• The Pure and Applied Mathematics
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• v.11 no.1
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• pp.37-49
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• 2004

We are interested in the problem of fitting a sphere to a set of data points in the three dimensional Euclidean space. In Spath [6] a descent algorithm already have been given to find the sphere of best fit in least squares sense of minimizing the orthogonal distances to the given data points. In this paper we present another new algorithm which computes a parametric represented sphere in order to minimize the sum of the squares of the distances to the given points. For any choice of initial approximations our algorithm has the advantage of ensuring convergence to a local minimum. Numerical examples are given.

• Bulletin of the Korean Chemical Society
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• v.12 no.3
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• pp.322-328
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• 1991

We have studied a characterization method of accurate size of spherical particles by fitting experimental light scattering profile to the rigorous theoretical scattering function. An efficient software has been developed for computation of the theoretical scattering function and regression analysis. A light scattering instrument has been built and the necessary data acquisition and analysis are carried out by use of a personal computer with an emphasis on the reduction of analysis and time aiming that this study will be extended toward a development of a practical particle sizing apparatus. The performance of the instrument and the software has been evaluated with latex spheres and found to be satisfactory.

• Proceedings of the IEEK Conference
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• 1999.11a
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• pp.507-510
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• 1999

Inspection of BGAs presents several challenges for modem measurement equipment. No only must these systems be fast and accurate, they must deal with the special challenges presented by very small shiny metal spheres. For accurate measurement, we propose an algorithm which fits for estimating the accurate ball height using 2-D curve-fitting algorithm. The real boundary between two adjacent pixels and the real ball diameter are measured with subpixel accuracy Experimental results show that the proposed method calculates the ball height and diameter with subpixel accuracy and is robust in local noise with low measurement error.

• 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.