1. The document describes a modification of an existing 2D Radial Point Interpolation Method (RPIM) code to construct 1D shape functions for meshless methods.
2. RPIM uses radial basis functions centered at nodes within a local support domain to interpolate values and construct shape functions. Three common radial basis functions - multi-quadratic, exponential, and thin plate spline - are used.
3. The modified 1D code calculates the RPIM shape functions and their first and second derivatives with respect to x for a 1D domain defined by six nodes, implementing the radial point interpolation approach in one dimension.
Face Alignment Using Active Shape Model And Support Vector MachineCSCJournals
The Active Shape Model (ASM) is one of the most popular local texture models for face alignment. It applies in many fields such as locating facial features in the image, face synthesis, etc. However, the experimental results show that the accuracy of the classical ASM for some applications is not high. This paper suggests some improvements on the classical ASM to increase the performance of the model in the application: face alignment. Four of our major improvements include: i) building a model combining Sobel filter and the 2-D profile in searching face in image; ii) applying Canny algorithm for the enhancement edge on image; iii) Support Vector Machine (SVM) is used to classify landmarks on face, in order to determine exactly location of these landmarks support for ASM; iv) automatically adjust 2-D profile in the multi-level model based on the size of the input image. The experimental results on CalTech face database and Technical University of Denmark database (imm_face) show that our proposed improvement leads to far better performance.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
In the VLSI physical design, Floorplanning is the very crucial step as it optimizes the chip. The goal of
floorplanning is to find a floorplan such that no module overlaps with other, optimize the interconnection between
the modules, optimize the area of the floorplan and minimize the dead space. In this Paper, Simulated Annealing (SA)
algorithm has been employed to shrink dead space to optimize area and interconnect of VLSI floorplanning problem.
Sequence pair representation is employed to perturb the solution. The outcomes received after the application of SA
on different benchmark files are compared with the outcomes of different algorithms on same benchmark files and
the comparison suggests that the SA gives the better result. SA is effective and promising in VLSI floorplan design.
Matlab simulation results show that our approach can give better results and satisfy the fixed-outline and nonoverlapping
constraints while optimizing circuit performance.
Image restoration based on morphological operationsijcseit
Image processing including noise suppression, feature extraction, edge detection, image segmentation,
shape recognition, texture analysis, image restoration and reconstruction, image compression etc uses
mathematical morphology which is a method of nonlinear filters.
It is modulated from traditional morphology to order morphology, soft mathematical morphology and fuzzy
soft mathematical morphology. This paper is covers 6 morphological operations which are implemented in
the matlab program, including erosion, dilation, opening, closing, boundary extraction and region filling.
Although fuzzy systems demonstrate their ability to
solve different kinds of problems in various applications, there is an increasing interest on developing solid mathematical implementations suitable for control applications such as that used in fuzzy logic controllers (FLC). It is well known that, wide range of parameters is needed to be specified before the construction of a fuzzy system. To simplify in a systematic way the design and construction of a general fuzzy system, and without loss for generality a full parameterization process for a singleton type FLC is proposed in this paper. The resented methodology is very helpful in developing a universal computing algorithm for a standard fuzzy like PID controllers. An illustrative example shows the simplicity of applying the new paradigm.
Recognition of Persian handwritten characters has been considered as a significant field of research for
the last few years under pattern analysing technique. In this paper, a new approach for robust handwritten
Persian numerals recognition using strong feature set and a classifier fusion method is scrutinized to
increase the recognition percentage. For implementing the classifier fusion technique, we have considered
k nearest neighbour (KNN), linear classifier (LC) and support vector machine (SVM) classifiers. The
innovation of this tactic is to attain better precision with few features using classifier fusion method. For
evaluation of the proposed method we considered a Persian numerals database with 20,000 handwritten
samples. Spending 15,000 samples for training stage, we verified our technique on other 5,000 samples,
and the correct recognition ratio achievedapproximately 99.90%. Additional, we got 99.97% exactness
using four-fold cross validation procedure on 20,000 databases.
Face recognition using selected topographical features IJECEIAES
This paper represents a new features selection method to improve an existed feature type. Topographical (TGH) features provide large set of features by assigning each image pixel to the related feature depending on image gradient and Hessian matrix. Such type of features was handled by a proposed features selection method. A face recognition feature selector (FRFS) method is presented to inspect TGH features. FRFS depends in its main concept on linear discriminant analysis (LDA) technique, which is used in evaluating features efficiency. FRFS studies feature behavior over a dataset of images to determine the level of its performance. At the end, each feature is assigned to its related level of performance with different levels of performance over the whole image. Depending on a chosen threshold, the highest set of features is selected to be classified by SVM classifier.
Face Alignment Using Active Shape Model And Support Vector MachineCSCJournals
The Active Shape Model (ASM) is one of the most popular local texture models for face alignment. It applies in many fields such as locating facial features in the image, face synthesis, etc. However, the experimental results show that the accuracy of the classical ASM for some applications is not high. This paper suggests some improvements on the classical ASM to increase the performance of the model in the application: face alignment. Four of our major improvements include: i) building a model combining Sobel filter and the 2-D profile in searching face in image; ii) applying Canny algorithm for the enhancement edge on image; iii) Support Vector Machine (SVM) is used to classify landmarks on face, in order to determine exactly location of these landmarks support for ASM; iv) automatically adjust 2-D profile in the multi-level model based on the size of the input image. The experimental results on CalTech face database and Technical University of Denmark database (imm_face) show that our proposed improvement leads to far better performance.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
In the VLSI physical design, Floorplanning is the very crucial step as it optimizes the chip. The goal of
floorplanning is to find a floorplan such that no module overlaps with other, optimize the interconnection between
the modules, optimize the area of the floorplan and minimize the dead space. In this Paper, Simulated Annealing (SA)
algorithm has been employed to shrink dead space to optimize area and interconnect of VLSI floorplanning problem.
Sequence pair representation is employed to perturb the solution. The outcomes received after the application of SA
on different benchmark files are compared with the outcomes of different algorithms on same benchmark files and
the comparison suggests that the SA gives the better result. SA is effective and promising in VLSI floorplan design.
Matlab simulation results show that our approach can give better results and satisfy the fixed-outline and nonoverlapping
constraints while optimizing circuit performance.
Image restoration based on morphological operationsijcseit
Image processing including noise suppression, feature extraction, edge detection, image segmentation,
shape recognition, texture analysis, image restoration and reconstruction, image compression etc uses
mathematical morphology which is a method of nonlinear filters.
It is modulated from traditional morphology to order morphology, soft mathematical morphology and fuzzy
soft mathematical morphology. This paper is covers 6 morphological operations which are implemented in
the matlab program, including erosion, dilation, opening, closing, boundary extraction and region filling.
Although fuzzy systems demonstrate their ability to
solve different kinds of problems in various applications, there is an increasing interest on developing solid mathematical implementations suitable for control applications such as that used in fuzzy logic controllers (FLC). It is well known that, wide range of parameters is needed to be specified before the construction of a fuzzy system. To simplify in a systematic way the design and construction of a general fuzzy system, and without loss for generality a full parameterization process for a singleton type FLC is proposed in this paper. The resented methodology is very helpful in developing a universal computing algorithm for a standard fuzzy like PID controllers. An illustrative example shows the simplicity of applying the new paradigm.
Recognition of Persian handwritten characters has been considered as a significant field of research for
the last few years under pattern analysing technique. In this paper, a new approach for robust handwritten
Persian numerals recognition using strong feature set and a classifier fusion method is scrutinized to
increase the recognition percentage. For implementing the classifier fusion technique, we have considered
k nearest neighbour (KNN), linear classifier (LC) and support vector machine (SVM) classifiers. The
innovation of this tactic is to attain better precision with few features using classifier fusion method. For
evaluation of the proposed method we considered a Persian numerals database with 20,000 handwritten
samples. Spending 15,000 samples for training stage, we verified our technique on other 5,000 samples,
and the correct recognition ratio achievedapproximately 99.90%. Additional, we got 99.97% exactness
using four-fold cross validation procedure on 20,000 databases.
Face recognition using selected topographical features IJECEIAES
This paper represents a new features selection method to improve an existed feature type. Topographical (TGH) features provide large set of features by assigning each image pixel to the related feature depending on image gradient and Hessian matrix. Such type of features was handled by a proposed features selection method. A face recognition feature selector (FRFS) method is presented to inspect TGH features. FRFS depends in its main concept on linear discriminant analysis (LDA) technique, which is used in evaluating features efficiency. FRFS studies feature behavior over a dataset of images to determine the level of its performance. At the end, each feature is assigned to its related level of performance with different levels of performance over the whole image. Depending on a chosen threshold, the highest set of features is selected to be classified by SVM classifier.
Enhanced Morphological Contour Representation and Reconstruction using Line S...CSCJournals
The paper proposes an enhanced morphological contour/edge representation algorithm for the representation of 2D binary shapes of digital images. The concise representation algorithm uses representative lines of different sizes and types to cover all the significant features of the binary contour/edge image. These well characterized representative line segments, which may overlap among different types, take minimum representative points than that of most other prominent shape representation algorithms including MST and MSD. The new algorithm is computationally efficient than most other algorithms in the literature and is also capable of approximating edge images. The approximated outputs produced by the proposed algorithm by using minimal number of representative points are more natural to the original shapes than that of MST and MSD.
Improved algorithm for road region segmentation based on sequential monte car...csandit
In recent years, many researchers and car makers put a lot of intensive effort into development
of autonomous driving systems. Since visual information is the main modality used by human
driver, a camera mounted on moving platform is very important kind of sensor, and various
computer vision algorithms to handle vehicle surrounding situation are under intensive
research. Our final goal is to develop a vision based lane detection system with ability to
handle various types of road shapes, working on both structured and unstructured roads, ideally
under presence of shadows. This paper presents a modified road region segmentation algorithm
based on sequential Monte-Carlo estimation. Detailed description of the algorithm is given,
and evaluation results show that the proposed algorithm outperforms the segmentation
algorithm developed as a part of our previous work, as well as an conventional algorithm based
on colour histogram.
An optimal general type-2 fuzzy controller for Urban Traffic NetworkISA Interchange
Urban traffic network model is illustrated by state-charts and object-diagram. However, they have limitations to show the behavioral perspective of the traffic information flow. Consequently, a state space model is used to calculate the half-value waiting time of vehicles. In this study, a combination of the general type-2 fuzzy logic sets and the modified backtracking search algorithm (MBSA) techniques are used in order to control the traffic signal scheduling and phase succession so as to guarantee a smooth flow of traffic with the least wait times and average queue length. The parameters of input and output membership functions are optimized simultaneously by the novel heuristic algorithm MBSA. A comparison is made between the achieved results with those of optimal and conventional type-1 fuzzy logic controllers.
Unimodal Multi-Feature Fusion and one-dimensional Hidden Markov Models for Lo...IJECEIAES
The objective of low-resolution face recognition is to identify faces from small size or poor quality images with varying pose, illumination, expression, etc. In this work, we propose a robust low face recognition technique based on one-dimensional Hidden Markov Models. Features of each facial image are extracted using three steps: firstly, both Gabor filters and Histogram of Oriented Gradients (HOG) descriptor are calculated. Secondly, the size of these features is reduced using the Linear Discriminant Analysis (LDA) method in order to remove redundant information. Finally, the reduced features are combined using Canonical Correlation Analysis (CCA) method. Unlike existing techniques using HMMs, in which authors consider each state to represent one facial region (eyes, nose, mouth, etc), the proposed system employs 1D-HMMs without any prior knowledge about the localization of interest regions in the facial image. Performance of the proposed method will be measured using the AR database.
Local Binary Fitting Segmentation by Cooperative Quantum Particle OptimizationTELKOMNIKA JOURNAL
Recently, sophisticated segmentation techniques, such as level set method, which using valid
numerical calculation methods to process the evolution of the curve by solving linear or nonlinear elliptic
equations to divide the image availably, has become being more popular and effective. In Local Binary
Fitting (LBF) algorithm, a simple contour is initialized in an image and then the steepest-descent algorithm
is employed to constrain it to minimize the fitting energy functional. Hence, the initial position of the contour
is difficult or impossible to be well chosen for the final performance. To overcoming this drawback, this
work treats the energy fitting problem as a meta-heuristic optimization algorithm and imports a varietal
particle swarm optimization (PSO) method into the inner optimization process. The experimental results of
segmentations on medical images show that the proposed method is not only effective to both simple and
complex medical images with adequate stochastic effects, but also shows the accuracy and high
efficiency.
Unconstrained Optimization Method to Design Two Channel Quadrature Mirror Fil...CSCJournals
This paper proposes an efficient method for the design of two-channel, quadrature mirror filter (QMF) bank for subband image coding. The choice of filter bank is important as it affects image quality as well as system design complexity. The design problem is formulated as weighted sum of reconstruction error in time domain and passband and stop-band energy of the low-pass analysis filter of the filter bank .The objective function is minimized directly, using nonlinear unconstrained method. Experimental results of the method on images show that the performance of the proposed method is better than that of the already existing methods. The impact of some filter characteristics, such as stopband attenuation, stopband edge, and filter length on the performance of the reconstructed images is also investigated.
A BINARY TO RESIDUE CONVERSION USING NEW PROPOSED NON-COPRIME MODULI SETcsandit
Residue Number System is generally supposed to use co-prime moduli set. Non-coprime moduli sets are a field in RNS which is little studied. That's why this work was devoted to them. The resources that discuss non-coprime in RNS are very limited. For the previous reasons, this paper analyses the RNS conversion using suggested non-coprime moduli set.
A New Approach to Linear Estimation Problem in Multiuser Massive MIMO SystemsRadita Apriana
A novel approach for solving linear estimation problem in multi-user massive MIMO systems is
proposed. In this approach, the difficulty of matrix inversion is attributed to the incomplete definition of the
dot product. The general definition of dot product implies that the columns of channel matrix are always
orthogonal whereas, in practice, they may be not. If the latter information can be incorporated into dot
product, then the unknowns can be directly computed from projections without inverting the channel
matrix. By doing so, the proposed method is able to achieve an exact solution with a 25% reduction in
computational complexity as compared to the QR method. Proposed method is stable, offers an extra
flexibility of computing any single unknown, and can be implemented in just twelve lines of code.
A Run Length Smoothing-Based Algorithm for Non-Manhattan Document SegmentationUniversity of Bari (Italy)
Layout analysis is a fundamental step in automatic document processing, because its outcome affects all subsequent processing steps. Many different techniques have been proposed to perform this task. In this work, we propose a general bottom-up strategy to tackle the layout analysis of (possibly) non-Manhattan documents, and two specializations of it to handle both bitmap and PS/PDF sources. A famous approach proposed in the literature for layout analysis was the RLSA. Here we consider a variant of RLSA, called RLSO (short for “Run Length Smoothing with OR”), that exploits the OR logical operator instead of the AND and is particularly indicated for the identification of frames in non-Manhattan layouts. Like RLSA, RLSO is based on thresholds, but based on different criteria than those that work in RLSA. Since setting such thresholds is a hard and unnatural task for (even expert) users, and no single threshold can fit all documents, we developed a technique to automatically define such thresholds for each specific document, based on the distribution of spacing therein. Application on selected sample documents, that cover a significant landscape of real cases, revealed that the approach is satisfactory for documents characterized by the use of a uniform text font size.
A Run Length Smoothing-Based Algorithm for Non-Manhattan Document SegmentationUniversity of Bari (Italy)
Layout analysis is a fundamental step in automatic document processing, because its outcome affects all subsequent processing steps. Many different techniques have been proposed to perform this task. In this work, we propose a general bottom-up strategy to tackle the layout analysis of (possibly) non-Manhattan documents, and two specializations of it to handle both bitmap and PS/PDF sources. A famous approach proposed in the literature for layout analysis was the RLSA. Here we consider a variant of RLSA, called RLSO (short for “Run Length Smoothing with OR”), that exploits the OR logical operator instead of the AND and is particularly indicated for the identification of frames in non-Manhattan layouts. Like RLSA, RLSO is based on thresholds, but based on different criteria than those that work in RLSA. Since setting such thresholds is a hard and unnatural task for (even expert) users, and no single threshold can fit all documents, we developed a technique to automatically define such thresholds for each specific document, based on the distribution of spacing therein. Application on selected sample documents, that cover a significant landscape of real cases, revealed that the approach is satisfactory for documents characterized by the use of a uniform text font size.
Enhanced Morphological Contour Representation and Reconstruction using Line S...CSCJournals
The paper proposes an enhanced morphological contour/edge representation algorithm for the representation of 2D binary shapes of digital images. The concise representation algorithm uses representative lines of different sizes and types to cover all the significant features of the binary contour/edge image. These well characterized representative line segments, which may overlap among different types, take minimum representative points than that of most other prominent shape representation algorithms including MST and MSD. The new algorithm is computationally efficient than most other algorithms in the literature and is also capable of approximating edge images. The approximated outputs produced by the proposed algorithm by using minimal number of representative points are more natural to the original shapes than that of MST and MSD.
Improved algorithm for road region segmentation based on sequential monte car...csandit
In recent years, many researchers and car makers put a lot of intensive effort into development
of autonomous driving systems. Since visual information is the main modality used by human
driver, a camera mounted on moving platform is very important kind of sensor, and various
computer vision algorithms to handle vehicle surrounding situation are under intensive
research. Our final goal is to develop a vision based lane detection system with ability to
handle various types of road shapes, working on both structured and unstructured roads, ideally
under presence of shadows. This paper presents a modified road region segmentation algorithm
based on sequential Monte-Carlo estimation. Detailed description of the algorithm is given,
and evaluation results show that the proposed algorithm outperforms the segmentation
algorithm developed as a part of our previous work, as well as an conventional algorithm based
on colour histogram.
An optimal general type-2 fuzzy controller for Urban Traffic NetworkISA Interchange
Urban traffic network model is illustrated by state-charts and object-diagram. However, they have limitations to show the behavioral perspective of the traffic information flow. Consequently, a state space model is used to calculate the half-value waiting time of vehicles. In this study, a combination of the general type-2 fuzzy logic sets and the modified backtracking search algorithm (MBSA) techniques are used in order to control the traffic signal scheduling and phase succession so as to guarantee a smooth flow of traffic with the least wait times and average queue length. The parameters of input and output membership functions are optimized simultaneously by the novel heuristic algorithm MBSA. A comparison is made between the achieved results with those of optimal and conventional type-1 fuzzy logic controllers.
Unimodal Multi-Feature Fusion and one-dimensional Hidden Markov Models for Lo...IJECEIAES
The objective of low-resolution face recognition is to identify faces from small size or poor quality images with varying pose, illumination, expression, etc. In this work, we propose a robust low face recognition technique based on one-dimensional Hidden Markov Models. Features of each facial image are extracted using three steps: firstly, both Gabor filters and Histogram of Oriented Gradients (HOG) descriptor are calculated. Secondly, the size of these features is reduced using the Linear Discriminant Analysis (LDA) method in order to remove redundant information. Finally, the reduced features are combined using Canonical Correlation Analysis (CCA) method. Unlike existing techniques using HMMs, in which authors consider each state to represent one facial region (eyes, nose, mouth, etc), the proposed system employs 1D-HMMs without any prior knowledge about the localization of interest regions in the facial image. Performance of the proposed method will be measured using the AR database.
Local Binary Fitting Segmentation by Cooperative Quantum Particle OptimizationTELKOMNIKA JOURNAL
Recently, sophisticated segmentation techniques, such as level set method, which using valid
numerical calculation methods to process the evolution of the curve by solving linear or nonlinear elliptic
equations to divide the image availably, has become being more popular and effective. In Local Binary
Fitting (LBF) algorithm, a simple contour is initialized in an image and then the steepest-descent algorithm
is employed to constrain it to minimize the fitting energy functional. Hence, the initial position of the contour
is difficult or impossible to be well chosen for the final performance. To overcoming this drawback, this
work treats the energy fitting problem as a meta-heuristic optimization algorithm and imports a varietal
particle swarm optimization (PSO) method into the inner optimization process. The experimental results of
segmentations on medical images show that the proposed method is not only effective to both simple and
complex medical images with adequate stochastic effects, but also shows the accuracy and high
efficiency.
Unconstrained Optimization Method to Design Two Channel Quadrature Mirror Fil...CSCJournals
This paper proposes an efficient method for the design of two-channel, quadrature mirror filter (QMF) bank for subband image coding. The choice of filter bank is important as it affects image quality as well as system design complexity. The design problem is formulated as weighted sum of reconstruction error in time domain and passband and stop-band energy of the low-pass analysis filter of the filter bank .The objective function is minimized directly, using nonlinear unconstrained method. Experimental results of the method on images show that the performance of the proposed method is better than that of the already existing methods. The impact of some filter characteristics, such as stopband attenuation, stopband edge, and filter length on the performance of the reconstructed images is also investigated.
A BINARY TO RESIDUE CONVERSION USING NEW PROPOSED NON-COPRIME MODULI SETcsandit
Residue Number System is generally supposed to use co-prime moduli set. Non-coprime moduli sets are a field in RNS which is little studied. That's why this work was devoted to them. The resources that discuss non-coprime in RNS are very limited. For the previous reasons, this paper analyses the RNS conversion using suggested non-coprime moduli set.
A New Approach to Linear Estimation Problem in Multiuser Massive MIMO SystemsRadita Apriana
A novel approach for solving linear estimation problem in multi-user massive MIMO systems is
proposed. In this approach, the difficulty of matrix inversion is attributed to the incomplete definition of the
dot product. The general definition of dot product implies that the columns of channel matrix are always
orthogonal whereas, in practice, they may be not. If the latter information can be incorporated into dot
product, then the unknowns can be directly computed from projections without inverting the channel
matrix. By doing so, the proposed method is able to achieve an exact solution with a 25% reduction in
computational complexity as compared to the QR method. Proposed method is stable, offers an extra
flexibility of computing any single unknown, and can be implemented in just twelve lines of code.
A Run Length Smoothing-Based Algorithm for Non-Manhattan Document SegmentationUniversity of Bari (Italy)
Layout analysis is a fundamental step in automatic document processing, because its outcome affects all subsequent processing steps. Many different techniques have been proposed to perform this task. In this work, we propose a general bottom-up strategy to tackle the layout analysis of (possibly) non-Manhattan documents, and two specializations of it to handle both bitmap and PS/PDF sources. A famous approach proposed in the literature for layout analysis was the RLSA. Here we consider a variant of RLSA, called RLSO (short for “Run Length Smoothing with OR”), that exploits the OR logical operator instead of the AND and is particularly indicated for the identification of frames in non-Manhattan layouts. Like RLSA, RLSO is based on thresholds, but based on different criteria than those that work in RLSA. Since setting such thresholds is a hard and unnatural task for (even expert) users, and no single threshold can fit all documents, we developed a technique to automatically define such thresholds for each specific document, based on the distribution of spacing therein. Application on selected sample documents, that cover a significant landscape of real cases, revealed that the approach is satisfactory for documents characterized by the use of a uniform text font size.
A Run Length Smoothing-Based Algorithm for Non-Manhattan Document SegmentationUniversity of Bari (Italy)
Layout analysis is a fundamental step in automatic document processing, because its outcome affects all subsequent processing steps. Many different techniques have been proposed to perform this task. In this work, we propose a general bottom-up strategy to tackle the layout analysis of (possibly) non-Manhattan documents, and two specializations of it to handle both bitmap and PS/PDF sources. A famous approach proposed in the literature for layout analysis was the RLSA. Here we consider a variant of RLSA, called RLSO (short for “Run Length Smoothing with OR”), that exploits the OR logical operator instead of the AND and is particularly indicated for the identification of frames in non-Manhattan layouts. Like RLSA, RLSO is based on thresholds, but based on different criteria than those that work in RLSA. Since setting such thresholds is a hard and unnatural task for (even expert) users, and no single threshold can fit all documents, we developed a technique to automatically define such thresholds for each specific document, based on the distribution of spacing therein. Application on selected sample documents, that cover a significant landscape of real cases, revealed that the approach is satisfactory for documents characterized by the use of a uniform text font size.
A BINARY TO RESIDUE CONVERSION USING NEW PROPOSED NON-COPRIME MODULI SETsipij
Residue Number System is generally supposed to use co-prime moduli set. Non-coprime moduli sets are a
field in RNS which is little studied. That's why this work was devoted to them. The resources that discuss
non-coprime in RNS are very limited. For the previous reasons, this paper analyses the RNS conversion
using suggested non-coprime moduli set.
This paper suggests a new non-coprime moduli set and investigates its performance. The suggested new
moduli set has the general representation as {2n
–2, 2n
, 2n+2}, where n ∈ {2,3,…..,∞}. The calculations
among the moduli are done with this n value. These moduli are 2 spaces apart on the numbers line from
each other. This range helps in the algorithm’s calculations as to be shown.
The proposed non-coprime moduli set is investigated. Conversion algorithm from Binary to Residue is
developed. Correctness of the algorithm was obtained through simulation program. Conversion algorithm
is implemented.
Human Arm Inverse Kinematic Solution Based Geometric Relations and Optimizati...Waqas Tariq
Kinematics for robotic systems with many degrees of freedom (DOF) and high redundancy are still an open issue. Namely, computation time in robotic applications is often too high to reach good solution, for parts of the kinematic chain; the problem of inverse kinematics is not linear, as rotations are involved. This means that analytical solutions are only available in limited situations. In all other cases, alternative methods will have to be an employed.The most-used alternative is numerical solutions optimization. This paper presents a strategy based on combine’s analytical solutions with nonlinear optimization algorithm solutions to solution the IKP. A analytical solutions is used to reduce the size of problem from seven variable of joint angle to single variable and nonlinear optimization algorithm was used to find approximate solution which make the computation time is very small
Improved Characters Feature Extraction and Matching Algorithm Based on SIFTNooria Sukmaningtyas
According to SIFT algorithm does not have the property of affine invariance, and the high
complexity of time and space, it is difficult to apply to real-time image processing for batch image
sequence, so an improved SIFT feature extraction algorithm was proposed in this paper. Firstly, the MSER
algorithm detected the maximally stable extremely regions instead of the DOG operator detected extreme
point, increasing the stability of the characteristics, and reducing the number of the feature descriptor;
Secondly, the circular feature region is divided into eight fan-shaped sub-region instead of 16 square subregion
of the traditional SIFT, and using Gaussian function weighted gradient information field to construct
the new SIFT features descriptor. Compared with traditional SIFT algorithm, The experimental results
showed that the algorithm not only has translational invariance, scale invariance and rotational invariance,
but also has affine invariance and faster speed that meet the requirements of real-time image processing
applications.
In this paper, a novel architecture of RNS based 1D Lifting Integer Wavelet Transform (IWT) has been introduced. Advantage of Residue Number System (RNS) based Lifting Scheme over RNS based Filter Bank and non-binary IWT has been discussed. The performance of traditional predicts and updates stage of binary Lifting Scheme (LS) for Discrete Wavelet Transform (DWT) generates huge carry propagation
delay, power and complexity. As a result non binary number system is becoming popular in the field of Digital Signal Processing (DSP) due to its efficient performance. In this paper also a new fixed number ROM based RNS division circuit has been proposed. The proposed architecture has been validated on Xilinx Vertex5 FPGA platform and the corresponding result and reports are shown in here.
CPREDICTION OF INVERSE KINEMATICS SOLUTION OF A REDUNDANT MANIPULATOR USING A...Ijripublishers Ijri
In this thesis, a method for forward and inverse kinematics analysis of a 5-DOF and a 7- DOF Redundant manipulator
is proposed. Obtaining the trajectory and computing the required joint angles for a higher DOF robot manipulator is one
of the important concerns in robot kinematics and control. The difficulties in solving the inverse kinematics equations
of these redundant robot manipulator arises due to the presence of uncertain, time varying and non-linear nature of
equations having transcendental functions. In this thesis, the ability of ANFIS is used to the generated data for solving
inverse kinematics problem. A single- output Sugeno-type FIS using grid partitioning has been modeled in this work.
The forward kinematics and inverse kinematics for a 5-DOF and 7-DOF manipulator are analyzed systemically. The Efficiency
of ANFIS can be concluded by observing the surface plot, residual plot and normal probability plot. This current
study in using different nonlinear models for the prediction of the IKs of a 5-DOF and 7-DOF Redundant manipulator
will give a valuable source of information for other modellers.
Keywords: 5-DOF and 7-DOF Redundant Robot Manipulator; Inverse kinematics; ANFIS; Denavit-Harbenterg (D-H)
notation.
An Interactive Decomposition Algorithm for Two-Level Large Scale Linear Multi...IJERA Editor
This paper extended TOPSIS (Technique for Order Preference by Similarity Ideal Solution) method for solving
Two-Level Large Scale Linear Multiobjective Optimization Problems with Stochastic Parameters in the righthand
side of the constraints (TL-LSLMOP-SP)rhs of block angular structure. In order to obtain a compromise (
satisfactory) solution to the (TL-LSLMOP-SP)rhs of block angular structure using the proposed TOPSIS
method, a modified formulas for the distance function from the positive ideal solution (PIS ) and the distance
function from the negative ideal solution (NIS) are proposed and modeled to include all the objective functions
of the two levels. In every level, as the measure of ―Closeness‖ dp-metric is used, a k-dimensional objective
space is reduced to two –dimentional objective space by a first-order compromise procedure. The membership
functions of fuzzy set theory is used to represent the satisfaction level for both criteria. A single-objective
programming problem is obtained by using the max-min operator for the second –order compromise operaion.
A decomposition algorithm for generating a compromise ( satisfactory) solution through TOPSIS approach is
provided where the first level decision maker (FLDM) is asked to specify the relative importance of the
objectives. Finally, an illustrative numerical example is given to clarify the main results developed in the paper.
We propose a novel imaging biomarker of lung cancer relapse from 3-D texture analysis of CT images. Three-dimensional morphological nodular tissue properties are described in terms of 3-D Riesz-wavelets. The responses of the latter are aggregated within nodular regions by means of feature covariances, which leverage rich intra- and inter-variations of the feature space dimensions. The obtained Riesz-covariance descriptors lie on a manifold governed by Riemannian geometry requiring specific geodesic metrics to locally approximate scalar products. The latter are used to construct a kernel for support vector machines (SVM). The effectiveness of the presented models is evaluated on a dataset of 92 patients with non-small cell lung carcinoma (NSCLC) and cancer recurrence information. Disease recurrence within a timeframe of 12 months could be predicted with an accuracy above 80, and highlighted the importance of covariance-based texture aggregation. At the end of the talk, computer tools will be presented to easily extract 3D radiomics quantitative features from PET-CT images.
The Geometric Characteristics of the Linear Features in Close Range Photogram...IJERD Editor
The accuracy of photogrammetry can be increased with better instruments, careful geometric
characteristics of the system, more observations and rigorous adjustment. The main objective of this research is
to develop a new mathematical model of two types of linear features (straight line, spline curve) in addition to
relating linear features in object space to the image space using the Direct Linear Transformation (DLT). The
second main objective of the present paper is to study of some geometric characteristics of the system, when the
linear features are used in close range photogrammetric reduction processes. In this research, the accuracy
improvement has been evaluated by adopting certain assessment criteria, this will be performed by computing
the positional discrepancies between the photogrammetrically calculated object space coordinates of some check
object points, with the original check points of the test field, in terms of their respective RMS errors values. In
addition, the resulting least squares estimated covariance matrices of the check object point's space coordinates.
To perform the above purposes, some experiments are performed with synthetic images. The obtained results
showed significant improvements in the positional accuracy of close range photogrammetry, when starting node,
end nodes, and interior node on straight line and spline curve are increased with certain specifications regarding
the location and magnitude of each type of them.
Farsi character recognition using new hybrid feature extraction methodsijcseit
Identification of visual words and writings has long been one of the most essential and the most attractive
operations in the field of image processing which has been studied since the last few decades and includes
security, traffic control, fields of psychology, medicine, and engineering, etc. Previous techniques in the
field of identification of visual writings are very similar to each other for the most parts of their analysis,
and depending on the needs of the operational field have presented different feature extraction. Changes in
style of writing and font and turns of words and other issues are challenges of characters identifying
activity. In this study, a system of Persian character identification using independent orthogonal moment
that is Zernike Moment and Fourier-Mellin Moment has been used as feature extraction technique. The
values of Zernike Moments as characteristics independent of rotation have been used for classification
issues in the past and each of their real and imaginary components have been neglected individually and
with the phase coefficients, each of them will be changed by rotation. In this study, Zernike and Fourier-
Mellin Moments have been investigated to detect Persian characters in noisy and noise-free images. Also,
an improvement on the k-Nearest Neighbor (k-NN) classifier is proposed for character recognition. Using
the results comparison of the proposed method with current salient methods such as Back Propagation
(BP) and Radial Basis Function (RBF) neural networks in terms of feature extraction in words, it has been
shown that on the Hoda database, the proposed method reaches an acceptable detection rate (96/5%).
International Journal of Computer Science, Engineering and Information Techno...ijcseit
Identification of visual words and writings has long been one of the most essential and the most attractive
operations in the field of image processing which has been studied since the last few decades and includes
security, traffic control, fields of psychology, medicine, and engineering, etc. Previous techniques in the
field of identification of visual writings are very similar to each other for the most parts of their analysis,
and depending on the needs of the operational field have presented different feature extraction. Changes in
style of writing and font and turns of words and other issues are challenges of characters identifying
activity. In this study, a system of Persian character identification using independent orthogonal moment
that is Zernike Moment and Fourier-Mellin Moment has been used as feature extraction technique. The
values of Zernike Moments as characteristics independent of rotation have been used for classification
issues in the past and each of their real and imaginary components have been neglected individually and
with the phase coefficients, each of them will be changed by rotation. In this study, Zernike and FourierMellin
Moments have been investigated to detect Persian characters in noisy and noise-free images. Also,
an improvement on the k-Nearest Neighbor (k-NN) classifier is proposed for character recognition. Using
the results comparison of the proposed method with current salient methods such as Back Propagation
(BP) and Radial Basis Function (RBF) neural networks in terms of feature extraction in words, it has been
shown that on the Hoda database, the proposed method reaches an acceptable detection rate (96/5%).
DevOps and Testing slides at DASA ConnectKari Kakkonen
My and Rik Marselis slides at 30.5.2024 DASA Connect conference. We discuss about what is testing, then what is agile testing and finally what is Testing in DevOps. Finally we had lovely workshop with the participants trying to find out different ways to think about quality and testing in different parts of the DevOps infinity loop.
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
Are you looking to streamline your workflows and boost your projects’ efficiency? Do you find yourself searching for ways to add flexibility and control over your FME workflows? If so, you’re in the right place.
Join us for an insightful dive into the world of FME parameters, a critical element in optimizing workflow efficiency. This webinar marks the beginning of our three-part “Essentials of Automation” series. This first webinar is designed to equip you with the knowledge and skills to utilize parameters effectively: enhancing the flexibility, maintainability, and user control of your FME projects.
Here’s what you’ll gain:
- Essentials of FME Parameters: Understand the pivotal role of parameters, including Reader/Writer, Transformer, User, and FME Flow categories. Discover how they are the key to unlocking automation and optimization within your workflows.
- Practical Applications in FME Form: Delve into key user parameter types including choice, connections, and file URLs. Allow users to control how a workflow runs, making your workflows more reusable. Learn to import values and deliver the best user experience for your workflows while enhancing accuracy.
- Optimization Strategies in FME Flow: Explore the creation and strategic deployment of parameters in FME Flow, including the use of deployment and geometry parameters, to maximize workflow efficiency.
- Pro Tips for Success: Gain insights on parameterizing connections and leveraging new features like Conditional Visibility for clarity and simplicity.
We’ll wrap up with a glimpse into future webinars, followed by a Q&A session to address your specific questions surrounding this topic.
Don’t miss this opportunity to elevate your FME expertise and drive your projects to new heights of efficiency.
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...Jeffrey Haguewood
Sidekick Solutions uses Bonterra Impact Management (fka Social Solutions Apricot) and automation solutions to integrate data for business workflows.
We believe integration and automation are essential to user experience and the promise of efficient work through technology. Automation is the critical ingredient to realizing that full vision. We develop integration products and services for Bonterra Case Management software to support the deployment of automations for a variety of use cases.
This video focuses on the notifications, alerts, and approval requests using Slack for Bonterra Impact Management. The solutions covered in this webinar can also be deployed for Microsoft Teams.
Interested in deploying notification automations for Bonterra Impact Management? Contact us at sales@sidekicksolutionsllc.com to discuss next steps.
State of ICS and IoT Cyber Threat Landscape Report 2024 previewPrayukth K V
The IoT and OT threat landscape report has been prepared by the Threat Research Team at Sectrio using data from Sectrio, cyber threat intelligence farming facilities spread across over 85 cities around the world. In addition, Sectrio also runs AI-based advanced threat and payload engagement facilities that serve as sinks to attract and engage sophisticated threat actors, and newer malware including new variants and latent threats that are at an earlier stage of development.
The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
State of global ICS asset and network exposure
Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
Cyberattack types and targets
Vulnerability exploit attempts on CVEs
Attacks on counties – USA
Expansion of bot farms – how, where, and why
In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
Systemic attacks in the Middle East
Download the full report from here:
https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
UiPath Test Automation using UiPath Test Suite series, part 3DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 3. In this session, we will cover desktop automation along with UI automation.
Topics covered:
UI automation Introduction,
UI automation Sample
Desktop automation flow
Pradeep Chinnala, Senior Consultant Automation Developer @WonderBotz and UiPath MVP
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
"Impact of front-end architecture on development cost", Viktor TurskyiFwdays
I have heard many times that architecture is not important for the front-end. Also, many times I have seen how developers implement features on the front-end just following the standard rules for a framework and think that this is enough to successfully launch the project, and then the project fails. How to prevent this and what approach to choose? I have launched dozens of complex projects and during the talk we will analyze which approaches have worked for me and which have not.
The Art of the Pitch: WordPress Relationships and SalesLaura Byrne
Clients don’t know what they don’t know. What web solutions are right for them? How does WordPress come into the picture? How do you make sure you understand scope and timeline? What do you do if sometime changes?
All these questions and more will be explored as we talk about matching clients’ needs with what your agency offers without pulling teeth or pulling your hair out. Practical tips, and strategies for successful relationship building that leads to closing the deal.
Connector Corner: Automate dynamic content and events by pushing a buttonDianaGray10
Here is something new! In our next Connector Corner webinar, we will demonstrate how you can use a single workflow to:
Create a campaign using Mailchimp with merge tags/fields
Send an interactive Slack channel message (using buttons)
Have the message received by managers and peers along with a test email for review
But there’s more:
In a second workflow supporting the same use case, you’ll see:
Your campaign sent to target colleagues for approval
If the “Approve” button is clicked, a Jira/Zendesk ticket is created for the marketing design team
But—if the “Reject” button is pushed, colleagues will be alerted via Slack message
Join us to learn more about this new, human-in-the-loop capability, brought to you by Integration Service connectors.
And...
Speakers:
Akshay Agnihotri, Product Manager
Charlie Greenberg, Host
Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024Tobias Schneck
As AI technology is pushing into IT I was wondering myself, as an “infrastructure container kubernetes guy”, how get this fancy AI technology get managed from an infrastructure operational view? Is it possible to apply our lovely cloud native principals as well? What benefit’s both technologies could bring to each other?
Let me take this questions and provide you a short journey through existing deployment models and use cases for AI software. On practical examples, we discuss what cloud/on-premise strategy we may need for applying it to our own infrastructure to get it to work from an enterprise perspective. I want to give an overview about infrastructure requirements and technologies, what could be beneficial or limiting your AI use cases in an enterprise environment. An interactive Demo will give you some insides, what approaches I got already working for real.
Dev Dives: Train smarter, not harder – active learning and UiPath LLMs for do...UiPathCommunity
💥 Speed, accuracy, and scaling – discover the superpowers of GenAI in action with UiPath Document Understanding and Communications Mining™:
See how to accelerate model training and optimize model performance with active learning
Learn about the latest enhancements to out-of-the-box document processing – with little to no training required
Get an exclusive demo of the new family of UiPath LLMs – GenAI models specialized for processing different types of documents and messages
This is a hands-on session specifically designed for automation developers and AI enthusiasts seeking to enhance their knowledge in leveraging the latest intelligent document processing capabilities offered by UiPath.
Speakers:
👨🏫 Andras Palfi, Senior Product Manager, UiPath
👩🏫 Lenka Dulovicova, Product Program Manager, UiPath
Epistemic Interaction - tuning interfaces to provide information for AI supportAlan Dix
Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
Software Delivery At the Speed of AI: Inflectra Invests In AI-Powered QualityInflectra
In this insightful webinar, Inflectra explores how artificial intelligence (AI) is transforming software development and testing. Discover how AI-powered tools are revolutionizing every stage of the software development lifecycle (SDLC), from design and prototyping to testing, deployment, and monitoring.
Learn about:
• The Future of Testing: How AI is shifting testing towards verification, analysis, and higher-level skills, while reducing repetitive tasks.
• Test Automation: How AI-powered test case generation, optimization, and self-healing tests are making testing more efficient and effective.
• Visual Testing: Explore the emerging capabilities of AI in visual testing and how it's set to revolutionize UI verification.
• Inflectra's AI Solutions: See demonstrations of Inflectra's cutting-edge AI tools like the ChatGPT plugin and Azure Open AI platform, designed to streamline your testing process.
Whether you're a developer, tester, or QA professional, this webinar will give you valuable insights into how AI is shaping the future of software delivery.
Software Delivery At the Speed of AI: Inflectra Invests In AI-Powered Quality
E041122335
1. IOSR Journal of Engineering (IOSRJEN) www.iosrjen.org
ISSN (e): 2250-3021, ISSN (p): 2278-8719
Vol. 04, Issue 11 (November. 2014), ||V2|| PP 23-35
International organization of Scientific Research 23 | P a g e
Construction Of Shape Function By Radial Point Interpolation
Method For 1d Case
A. Mjidila1
, S. Jalal2
, L. Bousshine3
, Z. Elmaskaoui4
1,2,3,4
(Ain Chock Hassan II University, NHSEM, Oasis, Eljadida road, PB8118 Casablanca
Laboratory of Technologies of Constructions and the Industrial Systems)
Abstract: - In this paper, is presented a construction of Shape function by Radial Point Interpolation Method
for 1D case. The original code 2D, developed by G.R. Lui and coworkers, was modified for 1D case. Treated
case is a 1D support Domain built over six nodes. Three basic functions were used to construct the shape
functions, Multi-Quadratic (MQ), exponential (Exp) and Thin Plate Spline (TPS) functions.
Keywords - Mesh-less method, Shape function, RPIM, Basis function.
I. INTRODUCTION
The method of function interpolation/approximation based on arbitrary nodes is one of the most important
issues in an MFree method. MFree methods may be classified according to the MFree
interpolation/approximation methods used.
1. Meshfree methods based on the moving least squares approximation
2. Meshfree methods based on the integral representation method for the function approximation
These two methods can be seen in specialized literature.
3. Meshfree methods based on the point interpolation method
The point interpolation method (PIM) is an MFree interpolation technique that was used by GR Liu
and his colleagues (GR Liu and Gu, 2001a) to construct shape functions using nodes distributed locally to
formulate Mf'ree weak-form methods. Different from the NILS approximation, PIM uses interpolations to
construct shape functions that possess Kronecker delta property. Two different types of PIM formulations using
the polynomial basis (GR Liu and Gu, 2001c) and the radial function basis (REF) (Wang and GR Liu, 2000)
have been developed.
A good method for creating MFree shape functions should satisfy some basic requirements.
It should be sufficiently robust for reasonably arbitrarily distributed nodes (arbitrary nodal distribution).
It should be numerically stable (stability).
It should satisfy up to a certain order of consistency (consistency).
It should be compactly supported, i.e., it should be regarded as zero outside a bounded region, the support
domain.
The approximated unknown function using the shape function should be compatible" (compatibility) throughout
the problem domain when a global weak-form is used, or should be compatible within the local quadrature
domain when a local weak-form is used.
It is ideal if the shape function possesses the Kronecker delta function property (Delta function property), i.e.
the shape function is unit at the node and zero at other nodes in the support domain.
It should be computationally efficient (efficiency)
II. RADIAL POINT INTERPOLATION SHAPE FUNCTION
In seeking for an approximate solution to a problem governed by PDEs and boundary conditions, one
first needs to approximate the unknown field function using trial (shape) functions, before any formulation
procedure can be applied to establish the discretized system equations. This paragraph discusses various
techniques for Mf'ree shape function constructions. These shape functions are locally supported, because only a
set of field nodes in a small local domain are used in the construction and the shape function is not used or
regarded as zero outside the local domain. Such a local domain is termed the support domain.
In the finite element method (FEM), the shape functions are created using interpolation techniques
based on elements formed by a set of fixed nodes. This type of interpolation is termed stationary element based
interpolation. In MFree methods, the problem domain is usually represented by field nodes that are, in general,
arbitrarily distributed. The field variables at an arbitrary point in the problem domain are approximated using a
group of field nodes in a local support domain. [2]
2. ConstructionOf ShapeFunction ByRadialPoint InterpolationMethod For1d Case
International organization of Scientific Research 24 | P a g e
The point interpolation method (PIM) is one of the series representation methods for the function
approximation, and is useful for creating MFree shape functions. In order to avoid the singularity problem in the
polynomial PIM, the radial basis function (REF) is used to develop the radial point interpolation method
(RPIM) shape functions for MFree weak-form methods (GR Liu and Gu, 2001c; Wang and Liu, 2000; 2002a,c).
The RPIM interpolation augmented with polynomials can be written as:
m
j
TT
jj
n
i
ii bxpaxRbxpaxRxu
11
)()()()()( (1)
where Ri(x) is a radial basis function (REF), n is the number of REFs, pj(x) is monomial in the space
coordinates xT=[x, y], and m is the number of polynomial basis functions. When m=0, pure REFs are used.
Otherwise, the REF is augmented with m polynomial basis functions. Coefficients a, and b, are constants to be
determined.
In the radial basis function Ri(x), the variable is only the distance between the point of interest x and a node at
xi,
problems1Dfor)(rand
problems2Dfor)()( 22
i
ii
xx
yyxxr
( 2)
There are a number of types of radial basis functions (REF), and the characteristics of RBFs have been widely
investigated (Kansa, 1990; Sharan et al.,1997; Franke and Schaback, 1997; etc.). Four often used REFs, the
multi-quadrics (MQ) function, the Gaussian (Exp) function, the thin plate spline (TPS) function and the
Logarithmic radial basis function are listed in table 1.
Table 1 Typical radial basis functions
Name Expression Shape Parametrs
1. Multi-Quadratics (MQ) q
ccii drxR ))(()( 22
qc ,0
2. Gaussian (Exp)
))(exp()( 2
c
i
ci
d
r
xR c
3. Thin Plate Spline
ii rxR )(
4. Logarithmic
iii rrxR log)(
In order to determine ai and bi in equation (1), a support domain is formed for the point of interest at x, and n
field nodes are included in the support domain. Coefficients ai and bj in Equation (1) can be determined by
enforcing Equation (1) to be satisfied at these n nodes surrounding the point of interest x. This leads to n linear
equations, one for each node. The matrix form of these equations can be expressed as
bPaRU ms 0 (3)
where the vector of function values Us is
T
ns uuuU ...21 (4)
The moment matrix of TBFs is
)()(2)(1
)2(1)2(2)2(1
)1()1(2)1(1
0
...
............
...
...
rnnrnrn
rrr
rnrr
RRR
RRR
RRR
R ( 5)
Tne polynomial moment matrix is
)(321
321
321
)()()()(
......
...
...
1...111
nmnmmmm
n
n
T
m
xpxpxpxp
yyyy
xxxx
P
(6)
The vector of coefficients for RBFs is
3. ConstructionOf ShapeFunction ByRadialPoint InterpolationMethod For1d Case
International organization of Scientific Research 25 | P a g e
T
n
T
aaaa ...21 (7)
The vector of coefficients for polynomial is
T
n
T
bbbb ...21 (8)
In equation (5) rk in Ri(rk) is defined as
)()( 22
ikikk yyxxr (9)
However, There are n+m variables in equation (4). The additional m equations can be added using the following
m constraint conditions.
n
i
T
miij aPaxp
1
m1,2,...,j,0)( (10)
Combing Equations (3) et (10) yields the following set of equations in the matrix form
0
0
00
Ga
b
a
P
PRU
U T
m
ms
s
(11)
Where
m21n210 b...bba...aaaT
(12)
T
ns uuuU 0...00...21 (13)
Because the matrix R0, is symmetric, the matrix G will also be symmetric. Solving Equation (11), we obtain
sUG
b
a
a
~1
0
(14)
Equation (14) can be re-written as
b
a
xpxRbxpaxRxu TTTT
)()()()()( (15)
Using Equation (14) we can obtain
s
T
s
TTTT
UxUGxpxRbxpaxRxu
~
)(
~
)()()()()( 1
(16)
Where the RPIM shape function can be expressed as
)(...)()(...)()(
)()()(
~
121
1
xxxxx
GxpxRx
mnnn
TTT
(17)
Finally, the RPIM shape functions corresponding to the nodal displacements vector Φ(x) are obtained as
)(...)()()(
~
21 xxxx n
T
(18)
Equation (16) can be re-written as
)(u(x)
n
1i
i
is
T
uUx (19)
The derivatives of u(x) are easily obtained as
)((x)u ,, s
T
ll Ux (20)
Where Ɩ denotes either the coordinate x or y. A comma designates a partial differentiation with respect to the
indicated spatial coordinate that follows.
There are several advantages of using RBFs as a basis in constructing PIM shape functions that use local
compact support domains.
Using REFs can effectively solve the singularity problem of the polynomial PIM.
RPIM shape functions are stable and hence flexible for arbitrary and irregular nodal distributions.
RPIM shape functions can be easily created for three-dimensional domains, because the only variable is the
distance r in a REF. For three-dimensional interpolation, we simply change the distance expression to
)()()( 222
iii zzyyxxr (21)
RPIM shape functions are better suited than MLS functions for fluid dynamics problems.
However, RPIM also has some shortcomings, such as
4. ConstructionOf ShapeFunction ByRadialPoint InterpolationMethod For1d Case
International organization of Scientific Research 26 | P a g e
RPIM shape functions usually give less accurate solutions for solid problems compared to MLS and the
polynomial PlM shape functions.
Some shape parameters must be determined carefully, because they can affect the accuracy and the
performance of the RPIM shape functions used in MFree methods.
RPIM shape functions are usually computationally more expensive than the polynomial PIM because more
nodes are required in the local support domain.
III. 1D-RPIM SHAPE FUNCTION CALCULUS
There a 2D-code developed by G.R. Lui and coworkers, was modified for 1D case to calculate the RPIM shape
function and theirs first and second derivatives to respect of x.
The case study is a domain formed by six nodes as shown in fig. 1
Figure 1: 1D domain formed by six nodes
The table 2 gives the spatial coordinate for each node. A set of six nodes of interest is chosen as is given in table
3.
In this study, the following coefficients are chosen : q=0.5, αc=2, dc=1, η=2 and ambasis=0 (RPIM is pure).
Table 2, Field nodes and their coordinates
Node 1 2 3 4 5 6
Coordinate 0 1 2 3 4 5
Table 3, Field node of interest
Node 1 2 3 4 5 6
Coordinate 0 1 2 3 4 5
The figure 2 gives the flowchart of modified code.
Figure 2, Flowchart of modified code
5. ConstructionOf ShapeFunction ByRadialPoint InterpolationMethod For1d Case
International organization of Scientific Research 27 | P a g e
IV. THE RESULT AND DISCUSSION
The following figures (3), (10) and (17) give the result obtained by the modified code in cases:
the Quadratic-RBF,
the exponential-RBF,
The TPS-RBF.
Figure 3, the result by MQ RBF
The following figures (4-9) show shape function Φ and theirs first and second derivatives to respect of x in each
node, for MQ-RBF.
Figure 4, Φ function and and its first and second derivatives to respect of x for node 1 by MQ method
6. ConstructionOf ShapeFunction ByRadialPoint InterpolationMethod For1d Case
International organization of Scientific Research 28 | P a g e
Figure 5, Φ function and and its first and second derivatives to respect of x for node 2 by MQ method
Figure 6, Φ function and and its first and second derivatives to respect of x for node 3 by MQ method
Figure 7, Φ function and and its first and second derivatives to respect of x for node 4 by MQ method
7. ConstructionOf ShapeFunction ByRadialPoint InterpolationMethod For1d Case
International organization of Scientific Research 29 | P a g e
Figure 8, Φ function and and its first and second derivatives to respect of x for node 5 by MQ method
Figure 9, Φ function and and its first and second derivatives to respect of x for node 6 by MQ method
Figure 10, the result by Exp RBF
8. ConstructionOf ShapeFunction ByRadialPoint InterpolationMethod For1d Case
International organization of Scientific Research 30 | P a g e
The following figures (10-15) show shape function Φ and theirs first and second derivatives to respect of x in
each node, for EXP-RBF.
Figure 11, Phi, Φ function and and its first and second derivatives to respect of x for node 1 by EXP
method
Figure 12,Φ function and and its first and second derivatives to respect of x for node 2 by EXP method
Figure 13, Φ function and and its first and second derivatives to respect of x for node 3 by EXP method
9. ConstructionOf ShapeFunction ByRadialPoint InterpolationMethod For1d Case
International organization of Scientific Research 31 | P a g e
Figure 14, Φ function and and its first and second derivatives to respect of x for node 4 by EXP method
Figure 15, Φ function and and its first and second derivatives to respect of x for node 5 by EXP method
Figure 16, Φ function and and its first and second derivatives to respect of x for node 6 by EXP method
10. ConstructionOf ShapeFunction ByRadialPoint InterpolationMethod For1d Case
International organization of Scientific Research 32 | P a g e
Figure 17, result by TPS-RBF
The following figures (18-23) show shape function Φ and theirs first and second derivatives to respect of x in
each node, for TPS-RBF.
Figure 18,Φ function and and its first and second derivatives to respect of x for node 1 by TPS method
11. ConstructionOf ShapeFunction ByRadialPoint InterpolationMethod For1d Case
International organization of Scientific Research 33 | P a g e
Figure 19,Φ function and and its first and second derivatives to respect of x for node 2 by TPS method
Figure 20,Φ function and and its first and second derivatives to respect of x for node 3 by TPS method
Figure 21,Φ function and and its first and second derivatives to respect of x for node 4 by TPS method
12. ConstructionOf ShapeFunction ByRadialPoint InterpolationMethod For1d Case
International organization of Scientific Research 34 | P a g e
Figure 22,Φ function and and its first and second derivatives to respect of x for node 5 by TPS method
Figure 23,Φ function and and its first and second derivatives to respect of x for node 6 by TPS method
If the points of interest are different from nodes, for example the field (0.5, 1.5, 2.5, 3.5, 4.5, 5.5) is chosen as a
set of interest points. In this case the Φ function and its derivatives for the interest point xv=2.5 are shown in
figures 23 to 25 by the three different methods.
Figure 24, Φ function and and its first and second derivatives for node xv =2.5 by MQ method.
13. ConstructionOf ShapeFunction ByRadialPoint InterpolationMethod For1d Case
International organization of Scientific Research 35 | P a g e
REFERENCES
Books:
[1] Rong Liu, Meshfree methods: moving beyond the finite element method (CRC Press LLC, 2003).
[2] Rong Liu and Y.T. Gu, An Introduction to Meshfree Methods and their programming, (2006 Springer )
[3] Youping Chen, James D. Lee, and Azim Eskandarian, Meshless Methods in Solid Mechanics(2006
Springer Science , Inc)