• Smart Media Journal
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• v.3 no.2
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• pp.9-13
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• 2014

The Levenberg-Marquardt (LM) algorithm is the most widely used fitting algorithm. It outperforms simple gradient descent and other conjugate gradient methods in a wide variety of problems. Based on the work of paper[1], we propose a modified Levenberg-Marquardt algorithm for better performance of mobile system. The LM parameter at the $k_{th}$ iteration is chosen ${\mu}=A{\bullet}{\parallel}f(x){\parallel}{\bullet}I$ where f is the residual function, and J is the Jacobi of f. In this paper, we show this method is more efficient than traditional method under the situation that the system iteration is limited.

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.8
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• pp.768-776
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• 2011

This paper considers a data fitting problem for rational function models using the LM (Levenberg-Marquardt) optimization method. Rational function models have various merits on representing a wide range of shapes and modeling complicated structures by polynomials of low degrees in both the numerator and denominator. However, rational functions are nonlinear in the parameter vector, thereby requiring nonlinear optimization methods to solve the fitting problem. In this paper, we propose a data fitting method for rational function models based on the LM algorithm which is renowned as an effective nonlinear optimization technique. Simulations show that the fitting results are robust against the measurement noises and uncertainties. The effectiveness of the proposed method is further demonstrated by the real application to a 3D depth camera calibration problem.

• Current Optics and Photonics
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• v.2 no.1
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• pp.69-78
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• 2018

This paper presents a precise edge detection algorithm for the critical dimension (CD) measurement of a Thin-Film Transistor Liquid-Crystal Display (TFT-LCD) pattern. The sigmoid surface function is proposed to model the blurred step edge. This model can simultaneously find the position and geometry of the edge precisely. The nonlinear least squares fitting method (Levenberg-Marquardt method) is used to model the image intensity distribution into the proposed sigmoid blurred edge model. The suggested algorithm is verified by comparing the CD measurement repeatability from high-magnified blurry and noisy TFT-LCD images with those from the previous Laplacian of Gaussian (LoG) based sub-pixel edge detection algorithm and error function fitting method. The proposed fitting-based edge detection algorithm produces more precise results than the previous method. The suggested algorithm can be applied to in-line precision CD measurement for high-resolution display devices.

• Korean Journal of Applied Biomechanics
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• v.23 no.1
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• pp.53-62
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• 2013

The methods of fitting a circle to measured data, geometric fit and algebraic fit, have been studied profoundly in various areas of science. However, they have not been applied exactly to a biomechanics discipline for locating the center of rotation of a human joint. The purpose of this study was to generalize the methods to fitting spheres to the points in 3-dimension, and to estimate the center of rotation of a hip joint by three of geometric fit methods(Levenberg-Marquardt, Landau, and Sp$\ddot{a}$th) and four of algebraic fit methods(Delogne-K${\aa}$sa, Pratt, Taubin, and Hyper). 1000 times of simulation experiments for flexion/extension and ad/abduction at an artificial hip joint with four levels of range of motion(10, 15, 30, and $60^{\circ}$) and three levels of angular velocity(30, 60, and $90^{\circ}$/s) were executed to analyze the responses of the estimated center of rotation. The results showed that the Sp$\ddot{a}$th estimate was very sensitive to the marker near the center of rotation. The bias of Delogne-K${\aa}$sa estimate existed in an even larger range of motion. The Levenberg-Marquardt algorithm of geometric fit and the Pratt of algebraic fit showed the best results. The combination of two methods, using the Pratt's estimate as initial values of the Levenberg-Marquardt algorithm, could be a candidate of more valid estimator.

• Journal of Biomedical Engineering Research
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• v.21 no.2
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• pp.157-163
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• 2000

최근 MR영상을 허혈성 뇌졸중의 초급성기에 뇌조직의 관류 이상을 조기에 진단하려는 연구들이 진행되고 있으나 아직 일반적인 진단용 소프트웨어만 있을 뿐 영상 자료를 후처리하여 뇌조직의 구조 및 기능적인 정보를 제공하는 mapping 영상을 특수 소프트웨어는 실용화되어 있지 않다. 본 논문에서는 Gamma-variate 곡선 정합을 이용한 뇌관류 파라미터 영상 mapping의 알고리즘 구현에 관해 연구하였다. 관류 MR영상의 각 화소마다 측정된 시간에 따른 신호강도의 변화 곡선은 비선형적이어서 뇌관류에 관한 여러 가지 혈역학적 변수들을 보다 정확하게 계산할 수 없었다. 그래서 수렴속도가 빠르고 안정성이 높은 비선형 최적화 알고리즘인 Levenberg-Marquardt 알고리즘(LMA)을 활용하였다. 즉 시간에 따른 신호강도의 변화 곡선을 Gamma-variate 함수를 이용하여 곡선 정합한 후, CBV, MTT, CBF, TTP, BAT, MS의 여러 가지 혈역학적 변수를 LMA에 의해 계산하였다. 그 결과로 관류 MR영상으로부터 얻은 mapping 영상은 초급성 허혈성 뇌졸중에서 관류에 관한 혈역학적 변화를 평가함으로써 나중에 생길 뇌경색의 범위를 예견하는 데에 유용하였다.

• Proceedings of the Korean Geotechical Society Conference
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• 2010.03a
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• pp.457-467
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• 2010

The settlement prediction is very important to preloading method for a construction site on a soft ground. At the design stage, however, it is hard to predict the settlement exactly due to limitations of the site survey. Most of the settlement prediction is performed by a regression settlement curve based on the field data during a construction. In Korea, hyperbolic method has been most commonly used to align the settlement curve with the field data, because of its simplicity and many application cases. The results from hyperbolic method, however, may be differed by data selections or data fitting methods. In this study, the analyses using hyperbolic method were performed about the field data of $\bigcirc\bigcirc$ site in Pusan. Two data fitting methods, using an axis transformation or an alternative method, were applied with the various data group. If data was used only after the ground water level being stabilized, fitting results using both methods were in good agreement with the measured data. Without the information about the ground water level, the alternative method gives better results with the field data than the method using an axis transformation.

• Journal of the Ergonomics Society of Korea
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• v.30 no.6
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• pp.715-725
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• 2011

Objective: This study is aimed at developing Articulated Human Models(AHM) using superquadrics to improve the geometric accuracy of the body shape. Background: The previous work presents the AHM with geometrical simplification such as ellipsoids to improve analysis efficiency. However, because of the simplicity, their physical properties such as a center of mass and moment of inertia are computed with errors compared to their actual values. Method: This paper introduces a three steps method to present the AHM with superquadrics. First, a 3D whole body scan data are divided into 17 body segments according to body joints. Second, superquadric fitting is employed to minimize the Euclidean distance between body segments and superquadrics. Finally, Fee-Form Deformation is used to improve accuracy over superquadric fitting. Results: Our computational experiment shows that the superquadric models give better accuracy of dynamic analysis than that of ellipsoid ones. Conclusion: We generate the AHM composed of 17 superquadrics and 16 joints using superquadric fitting. Application: The AHM using superquadrics can be used as the base model for dynamics and ergonomics applications with better accuracy because it presents the human motion effectively.

• Tunnel and Underground Space
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• v.20 no.2
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• pp.97-104
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• 2010

The materials failure relation $\ddot{\Omega}=A{(\dot{\Omega})}^\alpha$ where $\Omega$ is a measurable quantity such as displacement and the dot superscript is the time derivative, may be used to analyze the accelerating creep of materials. Coefficients, A and $\alpha$, are determined by fitting given data sets. In this study, it is tried to predict the failure time of tunnel using the materials failure relation. Four fitting techniques of applying the materials failure relation are attempted to forecast a failure time. Log velocity versus log acceleration technique, log time versus log velocity technique, inverse velocity technique are based on the linear least squares fits and non-linear least squares technique utilizes the Levenberg-Marquardt algorithm. Since the log velocity versus log acceleration technique utilizes a logarithmic representation of the materials failure relation, it indicates the suitability of the materials failure relation applied to predict a failure time of tunnel. A linear correlation between log velocity and log acceleration appears satisfactory(R=0.84) and this represents that the materials failure relation is a suitable model for predicting a failure time of tunnel. Through comparing the real failure time of tunnel with the predicted failure times from four curve fittings, it is shown that the log time versus log velocity technique results in the best prediction.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.4 no.1
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• pp.131-138
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• 2000

This paper works on development of an algorithm for mapping of cerebral perfusion parameters using the gamma-variate curve fitting. The signal intensity variate curve according to time measured in each pixel of perfusion MRI is nonlinear, and various hemodynamic parameters are not computed accurately. Levenberg-Marquardt algorithm(LMA), nonlinear optimum algorithm with high convergent speed and stability, is used to compute them. That is, the signal intensity variate curve is fitted by the gamma-variate function. Various hemodynamic parameters - Cerebral Blood Volume(C.B.V), Mean Transit Time(M.T.T), Cerebral Blood Flow(C.B.F), Time-to-Peak(T.T.P), Bolus Arrival Time(B.A.T), Maximum Slope(M.S) - are computed using LMA.

• Geomechanics and Engineering
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• v.27 no.5
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• pp.527-535
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• 2021

The creep characteristics of rock is of great significance for the study of long-term stability of engineering, so it is necessary to carry out indoor creep test and creep model of rock. First of all, in different water-bearing state and different positive pressure conditions, the granite is graded loaded to conduct indoor shear creep test. Through the test, the shear creep characteristics of granite are obtained. According to the test results, the stress-strain isochronous curve is obtained, and then the long-term strength of granite under different conditions is determined. Then, the fractional-order calculus software element is introduced, and it is connected in series with the spring element and the nonlinear viscoplastic body considering the creep acceleration start time to form a nonlinear viscoplastic creep model with fewer elements and fewer parameters. Finally, based on the shear creep test data of granite, using the nonlinear curve fitting of Origin software and Levenberg-Marquardt optimization algorithm, the parameter fitting and comparative analysis of the nonlinear creep model are carried out. The results show that the test data and the model curve have a high degree of fitting, which further explains the rationality and applicability of the established nonlinear visco-elastoplastic creep model. The research in this paper can provide certain reference significance and reference value for the study of nonlinear creep model of rock in the future.