POLYCOST and 100 speakers of YOHO speech database in three different noise environments. Experimental results show that the proposed estimator yields a higher improvement in identification accuracy compared to other estimators on popular Gaussian Mixture Model (GMM) based speaker model and Mel-Frequency Cepstral Coefficient (MFCC) features.

Keywords: Speaker Identification, Log Gabor Wavelet, Bayesian Bivariate Estimator, Circularly Symmetric Probability Density Function, SIRP.

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Authors: Carmen E. Zapata, Juan Bautista, Olga Montoya, Claudia Moreno, Marisol Suarez, Alejandra Betancur, Duvan Nanclares, Natalia A. Cano

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This study aims to evaluate the diversity of microorganisms in filters PM2.5 and PM10; and determine the genotoxic and cytotoxic activity of the complex mixture present in PM2.5 filters used in the Aburrá Valley Air Quality Monitoring Network (Colombia). The research results indicate that particulate matter PM2.5 of different monitoring stations are bacteria; however, this study of detection of bacteria and their phylogenetic relationship is not complete evidence to connect the microorganisms with pathogenic or degrading activities of compounds present in the air. Additionally, it was demonstrated the damage induced by the particulate material in the cell membrane, lysosomal and endosomal membrane and in the mitochondrial metabolism; this damage was independent of the PM2.5 concentrations in almost all the cases.

Keywords: Cytotoxic, genotoxic, microbiological analysis, PM10, PM2.5.

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Authors: K. Sakthivel, R. Nallusamy, C. Kavitha

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The goal of image segmentation is to cluster pixels into salient image regions. Segmentation could be used for object recognition, occlusion boundary estimation within motion or stereo systems, image compression, image editing, or image database lookup. In this paper, we present a color image segmentation using support vector machine (SVM) pixel classification. Firstly, the pixel level color and texture features of the image are extracted and they are used as input to the SVM classifier. These features are extracted using the homogeneity model and Gabor Filter. With the extracted pixel level features, the SVM Classifier is trained by using FCM (Fuzzy C-Means).The image segmentation takes the advantage of both the pixel level information of the image and also the ability of the SVM Classifier. The Experiments show that the proposed method has a very good segmentation result and a better efficiency, increases the quality of the image segmentation compared with the other segmentation methods proposed in the literature.

Keywords: Image Segmentation, Support Vector Machine, Fuzzy C–Means, Pixel Feature, Texture Feature, Homogeneity model, Gabor Filter.

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Authors: Iyad F. Jafar, Sandra J. Alrawashdeh, Ban K. Alhamayel

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High level synthesis (HLS) is a process which generates register-transfer level design for digital systems from behavioral description. There are many HLS algorithms and commercial tools. However, most of these algorithms consider a behavioral description for the system when a single token is presented to the system. This approach does not exploit extra hardware efficiently, especially in the design of digital filters where common operations may exist between successive tokens. In this paper, we modify the behavioral description to process multiple tokens in parallel. However, this approach is unlike the full processing that requires full hardware replication. It exploits the presence of common operations between successive tokens. The performance of the proposed approach is better than sequential processing and approaches that of full parallel processing as the hardware resources are increased.

Keywords: Digital filters, High level synthesis, Sub-token forwarding

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Authors: G. Sadashivappa, K. V. S. AnandaBabu

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The aim of this paper to characterize a larger set of wavelet functions for implementation in a still image compression system using SPIHT algorithm. This paper discusses important features of wavelet functions and filters used in sub band coding to convert image into wavelet coefficients in MATLAB. Image quality is measured objectively using peak signal to noise ratio (PSNR) and its variation with bit rate (bpp). The effect of different parameters is studied on different wavelet functions. Our results provide a good reference for application designers of wavelet based coder.

Keywords: Wavelet, image compression, sub band, SPIHT, PSNR.

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Authors: M. Almutairi, S. Hadjiloucas

Abstract:

The harmonic distortion of voltage is important in relation to power quality due to the interaction between the large diffusion of non-linear and time-varying single-phase and three-phase loads with power supply systems. However, harmonic distortion levels can be reduced by improving the design of polluting loads or by applying arrangements and adding filters. The application of passive filters is an effective solution that can be used to achieve harmonic mitigation mainly because filters offer high efficiency, simplicity, and are economical. Additionally, possible different frequency response characteristics can work to achieve certain required harmonic filtering targets. With these ideas in mind, the objective of this paper is to determine what size single tuned passive filters work in distribution networks best, in order to economically limit violations caused at a given point of common coupling (PCC). This article suggests that a single tuned passive filter could be employed in typical industrial power systems. Furthermore, constrained optimization can be used to find the optimal sizing of the passive filter in order to reduce both harmonic voltage and harmonic currents in the power system to an acceptable level, and, thus, improve the load power factor. The optimization technique works to minimize voltage total harmonic distortions (VTHD) and current total harmonic distortions (ITHD), where maintaining a given power factor at a specified range is desired. According to the IEEE Standard 519, both indices are viewed as constraints for the optimal passive filter design problem. The performance of this technique will be discussed using numerical examples taken from previous publications.

Keywords: Harmonics, passive filter, power factor, power quality.

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Authors: Kohei Inoue, Kenji Hara, Kiichi Urahama

Abstract:

We describe a relationship between integral images and differential images. First, we derive a simple difference filter from conventional integral image. In the derivation, we show that an integral image and the corresponding differential image are related to each other by simultaneous linear equations, where the numbers of unknowns and equations are the same, and therefore, we can execute the integration and differentiation by solving the simultaneous equations. We applied the relationship to an image fusion problem, and experimentally verified the effectiveness of the proposed method.

Keywords: Integral images, differential images, differential filters, image fusion.

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Authors: Young-Seok Choi

Abstract:

This paper proposes a complementary combination scheme of affine projection algorithm (APA) filters with different order of input regressors. A convex combination provides an interesting way to keep the advantage of APA having different order of input regressors. Consequently, a novel APA which has the rapid convergence and the reduced steady-state error is derived. Experimental results show the good properties of the proposed algorithm.

Keywords: Adaptive filter, affine projection algorithm, convex combination, input order.

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Authors: Annur Suhadi, Haris B. Harahap, Zaim Arrosyidi, Epan, Darmapala

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Oilfields under waterflood often face the problem of plugging injectors either by internal filtration or external filter cake built up inside pore throats. The content of suspended solids shall be reduced to required level of filtration since corrective action of plugging is costly expensive. The performance of nutshell filters, where filtration takes place, is good using pecan and walnut shells. Candlenut shells were used instead of pecan and walnut shells since they were abundant in Indonesia, Malaysia, and East Africa. Physical and chemical properties of walnut, pecan, and candlenut shells were tested and the results were compared. Testing, using full-scale nutshell filters, was conducted to determine the oil content, turbidity, and suspended solid removal, which was based on designed flux rate. The performance of candlenut shells, which were deeply bedded in nutshell filters for filtration process, was monitored. Cleaned water outgoing nutshell filters had total suspended solids of 17 ppm, while oil content could be reduced to 15.1 ppm. Turbidity, using candlenut shells, was below the specification for injection water, which was less than 10 Nephelometric Turbidity Unit (NTU). Turbidity of water, outgoing nutshell filter, was ranged from 1.7-5.0 NTU at various dates of operation. Walnut, pecan, and candlenut shells had moisture content of 8.98 wt%, 10.95 wt%, and 9.95 wt%, respectively. The porosity of walnut, pecan, and candlenut shells was significantly affected by moisture content. Candlenut shells had property of toluene solubility of 7.68 wt%, which was much higher than walnut shells, reflecting more crude oil adsorption. The hardness of candlenut shells was 2.5-3 Mohs, which was close to walnut shells’ hardness. It was advantage to guarantee the cleaning filter cake by fluidization process during backwashing.

Keywords: Candlenut shells, walnut shells, pecan shells, nutshell filter, filtration.

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Authors: S. K. Aruna, S. Chitra

Abstract:

This research paper presents a framework for classifying Magnetic Resonance Imaging (MRI) images for Dementia. Dementia, an age-related cognitive decline is indicated by degeneration of cortical and sub-cortical structures. Characterizing morphological changes helps understand disease development and contributes to early prediction and prevention of the disease. Modelling, that captures the brain’s structural variability and which is valid in disease classification and interpretation is very challenging. Features are extracted using Gabor filter with 0, 30, 60, 90 orientations and Gray Level Co-occurrence Matrix (GLCM). It is proposed to normalize and fuse the features. Independent Component Analysis (ICA) selects features. Support Vector Machine (SVM) classifier with different kernels is evaluated, for efficiency to classify dementia. This study evaluates the presented framework using MRI images from OASIS dataset for identifying dementia. Results showed that the proposed feature fusion classifier achieves higher classification accuracy.

Keywords: Magnetic resonance imaging, dementia, Gabor filter, gray level co-occurrence matrix, support vector machine.

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Authors: Bo Liu, Qingshan Kong, Weiqing Huang

Abstract:

With the rapid development of modern communication, diagnosing the fiber-optic quality and faults in real-time is widely focused. In this paper, a Labview-based system is proposed for fiber-optic faults detection. The wavelet threshold denoising method combined with Empirical Mode Decomposition (EMD) is applied to denoise the optical time domain reflectometer (OTDR) signal. Then the method based on Gabor representation is used to detect events. Experimental measurements show that signal to noise ratio (SNR) of the OTDR signal is improved by 1.34dB on average, compared with using the wavelet threshold denosing method. The proposed system has a high score in event detection capability and accuracy. The maximum detectable fiber length of the proposed Labview-based system can be 65km.

Keywords: Empirical mode decomposition (EMD), events detection, Gabor transform, optical time domain reflectometer (OTDR), wavelet threshold denoising.

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Authors: Ju-Hong Lee, Chong-Jia Ciou, Yuan-Hau Yang

Abstract:

This paper deals with the problem of two-dimensional (2-D) recursive doubly complementary (DC) digital filter design. We present a structure of 2-D recursive DC filters by using 2-D symmetric half-plane (SHP) recursive digital all-pass lattice filters (DALFs). The novelty of using 2-D SHP recursive DALFs to construct a 2-D recursive DC digital lattice filter is that the resulting 2-D SHP recursive DC digital lattice filter provides better performance than the existing 2-D SHP recursive DC digital filter. Moreover, the proposed structure possesses a favorable 2-D DC half-band (DC-HB) property that allows about half of the 2-D SHP recursive DALF’s coefficients to be zero. This leads to considerable savings in computational burden for implementation. To ensure the stability of a designed 2-D SHP recursive DC digital lattice filter, some necessary constraints on the phase of the 2-D SHP recursive DALF during the design process are presented. Design of a 2-D diamond-shape decimation/interpolation filter is presented for illustration and comparison.

Keywords: All-pass digital filter, doubly complementary, lattice structure, symmetric half-plane digital filter, sampling rate conversion.

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

Abstract:

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

Keywords: Depth estimation, image filters, stereo match.

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Authors: Hong Son Hoang, Remy Baraille

Abstract:

The (sub)-optimal soolution of linear filtering problem with correlated noises is considered. The special recursive form of the class of filters and criteria for selecting the best estimator are the essential elements of the design method. The properties of the proposed filter are studied. In particular, for Markovian observation noise, the approximate filter becomes an optimal Gevers-Kailath filter subject to a special choice of the parameter in the class of given linear recursive filters.

Keywords: Linear dynamical system, filtering, minimum meansquare filter, correlated noise

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Authors: Young-Seok Choi

Abstract:

We present a subband adaptive infinite-impulse response (IIR) filtering method, which is based on a polyphase decomposition of IIR filter. Motivated by the fact that the polyphase structure has benefits in terms of convergence rate and stability, we introduce the polyphase decomposition to subband IIR filtering, i.e., in each subband high order IIR filter is decomposed into polyphase IIR filters with lower order. Computer simulations demonstrate that the proposed method has improved convergence rate over conventional IIR filters.

Keywords: Subband adaptive filter, IIR filtering. Polyphase decomposition.

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Authors: Mounira RouaÐùnia, Noureddine Doghmane

Abstract:

In this paper we consider the problem of change detection and non stationary signals tracking. Using parametric estimation of signals based on least square lattice adaptive filters we consider for change detection statistical parametric methods using likelihood ratio and hypothesis tests. In order to track signals dynamics, we introduce a compensation procedure in the adaptive estimation. This will improve the adaptive estimation performances and fasten it-s convergence after changes detection.

Keywords: Change detection, Hypothesis test, likelihood ratioleast square lattice adaptive filters.

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Authors: Fatih Kara, Cabir Vural

Abstract:

In this work, a special case of the image superresolution problem where the only type of motion is global translational motion and the blurs are shift-invariant is investigated. The necessary conditions for exact reconstruction of the original image by using finite impulse-response reconstruction filters are developed. Given that the conditions are satisfied, a method for exact super-resolution is presented and some simulation results are shown.

Keywords: Image processing, image super-resolution, finite impulse-response filters, existence-uniqueness conditions.

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Authors: Ahmed Soltan, Ahmed G. Radwan, Ahmed M. Soliman

Abstract:

This work aims to generalize the integer order Sallen-Key filters into the fractional-order domain. The analysis in the case of two different fractional-order elements introduced where the general transfer function becomes four terms which is unusual in the conventional case. In addition, the effect of the transfer function parameters on the filter poles and hence the stability is introduced and closed forms for the filter critical frequencies are driven. Finally, different examples for the fractional order Sallen-Key filter design are presented with circuit simulations using ADS where a great matching between the numerical and simulation results is obtained.

Keywords: Analog Filter, Low-Pass Filter, Fractance, Sallen-Key, Stability.

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