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1

Zhang, Lu Ping, Biao Li, and Lu Ping Wang. "A Infrared Small Moving Object Extraction Method in the Context of Complex Background Motion." Advanced Materials Research 760-762 (September 2013): 1879–83. http://dx.doi.org/10.4028/www.scientific.net/amr.760-762.1879.

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The detection of small moving target in the context of complex background is a difficult issue. A method combining interframe differential registration and adaptive wiener filtering aimed to suppress background to detect moving object in complex background is proposed. The fixed background in the fore-and-aft frames can be filtered out by the interframe registration which preserves the moving target, parts of background and noise due to interframe movement and the gray-scale fluctuation. On one hand the complex background is estimated by an adaptive wiener filter, and the background suppression leaves the high-frequency regions containing the moving target in image. On the other hand, most of the high-frequency regions corresponding to non-target area are eliminated by the inter-frame registration in the differential images. The motion of target is continual in image sequences, while the position of the leaked background is relatively fixed and the noise is of small size. The fusion of the background suppression and inter-frame registration makes the discrimination of targets, background and noise possible. The small moving target is detected by trajectory association based on its interframe trajectory continuity. Experiment results verify the feasibility of the method.
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Higgins, W. E., C. J. Orlick, and B. E. Ledell. "Nonlinear filtering approach to 3-D gray-scale image interpolation." IEEE Transactions on Medical Imaging 15, no. 4 (1996): 580–87. http://dx.doi.org/10.1109/42.511761.

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Kim, Sang-Yup, and Seong-Whan Lee. "Gray-Scale Nonlinear Shape Normalization Method for Handwritten Oriental Character Recognition." International Journal of Pattern Recognition and Artificial Intelligence 12, no. 01 (1998): 81–95. http://dx.doi.org/10.1142/s0218001498000075.

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In general, nonlinear shape normalization methods for binary images have been used in order to compensate for the shape distortions of handwritten characters. However, in most document image analysis and recognition systems, a gray-scale image is first captured and digitized using a scanner or a video camera, then a binary image is extracted from the original gray-scale image using a certain extraction technique. This binarization process may remove some useful information of character images such as topological features, and introduce noises to character background. These errors are accumulated in nonlinear shape normalization step and transferred to the following feature extraction or recognition step. They may eventually cause incorrect recognition results. In this paper, we propose nonlinear shape normalization methods for gray-scale handwritten Oriental characters in order to minimize the loss of information caused by binarization and compensate for the shape distortions of characters. Two-dimensional linear interpolation technique has been extended to nonlinear space and the extended interpolation technique has been adopted in the proposed methods to enhance the quality of normalized images. In order to verify the efficiency of the proposed methods, the recognition rate, the processing time and the computational complexity of the proposed algorithms have been considered. The experimental results demonstrate that the proposed methods are efficient not only to compensate for the shape distortions of handwritten Oriental characters but also to maintain the information in gray-scale Oriental characters.
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Scollar, Irwin, Bernd Weidner, and Karel Segeth. "Display of archaeological magnetic data." GEOPHYSICS 51, no. 3 (1986): 623–33. http://dx.doi.org/10.1190/1.1442116.

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Magnetic data from archaeological sites have traditionally been displayed by contour, isometric, and dot‐density plotting, or by simulated gray‐scale techniques using symbol overprinting. These methods do not show fine linear structures in the data which are of great interest to archaeologists. If true gray‐scale methods using a modern video display, followed by film recording for hard copy are employed, image processing techniques can be applied to enhance the geometric structures of archaeological interest. Interpolation techniques for enlarging data to full screen size, along with compression methods to keep data within gray‐scale capabilities, are needed. Such techniques would introduce minimum distortion and allow faint details to be seen in the vicinity of strong anomalies. Postprocessing methods based on rapid image spatial filtering and enhancement algorithms could then be applied in an interactive environment.
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Wang, Zhen-xin, and Ji-hong Ouyang. "Curve length estimation based on cubic spline interpolation in gray-scale images." Journal of Zhejiang University SCIENCE C 14, no. 10 (2013): 777–84. http://dx.doi.org/10.1631/jzus.c1300056.

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Richard, William D., and R. Martin Arthur. "Real-Time Ultrasonic Scan Conversion via Linear Interpolation of Oversampled Vectors." Ultrasonic Imaging 16, no. 2 (1994): 109–23. http://dx.doi.org/10.1177/016173469401600204.

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Scan conversion is required in order to display conventional B-mode ultrasonic signals, which are acquired along radii at varying angles, on standard Cartesian-coordinate video monitors. For real-time implementations, either nearest-neighbor or bilinear interpolation is usually used in scan conversion. If the sampling rate along each radius is high enough, however, the gray-scale value of a given pixel can be interpolated accurately using the nearest samples on two adjacent vectors. The required interpolation then reduces to linear interpolation. Oversampling by a factor of 2 along with linear interpolation was superior to bilinear interpolation of vectors sampled to match pixel-to-pixel spacing in 6 representative B-mode images. A novel 8-bit linear interpolation algorithm was implemented as a CMOS VLSI circuit using a readily available, high-level synthesis tool. The circuit performed 30 million interpolations per second. Arithmetic results produced by the 8-bit interpolator on 7-bit samples were virtually identical to IEEE-format, single-precision, floating-point results.
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7

Xu, Guang Shen, and Gen Yang. "Distortion Correction of Image in Integral Stereolithography System." Applied Mechanics and Materials 63-64 (June 2011): 197–200. http://dx.doi.org/10.4028/www.scientific.net/amm.63-64.197.

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There is geometric distortion of image in integral Stereolithography (SL) system, and the geometric distortion will influence the building accuracy of the SL system. To improve the building accuracy of the SL system, researches of distortion correction of image in the SL system are carried out. The distortion model of binary cubic polynomial interpolation is established with least-square method. The gray scale rebuilding is implemented with space-variable linear interpolation by using VC++6.0. The experimental results indicate that the geometric distortion of the image in integral SL system has been eliminated remarkably, and the radial RMS error is 0.96 pixels. The research lays a foundation for improving building accuracy of the integral SL System.
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Cruz-Bernal, Alejandra, Martha M. Flores-Barranco, Dora L. Almanza-Ojeda, Sergio Ledesma, and Mario A. Ibarra-Manzano. "Analysis of the Cluster Prominence Feature for Detecting Calcifications in Mammograms." Journal of Healthcare Engineering 2018 (December 30, 2018): 1–11. http://dx.doi.org/10.1155/2018/2849567.

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In mammograms, a calcification is represented as small but brilliant white region of the digital image. Earlier detection of malignant calcifications in patients provides high expectation of surviving to this disease. Nevertheless, white regions are difficult to see by visual inspection because a mammogram is a gray-scale image of the breast. To help radiologists in detecting abnormal calcification, computer-inspection methods of mammograms have been proposed; however, it remains an open important issue. In this context, we propose a strategy for detecting calcifications in mammograms based on the analysis of the cluster prominence (cp) feature histogram. The highest frequencies of the cp histogram describe the calcifications on the mammography. Therefore, we obtain a function that models the behaviour of the cp histogram using the Vandermonde interpolation twice. The first interpolation yields a global representation, and the second models the highest frequencies of the histogram. A weak classifier is used for obtaining a final classification of the mammography, that is, with or without calcifications. Experimental results are compared with real DICOM images and their corresponding diagnosis provided by expert radiologists, showing that the cp feature is highly discriminative.
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Wang, Jang Ping, Guo Ming Huang, and Sheng Hua Yurs. "Profiles Detection in Ring Convex Forming by ACLN with Sub-Pixel Accuracy." Key Engineering Materials 364-366 (December 2007): 199–204. http://dx.doi.org/10.4028/www.scientific.net/kem.364-366.199.

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An optical measuring system for the ring test is proposed. In this approach, the machine vision inspection equipment is first built to record and capture the images of ring test from the digital camcorder.The image processing procedures to detect and locate the edge points of the inner and outer radii in ring convex forming are presented. Unlike the conventional sub-pixel estimation based on gray-level values, the quantity (8 bits) of color’s scale has been adopted. In image processing procedures, a clustering method called Adaptive Competitive Learning Network (ACLN) is first used to classify the image hues which represent the different heights of bulge profiles on the top of ring, and then the edge points can be searched by the interpolation step of subpixel accuracy. The calibration curves constructed by the mode of non-constant friction factor called F-value approach is designed to compare and check with the measurement data. The experimental results will be presented and discussed in this study.
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Sonehara, Noboru. "Special Issue Imaging Processing-Algorithm and System. Multi-level Representation and Intensity-level Interpolation of a Gray Scale Image by Relaxation Nueral Network Models." Journal of the Institute of Television Engineers of Japan 45, no. 10 (1991): 1190–98. http://dx.doi.org/10.3169/itej1978.45.1190.

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11

Lin, Jun. "Research on the Performance of Impressionist Painting Color Visual Communication Based on Wireless Communication and Machine Vision." Security and Communication Networks 2021 (March 5, 2021): 1–6. http://dx.doi.org/10.1155/2021/5511252.

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In order to solve the problem of poor visual communication effect of impressionist painting colors and low accuracy of painting color enhancement by existing methods, this thesis proposes a research on the performance of impressionist painting color visual communication based on machine vision under the background of wireless network. This method can improve the vision, speed, and efficiency of communication, through the analysis of the characteristics of impressionist paintings, and determine the visual communication objects of impressionist painting colors. The process of visual communication is analyzed, and the color matching of impressionist painting is completed with the help of BP neural network algorithm. On this basis, the histogram method is used to process the image brightness of impressionist paintings, the image interpolation method is used to process the image brightness of impressionist paintings, and the image is corrected by gamma correction to complete the image performance research. The color vision communication of impressionist painting needs to correct the gray scale error of impressionist painting and enhance the color of impressionist painting. The experimental results show that the accuracy of this method for the color matching of impressionist painting images is about 98%, which has a certain degree of credibility.
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12

RAO, Xiong, Run DU, Wenming CHENG, and Yi YANG. "Modified proportional topology optimization algorithm for multiple optimization problems." Mechanics 30, no. 1 (2024): 36–45. http://dx.doi.org/10.5755/j02.mech.34367.

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Three modified proportional topology optimization (MPTO) algorithms are presented in this paper, which are named MPTOc, MPTOs and MPTOm, respectively. MPTOc aims to address the minimum compliance problem with volume constraint, MPTOs aims to solve the minimum volume fraction problem under stress constraint, and MPTOm aims to tackle the minimum volume fraction problem under compliance and stress constraints. In order to get rid of the shortcomings of the original proportional topology optimization (PTO) algorithm and improve the comprehensive performance of the PTO algorithm, the proposed algorithms modify the material interpolation scheme and introduce the Heaviside threshold function based on the PTO algorithm. To confirm the effectiveness and superiority of the presented algorithms, multiple optimization problems for the classical MBB beam are solved, and the original PTO algorithm is compared with the new algorithms. Numerical examples show that MPTOc, MPTOs and MPTOm enjoy distinct advantages over the PTO algorithm in the matter of convergence efficiency and the ability to obtain distinct topology structure without redundancy. Moreover, MPTOc has the fastest convergence speed among these algorithms and can acquire the smallest (best) compliance value. In addition, the new algorithms are also superior to PTO concerning suppressing gray-scale elements.
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13

Pande, Sandeep D., and Manna S. R. Chetty. "Linear Bezier Curve Geometrical Feature Descriptor for Image Recognition." Recent Advances in Computer Science and Communications 13, no. 5 (2020): 930–41. http://dx.doi.org/10.2174/2213275912666190617155154.

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Background: Image retrieval has a significant role in present and upcoming usage for different image processing applications where images within a desired range of similarity are retrieved for a query image. Representation of image feature, accuracy of feature selection, optimal storage size of feature vector and efficient methods for obtaining features plays a vital role in Image retrieval, where features are represented based on the content of an image such as color, texture or shape. In this work an optimal feature vector based on control points of a Bezier curve is proposed which is computation and storage efficient. Aim: To develop an effective and storage, computation efficient framework model for retrieval and classification of plant leaves. Objective: The primary objective of this work is developing a new algorithm for control point extraction based on the global monitoring of edge region. This observation will bring a minimization in false feature extraction. Further, computing a sub clustering feature value in finer and details component to enhance the classification performance. Finally, developing a new search mechanism using inter and intra mapping of feature value in selecting optimal feature values in the estimation process. Methods: The work starts with the pre-processing stage that outputs the boundary coordinates of shape present in the input image. Gray scale input image is first converted into binary image using binarization then, the curvature coding is applied to extract the boundary of the leaf image. Gaussian Smoothening is then applied to the extracted boundary to remove the noise and false feature reduction. Further interpolation method is used to extract the control points of the boundary. From the extracted control points the Bezier curve points are estimated and then Fast Fourier Transform (FFT) is applied on the curve points to get the feature vector. Finally, the K-NN classifier is used to classify and retrieve the leaf images. Results: The performance of proposed approach is compared with the existing state-of-the-artmethods (Contour and Curve based) using the evaluation parameters viz. accuracy, sensitivity, specificity, recall rate, and processing time. Proposed method has high accuracy with acceptable specificity and sensitivity. Other methods fall short in comparison to proposed method. In case of sensitivity and specificity Contour method out performs proposed method. But in case accuracy and specificity proposed method outperforms the state-of-the-art methods. Conclusion: This work proposed a linear coding of Bezier curve control point computation for image retrieval. This approach minimizes the processing overhead and search delay by reducing feature vectors using a threshold-based selection approach. The proposed approach has an advantage of distortion suppression and dominant feature extraction simultaneously, minimizing the effort of additional filtration process. The accuracy of retrieval for the developed approach is observed to be improved as compared to the tangential Bezier curve method and conventional edge and contour-based coding. The approach signifies an advantage in low resource overhead in computing shape feature.
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Dragos, Nicolae VIZIREANU. "Generalized Morphological 3D Shape Decomposition Grayscale Interframe Interpolation Method." February 25, 2007. https://doi.org/10.5281/zenodo.1056635.

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One of the main image representations in Mathematical Morphology is the 3D Shape Decomposition Representation, useful for Image Compression and Representation,and Pattern Recognition. The 3D Morphological Shape Decomposition representation can be generalized a number of times,to extend the scope of its algebraic characteristics as much as possible. With these generalizations, the Morphological Shape Decomposition 's role to serve as an efficient image decomposition tool is extended to grayscale images.This work follows the above line, and further develops it. Anew evolutionary branch is added to the 3D Morphological Shape Decomposition's development, by the introduction of a 3D Multi Structuring Element Morphological Shape Decomposition, which permits 3D Morphological Shape Decomposition of 3D binary images (grayscale images) into "multiparameter" families of elements. At the beginning, 3D Morphological Shape Decomposition representations are based only on "1 parameter" families of elements for image decomposition.This paper addresses the gray scale inter frame interpolation by means of mathematical morphology. The new interframe interpolation method is based on generalized morphological 3D Shape Decomposition. This article will present the theoretical background of the morphological interframe interpolation, deduce the new representation and show some application examples.Computer simulations could illustrate results.
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Wang, Tianbo, Zhaoyi Luo, Minxiang Wei, Jiang Wu, Wenshuai Xue, and Ranran Liu. "An improved scheme based on the variable density method for structural topology optimization." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, March 12, 2025. https://doi.org/10.1177/09544062251324422.

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The Solid Isotropic Microstructure with Penalization (SIMP) model, a material interpolation model in the variable density method, has been widely applied in structural topology optimization. When combining the Sigmund sensitivity filtering method with the Optimality Criterion (OC) method for solving the SIMP model, numerical instabilities and relatively low optimization performance are often observed. To address these challenges, an improved scheme based on the variable density method is proposed. Firstly, an improved material interpolation model is proposed to overcome the deficiencies of the SIMP model in terms of penalty efficiency and convergence speed. Secondly, an improved sensitivity filtering method based on the Gaussian weight function is proposed, which not only successfully suppresses checkerboards and mesh-dependence but also contributes to a superior filtering effect. Furthermore, a new gray-scale suppression operator is designed to develop a function that suppresses gray-scale elements. This function is subsequently integrated into the iterative formula of the OC method, forming the improved OC method, which is capable of completely eliminating gray-scale elements. Finally, the feasibility and effectiveness of the improved scheme are verified through several typical numerical examples.
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Hong, Yu, Zhongkui Zhao, Qiwei Tian, and Shengyu Li. "Vibration measurement in machine vision based on ROI gray-scale projection feature matching algorithm." Advances in Structural Engineering, April 14, 2025. https://doi.org/10.1177/13694332251334829.

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The current machine vision-based vibration measurement faces numerous challenges, such as low sampling frequency, excessive computational time, and expensive high-definition, high-frame-rate industrial cameras. In response to these issues, this study proposed a feature-matching algorithm that combines ROI image interpolation with gray-scale projection. This algorithm allows cost-effective industrial cameras with lower resolution but higher frame rates. The system effectively identifies modal parameters by executing interpolation and gray-scale projection processing on the ROI images and matching the generated gray-scale projection features. This allows for precisely capturing dynamic positional changes at measurement points. To validate the effectiveness of the proposed method, this study performed impact tests on a laboratory-based model of a beam that was simply supported. The experiments aimed to simulate adverse real-world conditions such as non-uniform illumination and water vapor. An MV-CA003-21UM Hikvision industrial camera was used to capture vibration videos of the simply supported beam, and the algorithm successfully extracted the global displacement response. The comparison between the identified vibration displacement and the measurements from the eddy current displacement sensor showed an error of approximately 5%, reassuring the algorithm’s accuracy. Moreover, the algorithm accurately identified multiple modal parameters of the simply supported beam, confirming its effectiveness. Finally, this study applied the method to identify vibration displacement and modal parameters of a real reinforced concrete beam, reinforcing its potential application in practical engineering environments.
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Naderi, Mohammad Hossein, Sara Akhavan, and Hessam Babaee. "A cross algorithm for implicit time integration of random partial differential equations on low-rank matrix manifolds." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 481, no. 2309 (2025). https://doi.org/10.1098/rspa.2024.0658.

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Dynamical low-rank approximation allows for solving large-scale matrix differential equations (MDEs) with significantly fewer degrees of freedom and has been applied to a growing number of applications. However, most existing techniques rely on explicit time integration schemes. In this work, we introduce a cost-effective Newton’s method for the implicit time integration of stiff, nonlinear MDEs on low-rank matrix manifolds. Our methodology is focused on MDEs resulting from the discretization of random partial differential equations (PDEs), where the columns of the MDE can be solved independently. Cost-effectiveness is achieved by solving the MDE at the minimum number of entries required for a rank- r approximation. We present a novel cross low-rank approximation that requires solving the parametric PDE at r strategically selected parameters and O ( r ) grid points using Newton’s method. The selected random samples and grid points adaptively vary over time and are chosen using the discrete empirical interpolation method or similar techniques. The proposed methodology is developed for high-order implicit multi-step and Runge–Kutta schemes and incorporates rank adaptivity, allowing for dynamic rank adjustment over time to control error. Several analytical and PDE examples, including the stochastic Burgers’ and Gray–Scott equations, demonstrate the accuracy and efficiency of the presented methodology.
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Abbott, T. Bryce, and Fuh-Gwo Yuan. "A simple image correlation technique for imaging subsurface damage from low-velocity impacts in composite structures." Structural Health Monitoring, February 22, 2024. http://dx.doi.org/10.1177/14759217241228884.

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A robust computer vision system is proposed to visualize subsurface barely visible impact damage (BVID) in composite structures through a simple image correlation technique together with a damage imaging condition. This system uses a digital camera to record a video of the surface motion, capturing micron-scale dynamic movement from guided waves propagating on the surface of the structure generated via a sweeping frequency excitation (chirp) up to the ultrasonic frequency range. As the excitation frequency changes during the chirp, waves become trapped within this damaged region, forming standing waves to generate local resonance at specific frequencies. This localized resonance accumulates high wave energy in the region, generating a higher transverse displacement at the damage site compared to the remaining part of the structure. In this work, a simple image correlation technique is proposed to correlate each filtered video frame with the temporal mean of the filtered wavefield video to highlight standing waves at localized damage. The proposed image correlation technique is distinct from digital image correlation (DIC) since it does not use correlation for subset matching to track the movement of surface patterns between two images (video frames). Instead, it uses correlation to directly quantify similarities between corresponding image pixels (windows). Utilizing a single camera greatly simplifies system complexity and hence enhances the practicality and potential for real-time performance over a recently developed technique that utilized 3D DIC with a stereo camera for vision-based BVID detection. To realize the aim, work was conducted in two sequential steps: (1) off-axis 2D DIC was employed rather than 3D DIC to examine the potential of employing a single camera to capture images and extract not only in-plane displacement but also a fraction of transverse displacement in which local resonance is dominant and (2) image correlation was then employed, supplanting the off-axis 2D DIC image processing involved in the first step, to highlight the damage with significantly less processing complexity. This proposed technique using a zero-mean normalized cross-correlation imaging condition, rather than the total wave energy used for DIC-based approaches, is efficient and effective for identifying regions of minute surface movement from local resonance within the damage region without the use of the computationally intensive interpolation to get the sub-pixel gray level information followed by subset matching employed in DIC-based image processing. Two geometrically identical CFRP composite honeycomb panels that had been subjected to low-velocity impacts were used for verification and validation, and two excitation location configurations were tested for each panel. Damaged images produced with correlation for a 100 mm × 100 mm field of view using a single 3-s video, or a total of 19,200 video frames, show accurate damage imaging capabilities regardless of excitation location that exceed that of DIC techniques and is comparable to benchmark damage images obtained from laser Doppler vibrometry, ultrasonic C-scans, and X-ray CT scans. This success of correlation-based imaging of subsurface BVID demonstrates substantial improvements in efficiency and practicality and shows high potential for in situ and real-time computer vision-based nondestructive inspection or structural health monitoring of subsurface BVID in composite aircraft and other critical structures.
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Ashish, Bhangale. "Human Gait Model for Automatic Extraction and Description for Gait Recognition." June 29, 2012. https://doi.org/10.5121/ijbb.2012.2202.

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International Journal on Bioinformatics & Biosciences (IJBB) Vol.2, No.2, June 2012 DOI : 10.5121/ijbb.2012.2202 15 Human Gait Model for Automatic Extraction and Description for Gait Recognition Ashish Bhangale1 , Navneet Manjhi2 and Jyoti Bharti3 1Research Scholar, CSE Dept. MANIT-Bhopal, India ashishbhangale.info@yahoo.com 2Research Scholar, CSE Dept. MANIT-Bhopal, India navneetmanjhi2010@gmail.com 3Asst. Professor, CSE Dept., MANIT-Bhopal, India jyoti2202@gmail.com ABSTRACT The gait signature is extracted directly from the evidence gathering process. This is possible by using a Fourier series to describe the motion of the upper leg and apply temporal evidence gathering techniques to extract the moving model from a sequence of images. The improved classification capability of the phase-weighted magnitude information is verified using statistical analysis of the separation of clusters in the feature space. Furthermore, the technique is shown to be able to handle high levels of occlusion, which is of especial importance in gait as the human body is self-occluding. As such, a new technique has been developed to automatically extract and describe a moving articulated shape, the human leg, and shown its potential in gait as a biometric. KEYWORDS Fourier series, sequence of images, classification, phase-weighted magnitude, statistical analysis, occulation, articulated shape, biometric, VHT, HVHT, GAVHT, GA, SHT, CCD, FS & HHT 1. INTRODUCTION Most people can recognize acquaintances by the way they walk, although it is not just their gait that identifies them for example, their hair style or clothing is usually recognizable. This research investigates the possibility of recognizing people by way of a gait signature as obtained by computer vision. We first review the field of biometrics and present current approaches to gait recognition by computer vision. There has been considerable study of gait in a number of fields, although there has been little cross-fertilization of ideas between these fields: psychological gait cues have yet to find deployment elsewhere. Amongst this work, there are emergent techniques aimed at recognizing people by their gait. None of these techniques use a known mechanical topology or medical studies, but concentrate more on heuristic and statistical metrics. It is however possible to develop a model-based gait extraction technique from which a metric directly applicable to the mechanics of walking can be generated. Before the performance advantages associated with such an approach are detailed, current research in gait and its allied fields shall be reviewed. 2. MODELING HUMAN GAIT Gait was considered by as a total walking cycle the action of walking can be thought of as a periodic signal, with an associated frequency spectrum. International Journal on Bioinformatics & Biosciences (IJBB) Vol.2, No.2, June 2012 16 2.1 Medical Studies The goal of most gait research has been to classify the components of gait. [7] And [6] produced standard movement patterns for normal people that were compared to the gait patterns for pathological patients [6]. No statistical or mathematical analysis was performed on the collected data. Gait was considered by [6] as a total walking cycle the action of walking can be thought of as a periodic signal, with an associated frequency spectrum [1,2]. 2.2 Gait Description The following terms are used to describe the gait cycle, as given in [7]. Fig. 1 illustrates the terms described. A gait cycle is the time interval between successive instances of initial foot-tofloor contact (heel strike) for the same foot. Each leg has two distinct periods; a stance phase, when the foot is in contact with the floor, and a swing phase, when the foot is off the floor moving forward to the next step. The cycle begins with the heel strike of one foot, the left foot for example. This marks the start of the stance phase. The ankle flexes to bring the left foot flat on the floor (foot-flat) and the body weight is transferred onto it. The right leg swings through in front of the left leg as the left heel lifts of the ground (heel-off). As the body weight moves onto the right foot, the supporting left knee flexes. The remainder of the left foot, which is now behind, lifts of the ground ending the stance phase with toe-off. Figure 1. Relationship between temporal components of the walking cycle and the step and stride lengths during the cycle. The start of the swing phase is when the toes of the left foot leave the ground. The weight is transferred onto the right leg and the left leg swings forward to strike the ground in front of the right foot. The gait cycle ends with the heel strike of the left foot. Stride length is the linear distance in the plane of progression between successive points of contact of the same foot. Step length is the distance between successive contact points of opposite feet. A step is the motion between successive heel strikes of opposite feet. A complete gait cycle is comprised of two steps. 2.3 Characteristics of human gait From the work carried out by [7] and [6] it can be concluded that if all gait movements were considered, gait is unique. In all there appear to be 20 distinct gait components, some of which can only be measured from an overhead view of the subject. Murray [6] found the pelvic and International Journal on Bioinformatics & Biosciences (IJBB) Vol.2, No.2, June 2012 17 thorax rotations to be highly variable from one subject to another. These patterns would be difficult to measure even from an overhead view of the subject, which would not be suited to application in many practical situations [6]. As such, they would not appear suited to an automated computer vision-based biometric system. In [7] and [6], ankle rotation, pelvic tipping, and the spatial displacements of the trunk (vertical oscillation, lateral oscillation, and forward displacement) were shown to possess individual consistency in repeated trials. Naturally, given the resolution of most general purpose cameras, the ankle is difficult to extract consistently, let alone its rotation. Equally, the pelvis can easily be obscured by clothing, making a measurement of its inclination easily prone to confusion and error. The spatial displacements of the trunk are measured from the neck. As such, these components would be difficult to extract accurately from real images. Again, these would appear unsuited to an automated system. Since many features established by medical studies appear unsuited to a computer vision-based system, the components for this investigation have been limited to the rotation patterns of the hip and knee. 2.4 Rotation pattern of the hip Fig. 2 shows the rotation angles for the hip and knee, as measured by [6]. The normal hip rotation pattern is characterized by one period of extension and one period of flex-ion in every gait cycle. Figure 2. (a) Hip and (b) knee rotation The gait cycle, the hip is in continuous extension as the trunk moves forward over the supporting limb. In the second phase of the cycle, once the weight has been passed onto the other limb, the hip begins to flex in preparation for the swing phase. This flexing action accelerates the hip so as to direct the swinging limb forward for the next step. The angle of rotation is measured as the angle between the line joining the hip and knee, and the line passing through the hip point parallel to the ground. 2.5 Model of legs for gait motion The potential of the periodic nature of gait for an analytic approach was first investigated by [5], who performed a feasibility study into using gait as a biometric. An analytic approach was used, describing the legs and the motion of walking as a model based on medical and perceptual studies. The human leg was modeled as two pendula joined in series (Fig. 3). The upper pendulum modeled the thigh and was suspended between the hip and the knee. The lower pendulum modeled the lower leg suspended from the knee to the ankle. This pendulum model is backed by [6] for normal gait, the duration of successive temporal components and the length of successive steps are rhythmic. International Journal on Bioinformatics & Biosciences (IJBB) Vol.2, No.2, June 2012 18 Figure 3. (a) Leg outline. (b) Pendulum model of a leg Kuan [5] extracted the hip rotation pattern for three subjects from a sequence of images using computer vision techniques. The rotation patterns were curve fitted manually to in-fill for missing data points. Fourier analysis was performed on the rotation patterns, and the magnitude and phase spectra for each subject were examined. The magnitude plots showed some variation between subjects, whilst the phase plots exhibited greater variation between subjects. The greater inter-individual variation of the phase spectra makes the phase information an attractive measure for recognition. The manner in which the hip inclination changes is of as much interest as the actual angle itself, and as such both the magnitude and phase information were of use. Kuan concluded that this model-based approach looked promising, but as yet insufficient for an automated non-invasive technique. 3. GAIT SIGNATURE BY EVIDENCE GATHERING The preliminary study described in [3] demonstrated positive results in the use of gait as a biometric measure. A gait signature was extracted, but not automatically, using computer vision techniques and produced a high correct classification rate on a small database of subjects. However, the techniques used in [3] had inherent problems which would be likely to affect more general use of the technique, especially on a larger database. These are discussed in this section. Novel vision techniques have been developed specifically to overcome these problems and their motivation, as well as their implementation, is described. Further experimentation shows how these novel techniques can extract and describe gait, and results are presented showing how they can be used to recognize people by their gait. Furthermore, the new technique extracts the gait signature automatically from the image sequence, without human intervention, one of the major aims of this work. 3.1 Previous work The study performed in [3] described a novel model-based approach to gait recognition, using the notion of gait as a periodic signal to create a gait signature. The lower limbs were modeled as two inter-connected pendula and gait was considered as the motion of these pendula. Using image processing techniques, lines representing legs in a sequence of images were extracted using the standard Hough transform (SHT). The inclination of the line representing the leg in each frame was collated to create the hip rotation pattern for the subject. In-filling for missing data points was done by least-squares analysis of the collected data points to an eighth-order polynomial. This could, in hindsight, have been achieved by Fourier interpolation. Fourier analysis was performed on the extracted hip rotation pattern using the Discrete Fourier transform to find magnitude and phase information. The magnitude data and the phase weighted magnitude data were classified using the k-nearest neighbor rule. The phase-weighted magnitude data was found to give a better International Journal on Bioinformatics & Biosciences (IJBB) Vol.2, No.2, June 2012 19 correct classification rate than just the magnitude data. This model-based approach uniquely gave a signature which could be directly related to the original image sequence. However, images were analyzed singly, without reference to the whole sequence. As such, the technique would be unable to handle occlusion, except by interpolation such as by least squares. Although the extracted hip rotation patterns in [3] concurred with those presented in medical research [6, 7], the idea of gait as a periodic function was not reflected in the use of a polynomial to model the motion of the thigh. Any periodic signal, with period T, can be represented by a Fourier series (FS). The motion of the thigh is better represented as an FS rather than by polynomial fitting to the extracted data. Also, greater noise immunity can be achieved when extracting temporal features in a sequence of images by including the entire sequence in the evidence gathering process [8]. Described a Velocity Hough transform (VHT) technique that enables the concurrent determination of structural and motion parameters of moving parametric shapes in an image sequence. Essentially, the VHT includes motion within the parametric model. The polar representation of a circle radius r with co-ordinates x0, y0 in the first frame and moving with horizontal and vertical velocity, vx and vy , respectively, has x and y co-ordinates at time t as x(t) = x0+rcos( ѳ)+tvx (1) y(t) = y0+rsin(ѳ)+tvy (2) where h is an index to points on the circle’s perimeter. Votes are accumulated in a 5- dimensional accumulator (x0; y0; vx; vy; r) from edge images of each image in the sequence. By combining VHT techniques with the FS representation of the hip rotation, a feature-based human gait model can be extracted from a sequence of images. This feature-based model has a high fidelity to the data, with a clear analytic justification. Evidence gathering using the VHT offers greater immunity to noise and occlusion, and produces a maximum likelihood estimate of the model parameters. By modeling the hip rotation as an FS, the gait signature described in [3] can be extracted directly, without intervention. Lee et al., (2009) proposed for efficient gait recognition with carrying backpack. They have been constructed gait energy image (GEI) to apply recursive principle component analysis technique. This method is aim to remove subject backpack without losing subject original shape and information. They applied to their method to normal walk, slow walk, and fast walk for experiment. They have used CASIA C dataset for conducting the test. They achieved better recognition rate after comparing others result [9]. Shingh and Biswas (2009) are approached gait energy image (GEI) method for human identification. They selected normal walk, wearing a coat or jacket or carrying a bag for recognition purposes. They informed that normal walk sequence is obtaining better recognition rate compared to carrying a bag or wearing a jacket or coat. They focused on subject body alignment with bottom and upper part of the body as feature. They also reported that gait recognition rate can be improved by applying GEI method. They selected large CASIA gait database for the experiment [10]. Ju and Bir (2006) proposed gait energy image (GEI) method for person recognition individually. They created statistical gait features from actual and artificial gait templates for the experiment. They selected USF Human ID gait database for gait recognition purposes. They also used others gait database to compare recognition rate with current method with selected gait database. The GEI method is obtained better recognition rate after comparing published gait result [11]. International Journal on Bioinformatics & Biosciences (IJBB) Vol.2, No.2, June 2012 20 Okumura et al., (2010) described a large scale gait database that can use widely for vision based gait recognition. They focused on gait energy image method for recognition on gender or age groups. From the experiment, female subjects are achieving better recognition rate compared to male. For the age grouping, it’s evaluated according to maturity of walking ability and also physical strength. They have got different fluctuation from different age groups. They also compared with several gait databases to evaluate their method performance [12]. Cheng et al., (2006) proposed gait recognition based on PCA and LDA. PCA is mainly used for dimensional reduction technique and LDA is performed to optimize the pattern class. For the experiment, they used their own database and achieved better recognition rate from PCA compared to LDA [13]. 3.2 Implementation by genetic Algorithm Extracting model instances from images is effectively a problem in optimising the defining function of the model for a given set of edge points. A Genetic Algorithm (GA) [4] is an optimisation method that is shown to consistently outperform many other search methods in solving hard optimisation problems. For a satisfactory sized parameter space, the VHT implementation took the order of days to run on a P75 PC. The GA based VHT to extract the human gait model takes approximately 20 min on the same parameter space, offering a speed-up factor of approximately 100. As such, all further experimentation was performed using a GA based implementation. In this GA implementation, each individual’s chromosome was the binary coding of the parameters of the gait model. Each parameter was represented by n bits which gave an integer index to a position within a specified range. Naturally, the value of n controlled the resolution for each parameter. The fitness was derived from the number of edge points matching those calculated for the (moving) template described by the current values within the chromosome. The fittest individuals were selected as those that had a greater probability that a spin of a biased roulette wheel would select them. Crossover was set to occur with a probability of 0.7 and mutation with a probability equalling the reciprocal of the maximum population (the effect of which was to complement the mutated bit). 3.3 GA Performance for Occluded Features A characteristic of the VHT is that it can extract temporal features in scenes where the feature has been occluded. This is attractive in extracting human gait models as the human body is selfoccluding in almost all its motions. As such, the GA based VHT for gait analysis, GAVHT, was tested for the presence or absence of this characteristic, at increasing levels of occlusion. A major advantage of the VHT method of moving feature extraction over the traditional static, frame-by-frame moving feature extraction is its improved performance in sequences where the feature has been occluded in some frames. As such, an analysis of the GAVHT’s performance in extracting the gait model for an occluded subject was performed to verify that this occlusion immunity characteristic of the VHT extraction method had been maintained in its translation to a GA. Fig. 5 shows the extracted model for the unoccluded sequence for subject CM using the GAVHT. The model used only a first-order FS to represent the hip rotation. As Fig. 5 shows, the inclination of the hip is tracked throughout the cycle although without much precision. This was due to the low order of FS used to model the motion of the hip rotation, but for the purposes of this exercise it was sufficient. International Journal on Bioinformatics & Biosciences (IJBB) Vol.2, No.2, June 2012 21 Figure 4. Example of occluded image Figure 5. Extracted reduced human gait model using GA implementation of VHT techniques for subject CM. The subject CM in Fig. 5 was occluded by simulating a column in the centre of the field of view of the camera, between the subject and the camera. The illusion was created by setting the pixels with the column to zero (black). Fig. 4 shows an example of this process, with the column width set to 90 pixels, representing almost two fifths of the image width. A series of tests was then conducted on the sequence in Fig. 5. International Journal on Bioinformatics & Biosciences (IJBB) Vol.2, No.2, June 2012 22 Figure 6. Walking sequence with extracted thigh model for subject DC. Frames run from left to right, and top to bottom. 4.EXPERIMENTAL RESULTS 4.1 Result Analysis. For the classification analysis, two measures were compared; the Fourier magnitude and the phase-weighted Fourier magnitude. Walking sequences for ten subjects were used, each subject having four walking sequences; three training sequences and one test sequence. The measure for each test sequence was compared against those for the training sequences. The k-nearest neighbour rule was used to classify the differences in these measures for k=1 and k=3. Table 4summarises the correct classification rates (CCR) for the two measures. Unlike the earlier study [5], the nearest neighbour classification led to the same classification performance as the 3- nearest neighbour rule. Figure 7. Hip rotation pattern extracted with the thigh model for the sequence in Figure 5. International Journal on Bioinformatics & Biosciences (IJBB) Vol.2, No.2, June 2012 23 Figure 8. Magnitude and phase plots for hip rotation as described by FS coefficients for gait cycle of subject DC in Figure 5. Figure 9. Magnitude and phase plots for hip rotation as described by FS coefficients for gait cycle of subject IM in Figure 6. Table 1. Overall classification performance. No. of nearest neighbors Magnitude CCR Phase-weighted magnitude CCR k=1 80% 100% k=3 80% 100% Classification analysis showed that the phase-weighted Fourier magnitude offered a better classification rate (100%) than just the Fourier magnitude (80%), verifying earlier work in [5]. This suggests that subjects are recognised not only by flexion, but also by the time when it occurs; both the phase and the magnitude of the oscillatory motion would intuitively appear to describe a particular pendulum better. Direct generation of the Fourier information from the evidence gathering process was possible using the FS coefficients, and as such no further transform processing was required. Using this evidence gathering technique, improved classification rates, of 100% for both k=1 and k=3, were achieved compared to those obtained using the computer vision techniques in [5], on the same data being 80% and 90% for k=1 and k=3, respectively. International Journal on Bioinformatics & Biosciences (IJBB) Vol.2, No.2, June 2012 24 4.2 Comparisons. Identification of people by gait is a challenging problem and has attracted growing interest in the computer vision community. However, there is no baseline algorithm or standard database for measuring and determining what factors affect performance. The unavailability of an accredited common database (e.g., something like the FERET database in face recognition) of a reasonable size and evaluation methodology has been a limitation in the development of gait recognition algorithms. A large number of papers in the literature reported good recognition results usually on a small database, but few of them made informed comparisons among various algorithms. To examine the performance of the proposed algorithm, here we provide some basic comparative experiments. Tables 2. Comparison of several different approaches on SOTON database. Methods Data sets CCR (%) Shutler 2000 [14] 4 Subjects, 4 Sequences per subject 87.5(k=1), 93.75(k=3) Hayfron-Acquah 2001 [15] 4 Subjects, 4 Sequences per subject 100(k=1), 100(k=3) Foster 2001 [16] 6 Subjects, 4 Sequences per subject 83(k=1) Our Method Magnitude CCR 6 Subjects, 4 Sequences per subject 90.25(k=1), 98(k=3) Phase-weighted magnitude CCR 6 Subjects, 4 Sequences per subject 92(k=1), 98.5(k=3) The first comparative experiment is to test our method on the early SOTON gait database [15]. This database collected six subjects and four sequences of each subject. Walkers are required to move frontal-parallel to the image plane. The gray images were captured by a fixed camera with a stationary indoor background at a rate of 25 fps, and the original resolution is 384x288. The length of each sequence is about 60 frames except that the sequences of two subjects have only 30 frames. Fig. 6 gives several samples in the SOTON gait database. Nixon and his research group have made one of the first attempts on gait recognition and have developed many algorithms [21], [22], [14], [15], [16], [23], [24], [25], [26], most of which evaluate performance on the whole or a subset of the SOTON database. Hence we evaluate the proposed algorithm on such a database so as to make a direct quantitative comparison with some of their recent methods. Table 2 shows the comparison results of several different approaches, where we directly select the best recognition accuracy reported in [14], [15], and [16] without reimplementing them. From Table 2, we can see that the recognition performance of our method is superior to others. Also, we plan to test the proposed method on their new larger dataset if available. Tables 3. Comparison of several different approaches on NLPR database (0°). Methods Rank-1 (%) Rank-5 (%) BenAbdelkader 2001 [27] 72.50 88.75 BenAbdelkader 2002 [20] 82.50 93.75 Collins 2002 [17] 71.25 78.75 International Journal on Bioinformatics & Biosciences (IJBB) Vol.2, No.2, June 2012 25 Lee 2002 [18] 87.50 98.75 Phillips 2002 [19] 78.75 91.25 Our method 89.00 99.25 Another comparative experiment is to compare the performance of the proposed algorithm with those of five recent methods which are from Maryland [20], [27] CMU [17], MIT [18] and USF [19] respectively, and to some extent reflect the best work of these research groups in gait recognition. BenAbdelkader et al. [27] used image self-similarity plots as the original measurements to recognize gait based on the idea that the image self-similarity plot of a moving person is a projection of its planar dynamics. Reference [20] is a slight extension of [27]. Based on body shape and gait, Collins et al. [17] established a template matching method based on body silhouettes in key frames for human identification. Lee et al. [18] described a momentbased representation of gait appearance features for the purpose of person identification and classification. Phillips et al. [19] proposed a baseline algorithm for human identification using spatio-temporal correlation of silhouette images. Here, we re-implement these methods using the same silhouette data from the NLPR database with a lateral viewing angle. The results are summarized in Table 3. The above only provides preliminary comparative results and may not be generalized to say that a certain algorithm is always better than others. Algorithm performance is dependent on the gallery and probe sets. Some similar-size [17], [18], [20] or larger [19] databases have concurrently emerged, so further evaluations and comparisons on a larger and more realistic database are needed in future work. 5.FUTURE WORK The aims of the research initially outlined were fulfilled. In this process, several areas were identified for further study. Firstly, there is the problem of how to handle the ever increasing dimensionality of the model. This will allow the variability of signatures for a given individual to be assessed to establish possible class bounds. It would also appear worthwhile to assess the potential effect of background, though the simulation tests in noise have indicated good ability to handle background. Essentially, the human gait model describes a moving line whose inclination is constrained by a periodic signal and velocity governed by some initial conditions and characteristics. Further work could explore the effect on the model parameter extraction when the evidence gathering process is performed on line images rather than edge images. These line images can be produced by SHT for lines. Due to the nature of the voting method in the SHT, in complex noisy scenes containing many various sized lines the shortest lines are unlikely to be detected. The HHT could be used as a second stage of pre-processing to the GA for gait analysis. Accordingly, this promotes the investigation into a technique that incorporates HHT methodology for extracting temporal feature a Hierarchical Velocity Hough transforms (HVHT), perhaps. A CCD array camera on a tripod without a shutter was used to collect data, and its output was recorded on a video recorder. The camera was situated with a plane normal to the subject- path in an environment with controlled illumination. International Journal on Bioinformatics & Biosciences (IJBB) Vol.2, No.2, June 2012 26 Figure 10. image involve in optical flow information However, the presence of the stripe allows clearer assessment of extraction accuracy. Gait recognition, a characteristic word which is applied to computer vision field, is a process in which human motion features are extracted automatically and applied to recognize passerby’s identity. Comparing the line extraction of the HHT with the results of the SHT applied to the same image (Fig. 6), shows that the HHT line extraction produces a less noisy image. 6.CONCLUSION Previous work in [5] showed that a feature-based method could be used for gait recognition. Greater immunity to moderate noise and feature occlusion when extracting temporal features in a sequence of images was achieved by using VHT evidence gathering techniques. All the frames in the image sequence were used in the evidence gathering process, allowing the concurrent extraction of both structural and temporal parameters of the feature. An improved human gait model was described, having both a structural and temporal description of the upper leg. The hip rotation was modelled by a FS, paralleling earlier medical studies that described gait as a periodic signal. This FS description of the thigh motion allowed the generation of the gait signature directly from the evidence gathering process, via the FS coefficients. REFERENCES [1] J.K. Aggarwal & Q. Wai, (1999) “Human motion analysis: a review”, Computer Vision Image Understanding 73 (3), pp 428–440. [2] C. Angeloni, P.O. Riley & D.E. Krebs, (1994) “Frequency content of whole body gait kinematic data”, IEEE Trans., pp 40–46. [3] D. Cunado, M.S. Nixon & J.N. Carter, (1997) “Using gait as a biometric, via phase-weighted magnitude spectra”, in: J. Bigun, G. Chollet, G. 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Carter, (2002), “Gait recognition by walking and running: A modelbased approach,” in Proc. 5th Asian Conf. Computer Vision, Melbourne, Australia, pp 1–6. International Journal on Bioinformatics & Biosciences (IJBB) Vol.2, No.2, June 2012 28 [24]D. Cunado, M. S. Nixon & J. N. Carter, (1999), “Automatic gait recognition via model-based evidence gathering,” in Proc. Workshop on Automatic Identification Advanced Technologies, pp 27– 30. [25]P. S. Huang, C. J. Harris & M. S. Nixon, (1998), “Comparing different template features for recognizing people by their gait,” in Proc. Brit. Machine Vision Conf. [26]C. Y. Yam, M. S. Nixon & J. N. Carter, (2002), “On the relationship of human walking and running: Automatic person identification by gait,” in Proc. Int. Conf. Pattern Recognition. [27]C. BenAbdelkader, R. Culter, H. Nanda & L. Davis, (2001), “Eigen Gait: Motion- based recognition of people using image self-similarity,” in Proc. 3rd Int. Conf. Audio- and Video-Based Biometric Person Authentication, pp 284–294. Authors Ashish Bhangale received the B.E. degree in 2010 in Information Technology from the Department of Information Technology of Mahakal Institute Of Technology-Ujjain affiliated to Rajiv Gandhi Technical University, Bhopal. He is currently a master candidate in the Maulana Azad National Institute of Technology-Bhopal, India. He has published several papers on major national journals and international conferences & Journals. His main research interests include gait recognition, computer vision, image processing. Navneet Manjhi received the B.E. degree in 2010 in Information Technology from the Department of Information Technology of Radharaman Institute Of Technology-Bhopal affiliated to Rajiv Gandhi Technical University, Bhopal. He is currently a master candidate in the Maulana Azad National Institute of Technology-Bhopal, India. He has published several papers on major national journals and international conferences & Journals. His main research interests include gait recognition, video computing, tracking.
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