Search results for: Contour Direction Technique

Authors: Pinaki Pratim Acharjya, Esha Dutta

Abstract:

In image segmentation contour detection is one of the important pre-processing steps in recent days. Contours characterize boundaries and contour detection is one of the most difficult tasks in image processing. Hence it is a problem of fundamental importance in image processing. Contour detection of an image decreases the volume of data considerably and useless information is removed, but the structural properties of the image remain same. In this research, a robust and effective contour detection technique has been proposed using mathematical morphology. Three different contour detection results are obtained by using morphological dilation and erosion. The comparative analyses of three different results also have been done.

Keywords: Image segmentation, contour detection, mathematical morphology.

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Authors: U.A.A. Niroshika, Ravinda G.N. Meegama

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Deformable active contours are widely used in computer vision and image processing applications for image segmentation, especially in biomedical image analysis. The active contour or “snake" deforms towards a target object by controlling the internal, image and constraint forces. However, if the contour initialized with a lesser number of control points, there is a high probability of surpassing the sharp corners of the object during deformation of the contour. In this paper, a new technique is proposed to construct the initial contour by incorporating prior knowledge of significant corners of the object detected using the Harris operator. This new reconstructed contour begins to deform, by attracting the snake towards the targeted object, without missing the corners. Experimental results with several synthetic images show the ability of the new technique to deal with sharp corners with a high accuracy than traditional methods.

Keywords: Active Contours, Image Segmentation, Harris Operator, Snakes

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Authors: Atisthan Wuttimanop, Suchada Rianmora

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To support design process for launching the product on time, reverse engineering (RE) process has been introduced for quickly generating 3D CAD model from its physical object. The accuracy of the 3D CAD model depends upon the data acquisition technique selected, contact or non-contact methods. In order to reduce times used for acquiring surface and eliminating noises, the automated selective acquisition system has been developed and presented in this research as the alternative channel for non-contact acquisition technique where the data is selectively and locally scanned contour by contour without performing data reduction process. The results present as the organized contour points which are directly used to generate 3D virtual model. The comparison between the proposed technique and another non-contact scanning technique has been presented and discussed.

Keywords: Automated selective acquisition system, Non-contact acquisition, Reverse engineering, 3D scanners.

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Authors: K. Bommanna Raja, M.Madheswaran, K.Thyagarajah

Abstract:

A higher order spline interpolated contour obtained with up-sampling of homogenously distributed coordinates for segmentation of kidney region in different classes of ultrasound kidney images has been developed and presented in this paper. The performance of the proposed method is measured and compared with modified snake model contour, Markov random field contour and expert outlined contour. The validation of the method is made in correspondence with expert outlined contour using maximum coordinate distance, Hausdorff distance and mean radial distance metrics. The results obtained reveal that proposed scheme provides optimum contour that agrees well with expert outlined contour. Moreover this technique helps to preserve the pixels-of-interest which in specific defines the functional characteristic of kidney. This explores various possibilities in implementing computer-aided diagnosis system exclusively for US kidney images.

Keywords: Ultrasound Kidney Image – Kidney Segmentation –Active Contour – Markov Random Field – Higher Order SplineInterpolation

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Authors: Boontee Kruatrachue, Narongchai Moongfangklang, Kritawan Siriboon

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This paper describes fast and efficient method for page segmentation of document containing nonrectangular block. The segmentation is based on edge following algorithm using small window of 16 by 32 pixels. This segmentation is very fast since only border pixels of paragraph are used without scanning the whole page. Still, the segmentation may contain error if the space between them is smaller than the window used in edge following. Consequently, this paper reduce this error by first identify the missed segmentation point using direction information in edge following then, using X-Y cut at the missed segmentation point to separate the connected columns. The advantage of the proposed method is the fast identification of missed segmentation point. This methodology is faster with fewer overheads than other algorithms that need to access much more pixel of a document.

Keywords: Contour Direction Technique, Missed SegmentationPoints, Page Segmentation, Recursive X-Y Cut Technique

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Authors: Petre Alexandru, Dragos Macaveiu, Catalin Alexandru

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This paper addresses issues of integral steering of vehicles with two steering axles, where the rear wheels are pivoted in the direction of the front wheels, but also in the opposite direction. The steering box of the rear axle is presented with simple linkages (single contour) that correlate the pivoting of the rear wheels according to the direction of the front wheels, respectively to the rotation angle of the steering wheel. The functionality of the system is analyzed – the extent to which the requirements of the integral steering are met by the considered/proposed mechanisms. The paper highlights the quality of the single contour linkages, with two driving elements for meeting these requirements, emphasizing diagrams of mechanisms with 2 driving elements. Cam variants are analyzed and proposed for the rear axle steering box. Cam profiles are determined by various factors.

Keywords: Cam gear, four wheel drive, integral steering, linkage.

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Authors: Ahmad Fahim Nasiry, Shigeo Honma

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We examine two-dimensional oil displacement by water in a petroleum reservoir. The pore fluid is immiscible, and the porous media is homogenous and isotropic in the horizontal direction. Buckley-Leverett theory and a combination of Laplacian and Darcy’s law are used to study the fluid flow through porous media, and the Laplacian that defines the dispersion and diffusion of fluid in the sand using heavy oil is discussed. The reservoir is homogenous in the horizontal direction, as expressed by the partial differential equation. Two main factors which are observed are the water saturation and pressure distribution in the reservoir, and they are evaluated for predicting oil recovery in two dimensions by a physical and mathematical simulation model. We review the numerical simulation that solves difficult partial differential reservoir equations. Based on the numerical simulations, the saturation and pressure equations are calculated by the iterative alternating direction implicit method and the iterative alternating direction explicit method, respectively, according to the finite difference assumption. However, to understand the displacement of oil by water and the amount of water dispersion in the reservoir better, an interpolated contour line of the water distribution of the five-spot pattern, that provides an approximate solution which agrees well with the experimental results, is also presented. Finally, a computer program is developed to calculate the equation for pressure and water saturation and to draw the pressure contour line and water distribution contour line for the reservoir.

Keywords: Numerical simulation, immiscible, finite difference, IADI, IADE, waterflooding.

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Authors: Mehran Yazdi, Mehdi Seyfi, Amirhossein Rafati, Meghdad Asadi

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Detection and tracking of the lip contour is an important issue in speechreading. While there are solutions for lip tracking once a good contour initialization in the first frame is available, the problem of finding such a good initialization is not yet solved automatically, but done manually. We have developed a new tracking solution for lip contour detection using only few landmarks (15 to 25) and applying the well known Active Shape Models (ASM). The proposed method is a new LMS-like adaptive scheme based on an Auto regressive (AR) model that has been fit on the landmark variations in successive video frames. Moreover, we propose an extra motion compensation model to address more general cases in lip tracking. Computer simulations demonstrate a fair match between the true and the estimated spatial pixels. Significant improvements related to the well known LMS approach has been obtained via a defined Frobenius norm index.

Keywords: Lip contour, Tracking, LMS-Like

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Authors: Ali Abdrhman Ukasha

Abstract:

This paper presented two new efficient algorithms for contour approximation. The proposed algorithm is compared with Ramer (good quality), Triangle (faster) and Trapezoid (fastest) in this work; which are briefly described. Cartesian co-ordinates of an input contour are processed in such a manner that finally contours is presented by a set of selected vertices of the edge of the contour. In the paper the main idea of the analyzed procedures for contour compression is performed. For comparison, the mean square error and signal-to-noise ratio criterions are used. Computational time of analyzed methods is estimated depending on a number of numerical operations. Experimental results are obtained both in terms of image quality, compression ratios, and speed. The main advantages of the analyzed algorithm is small numbers of the arithmetic operations compared to the existing algorithms.

Keywords: Polygonal approximation, Ramer, Triangle and Trapezoid methods.

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Authors: Harshit Mehrotra, Gaurav Agrawal, M.C. Srivastava

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Computerized lip reading has been one of the most actively researched areas of computer vision in recent past because of its crime fighting potential and invariance to acoustic environment. However, several factors like fast speech, bad pronunciation, poor illumination, movement of face, moustaches and beards make lip reading difficult. In present work, we propose a solution for automatic lip contour tracking and recognizing letters of English language spoken by speakers using the information available from lip movements. Level set method is used for tracking lip contour using a contour velocity model and a feature vector of lip movements is then obtained. Character recognition is performed using modified k nearest neighbor algorithm which assigns more weight to nearer neighbors. The proposed system has been found to have accuracy of 73.3% for character recognition with speaker lip movements as the only input and without using any speech recognition system in parallel. The approach used in this work is found to significantly solve the purpose of lip reading when size of database is small.

Keywords: Contour Velocity Model, Lip Contour Tracking, LipReading, Visual Character Recognition.

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Authors: M. Tridi, N. Nacereddine, N. Oucief

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This paper describes a novel method for automatic estimation of the contours of weld defect in radiography images. Generally, the contour detection is the first operation which we apply in the visual recognition system. Our approach can be described as a region based maximum likelihood formulation of parametric deformable contours. This formulation provides robustness against the poor image quality, and allows simultaneous estimation of the contour parameters together with other parameters of the model. Implementation is performed by a deterministic iterative algorithm with minimal user intervention. Results testify for the very good performance of the approach especially in synthetic weld defect images.

Keywords: Contour, gaussian, likelihood, rayleigh.

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Authors: Prasannakumar Palaniappan, Dong Ho Shin, Chul Gyu Song

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The photoacoustic images are obtained from a custom developed linear array photoacoustic tomography system. The biological specimens are imitated by conducting phantom tests in order to retrieve a fully functional photoacoustic image. The acquired image undergoes the active region based contour filtering to remove the noise and accurately segment the object area for further processing. The universal back projection method is used as the image reconstruction algorithm. The active contour filtering is analyzed by evaluating the signal to noise ratio and comparing it with the other filtering methods.

Keywords: Contour filtering, linear array, photoacoustic tomography, universal back projection.

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Authors: Marc C. Robini, Pierre-Jean Viverge, Yuemin Zhu, Jianhua Luo

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The standard approach to image reconstruction is to stabilize the problem by including an edge-preserving roughness penalty in addition to faithfulness to the data. However, this methodology produces noisy object boundaries and creates a staircase effect. The existing attempts to favor the formation of smooth contour lines take the edge field explicitly into account; they either are computationally expensive or produce disappointing results. In this paper, we propose to incorporate the smoothness of the edge field in an implicit way by means of an additional penalty term defined in the wavelet domain. We also derive an efficient half-quadratic algorithm to solve the resulting optimization problem, including the case when the data fidelity term is non-quadratic and the cost function is nonconvex. Numerical experiments show that our technique preserves edge sharpness while smoothing contour lines; it produces visually pleasing reconstructions which are quantitatively better than those obtained without wavelet-domain constraints.

Keywords:

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Authors: M.Asif, M.R.Arshad, P.A.Wilson

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In this paper, a simple active contour based visual tracking algorithm is presented for outdoor AGV application which is currently under development at the USM robotic research group (URRG) lab. The presented algorithm is computationally low cost and able to track road boundaries in an image sequence and can easily be implemented on available low cost hardware. The proposed algorithm used an active shape modeling using the B-spline deformable template and recursive curve fitting method to track the current orientation of the road.

Keywords: Active contour, B-spline, recursive curve fitting.

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Authors: Roy R. Gu, Mahesh Sahu

Abstract:

The use of contour strips of perennial vegetation with bio-fuel potential can improve surface water quality by reducing NO3-N and sediment outflow from cropland to surface water-bodies. It also has economic benefits of producing ethanol. In this study, The Soil and Water Assessment Tool (SWAT) model was applied to a watershed in Iowa, USA to examine the effectiveness of contour strips of switch grass in reducing the NO3-N outflows from crop fields to rivers or lakes. Numerical experiments were conducted to identify potential subbasins in the watershed that have high water quality impact, and to examine the effects of strip size on NO3-N reduction under various meteorological conditions, i.e. dry, average and wet years. Useful information was obtained for the evaluation of economic feasibility of growing switch grass for bio-fuel in contour strips. The results can assist in cost-benefit analysis and decisionmaking in best management practices for environmental protection.

Keywords: ethanol, modeling, water quality, NO3-N, watershed.

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Authors: Chen Sun, Nemai Chandra Karmakar

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A novel direction-of-arrival (DOA) estimation technique, which uses a conventional multiple signal classification (MUSIC) algorithm with periodic signals, is applied to a single RF-port parasitic array antenna for direction finding. Simulation results show that the proposed method gives high resolution (1 degree) DOA estimation in an uncorrelated signal environment. The novelty lies in that the MUSIC algorithm is applied to a simplified antenna configuration. Only one RF port and one analogue-to-digital converter (ADC) are used in this antenna, which features low DC power consumption, low cost, and ease of fabrication. Modifications to the conventional MUSIC algorithm do not bring much additional complexity. The proposed technique is also free from the negative influence by the mutual coupling between elements. Therefore, the technique has great potential to be implemented into the existing wireless mobile communications systems, especially at the power consumption limited mobile terminals, to provide additional position location (PL) services.

Keywords: Direction-of-arrival (DOA) estimation, electronically steerable parasitic array radiator (ESPAR), multiple single classifications (MUSIC), position location.

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Authors: Hiren Mewada, Suprava Patnaik

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Object identification and segmentation application requires extraction of object in foreground from the background. In this paper the Bhattacharya distance based probabilistic approach is utilized with an active contour model (ACM) to segment an object from the background. In the proposed approach, the Bhattacharya histogram is calculated on non-linear structure tensor space. Based on the histogram, new formulation of active contour model is proposed to segment images. The results are tested on both color and gray images from the Berkeley image database. The experimental results show that the proposed model is applicable to both color and gray images as well as both texture images and natural images. Again in comparing to the Bhattacharya based ACM in ICA space, the proposed model is able to segment multiple object too.

Keywords: Active Contour, Bhattacharya Histogram, Structure tensor, Image segmentation.

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Authors: Alexandra Oliveros, Miguel Sotaquirá

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DNA microarray technology is widely used by geneticists to diagnose or treat diseases through gene expression. This technology is based on the hybridization of a tissue-s DNA sequence into a substrate and the further analysis of the image formed by the thousands of genes in the DNA as green, red or yellow spots. The process of DNA microarray image analysis involves finding the location of the spots and the quantification of the expression level of these. In this paper, a tool to perform DNA microarray image analysis is presented, including a spot addressing method based on the image projections, the spot segmentation through contour based segmentation and the extraction of relevant information due to gene expression.

Keywords: Contour segmentation, DNA microarrays, edge detection, image processing, segmentation, spot addressing.

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Authors: Ahmad Tariq Sheikh, Shahzad Amin Sheikh

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A new distance-adjusted approach is proposed in which static square contours are defined around an estimated symbol in a QAM constellation, which create regions that correspond to fixed step sizes and weighting factors. As a result, the equalizer tap adjustment consists of a linearly weighted sum of adaptation criteria that is scaled by a variable step size. This approach is the basis of two new algorithms: the Variable step size Square Contour Algorithm (VSCA) and the Variable step size Square Contour Decision-Directed Algorithm (VSDA). The proposed schemes are compared with existing blind equalization algorithms in the SCA family in terms of convergence speed, constellation eye opening and residual ISI suppression. Simulation results for 64-QAM signaling over empirically derived microwave radio channels confirm the efficacy of the proposed algorithms. An RTL implementation of the blind adaptive equalizer based on the proposed schemes is presented and the system is configured to operate in VSCA error signal mode, for square QAM signals up to 64-QAM.

Keywords: Adaptive filtering, Blind Equalization, Square Contour Algorithm.

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Authors: Renato Dedic, Madjid Allili, Roger Lecomte, Adbelhamid Benchakroun

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The class of geometric deformable models, so-called level sets, has brought tremendous impact to medical imagery. In this paper we present yet another application of level sets to medical imaging. The method we give here will in a way modify the speed term in the standard level sets equation of motion. To do so we build a potential based on the distance and the gradient of the image we study. In turn the potential gives rise to the force field: F~F(x, y) = P ∀(p,q)∈I ((x, y) - (p, q)) |ÔêçI(p,q)| |(x,y)-(p,q)| 2 . The direction and intensity of the force field at each point will determine the direction of the contour-s evolution. The images we used to test our method were produced by the Univesit'e de Sherbrooke-s PET scanners.

Keywords: PET, Cardiac, Heart, Mouse, Geodesic, Geometric, Level Sets, Deformable Models, Edge Detection, Segmentation.

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Authors: Kuo-Lung Lor, Chi-Hsuan Tsou, Yeun-Chung Chang, Chung-Ming Chen

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For evaluating the severity of Chronic Obstructive Pulmonary Disease (COPD), one is interested in inspecting the airway wall thickening due to inflammation. Although airway segmentations have being well developed to reconstruct in high order, airway wall segmentation remains a challenge task. While tackling such problem as a multi-surface segmentation, the interrelation within surfaces needs to be considered. We propose a new method for three-dimensional airway wall segmentation using spring structural active contour model. The method incorporates the gravitational field of the image and repelling force field of the inner lumen as the soft constraint and the geometric spring structure of active contour as the hard constraint to approximate a three-dimensional coupled surface readily for thickness measurements. The results show the preservation of topology constraints of coupled surfaces. In conclusion, our springy, soft-tissue-like structure ensures the globally optimal solution and waives the shortness following by the inevitable improper inner surface constraint.

Keywords: active contour model, airway wall, COPD, geometric spring structure

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Authors: Yasusi Kanada

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Objects are usually horizontally sliced when printed by 3D printers. Therefore, if an object to be printed, such as a collection of fibers, originally has natural direction in shape, the printed direction contradicts with the natural direction. By using proper tools, such as field-oriented 3D paint software, field-oriented solid modelers, field-based tool-path generation software, and non-horizontal FDM 3D printers, the natural direction can be modeled and objects can be printed in a direction that is consistent with the natural direction. This consistence results in embodiment of momentum or force in expressions of the printed object. To achieve this goal, several design and manufacturing problems, but not all, have been solved. An application of this method is (Japanese) 3D calligraphy.

Keywords: 3D printing, Three-dimensional printing, Solid free-form fabrication, SFF, Fused deposition modeling, FDM, Additive manufacturing.

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Authors: Ehsan Saghapour, Somayeh Zandian

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Image segmentation is an important step in image processing. Major developments in medical imaging allow physicians to use potent and non-invasive methods in order to evaluate structures, performance and to diagnose human diseases. In this study, an active contour was used to extract vessel networks from color retina images. Automatic analysis of retina vessels facilitates calculation of arterial index which is required to diagnose some certain retinopathies.

Keywords: Active contour, retinal vessel segmentation, image processing.

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Authors: Mohammad Izadkhah, Mojtaba Hoseini, Alireza Khalili Tehrani

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In this paper we presented a new method for tracking flying targets in color video sequences based on contour and kernel. The aim of this work is to overcome the problem of losing target in changing light, large displacement, changing speed, and occlusion. The proposed method is made in three steps, estimate the target location by particle filter, segmentation target region using neural network and find the exact contours by greedy snake algorithm. In the proposed method we have used both region and contour information to create target candidate model and this model is dynamically updated during tracking. To avoid the accumulation of errors when updating, target region given to a perceptron neural network to separate the target from background. Then its output used for exact calculation of size and center of the target. Also it is used as the initial contour for the greedy snake algorithm to find the exact target's edge. The proposed algorithm has been tested on a database which contains a lot of challenges such as high speed and agility of aircrafts, background clutter, occlusions, camera movement, and so on. The experimental results show that the use of neural network increases the accuracy of tracking and segmentation.

Keywords: Video tracking, particle filter, greedy snake, neural network.

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Authors: Dia I. Abu-Al-Nadi, M. J. Mismar, T. H. Ismail

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A technique for estimating the direction-of-arrival (DOA) of unknown number of source signals is presented using the eigen-approach. The eigenvector corresponding to the minimum eigenvalue of the autocorrelation matrix yields the minimum output power of the array. Also, the array polynomial with this eigenvector possesses roots on the unit circle. Therefore, the pseudo-spectrum is found by perturbing the phases of the roots one by one and calculating the corresponding array output power. The results indicate that the DOAs and the number of source signals are estimated accurately in the presence of a wide range of input noise levels.

Keywords: Array signal processing, direction-of-arrival, antenna arrays, eigenvalues, eigenvectors.

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Authors: Tao Peng, Jing Zhao, Yanqing Xu, Jing Cai

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Due to missing/ambiguous boundaries between the prostate and neighboring structures, the presence of shadow artifacts, as well as the large variability in prostate shapes, ultrasound prostate segmentation is challenging. To handle these issues, this paper develops a hybrid method for ultrasound prostate segmentation by combining an optimized closed principal curve-based method and the evolutionary neural network; the former can fit curves with great curvature and generate a contour composed of line segments connected by sorted vertices, and the latter is used to express an appropriate map function (represented by parameters of evolutionary neural network) for generating the smooth prostate contour to match the ground truth contour. Both qualitative and quantitative experimental results showed that our proposed method obtains accurate and robust performances.

Keywords: Ultrasound prostate segmentation, optimized closed polygonal segment method, evolutionary neural network, smooth mathematical model.

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Authors: Nuseiba M. Altarawneh, Suhuai Luo, Brian Regan, Guijin Tang

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Liver segmentation from medical images poses more challenges than analogous segmentations of other organs. This contribution introduces a liver segmentation method from a series of computer tomography images. Overall, we present a novel method for segmenting liver by coupling density matching with shape priors. Density matching signifies a tracking method which operates via maximizing the Bhattacharyya similarity measure between the photometric distribution from an estimated image region and a model photometric distribution. Density matching controls the direction of the evolution process and slows down the evolving contour in regions with weak edges. The shape prior improves the robustness of density matching and discourages the evolving contour from exceeding liver’s boundaries at regions with weak boundaries. The model is implemented using a modified distance regularized level set (DRLS) model. The experimental results show that the method achieves a satisfactory result. By comparing with the original DRLS model, it is evident that the proposed model herein is more effective in addressing the over segmentation problem. Finally, we gauge our performance of our model against matrices comprising of accuracy, sensitivity, and specificity.

Keywords: Bhattacharyya distance, distance regularized level set (DRLS) model, liver segmentation, level set method.

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Authors: W. Kultangwattana, K. Somkantha, P. Phuangsuwan

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This paper presents a technique for diagnosis of the abdominal aorta aneurysm in magnetic resonance imaging (MRI) images. First, our technique is designed to segment the aorta image in MRI images. This is a required step to determine the volume of aorta image which is the important step for diagnosis of the abdominal aorta aneurysm. Our proposed technique can detect the volume of aorta in MRI images using a new external energy for snakes model. The new external energy for snakes model is calculated from Law-s texture. The new external energy can increase the capture range of snakes model efficiently more than the old external energy of snakes models. Second, our technique is designed to diagnose the abdominal aorta aneurysm by Bayesian classifier which is classification models based on statistical theory. The feature for data classification of abdominal aorta aneurysm was derived from the contour of aorta images which was a result from segmenting of our snakes model, i.e., area, perimeter and compactness. We also compare the proposed technique with the traditional snakes model. In our experiment results, 30 images are trained, 20 images are tested and compared with expert opinion. The experimental results show that our technique is able to provide more accurate results than 95%.

Keywords: Adbominal Aorta Aneurysm, Bayesian Classifier, Snakes Model, Texture Feature.

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Authors: Zia R. Tahir, P. Mandal

Abstract:

This paper presents the details of a numerical study of buckling and post buckling behaviour of laminated carbon fiber reinforced plastic (CFRP) thin-walled cylindrical shell under axial compression using asymmetric meshing technique (AMT) by ABAQUS. AMT is considered to be a new perturbation method to introduce disturbance without changing geometry, boundary conditions or loading conditions. Asymmetric meshing affects both predicted buckling load and buckling mode shapes. Cylindrical shell having lay-up orientation [0^o/+45^o/-45^o/0^o] with radius to thickness ratio (R/t) equal to 265 and length to radius ratio (L/R) equal to 1.5 is analysed numerically. A series of numerical simulations (experiments) are carried out with symmetric and asymmetric meshing to study the effect of asymmetric meshing on predicted buckling behaviour. Asymmetric meshing technique is employed in both axial direction and circumferential direction separately using two different methods, first by changing the shell element size and varying the total number elements, and second by varying the shell element size and keeping total number of elements constant. The results of linear analysis (Eigenvalue analysis) and non-linear analysis (Riks analysis) using symmetric meshing agree well with analytical results. The results of numerical analysis are presented in form of non-dimensional load factor, which is the ratio of buckling load using asymmetric meshing technique to buckling load using symmetric meshing technique. Using AMT, load factor has about 2% variation for linear eigenvalue analysis and about 2% variation for non-linear Riks analysis. The behaviour of load end-shortening curve for pre-buckling is same for both symmetric and asymmetric meshing but for asymmetric meshing curve behaviour in post-buckling becomes extraordinarily complex. The major conclusions are: different methods of AMT have small influence on predicted buckling load and significant influence on load displacement curve behaviour in post buckling; AMT in axial direction and AMT in circumferential direction have different influence on buckling load and load displacement curve in post-buckling.

Keywords: CFRP Composite Cylindrical Shell, Asymmetric Meshing Technique, Primary Buckling, Secondary Buckling, Linear Eigenvalue Analysis, Non-linear Riks Analysis.

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Authors: Usman Ali Khan, Bismah Tariq, Khalida Raza, Saima Malik, Aoun Muhammad

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This research paper is based upon the simulation of gradient of mathematical functions and scalar fields using MATLAB. Scalar fields, their gradient, contours and mesh/surfaces are simulated using different related MATLAB tools and commands for convenient presentation and understanding. Different mathematical functions and scalar fields are examined here by taking their gradient, visualizing results in 3D with different color shadings and using other necessary relevant commands. In this way the outputs of required functions help us to analyze and understand in a better way as compared to just theoretical study of gradient.

Keywords: MATLAB, Gradient, Contour, Scalar Field, Mesh

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