• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권1호
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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.

• 한국공작기계학회논문집
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• 제12권4호
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• pp.17-22
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• 2003

This paper presents a new circular curve fitting approach of articulated manipulators, based on least square. The approach aims at gaining the interpolation of circle from n data points, under the condition that the fitted circle should pass both a starting point and an ending point. First a spherical fitting should be performed, using least squares. Then the circular curve fitting can be resulted from the intersection of the fitted sphere and the plane obtained from 3 points, i. e., a starting point, an ending point and the center of a sphere. The proposed algorithms are shown to be efficient by using MATLAB-based simulation.

• 정보처리학회논문지:소프트웨어 및 데이터공학
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• 제3권8호
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• pp.329-334
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• 2014

본 논문에서는 마이크로 CT 영상에서 해면뼈의 형태학적 분석을 위하여 해면뼈를 자동 분할하는 방법을 제안한다. 제안된 방법에서는 임계값을 이용하여 뼈 영역을 추출하고 뼈의 바깥쪽 경계선을 검출한다. 뼈 영역의 각 복셀에 대하여 구 정합을 적용하여 해당 복셀을 중심으로 하는 최대 크기의 구를 구한다. 이 구에 뼈의 바깥쪽 경계선이 포함되면 이 구에 포함된 복셀들은 치밀뼈로 분류되고 그렇지 않으면 해면뼈로 분류된다. 제안된 방법을 쥐의 15개 대퇴골 원위부 영상에 적용하였으며 사람이 수작업으로 분할한 결과와 비교 실험을 수행하였다. 분할된 해면뼈에 대하여 BV/TV, Tb.Th, Tb.Sp, Tb.N의 네 가지 형태학적 지표자를 측정하였다. 회귀분석과 Bland-Altman 방법으로 비교해본 결과 BV/TV, Tb.Th, Tb.Sp, Tb.N 모두 신뢰할 만한 수준의 범위 안에 있었다. 또한 구 정합 방법은 단순하게 구현할 수 있으면서도 3차원 정보를 이용함으로써 해면뼈를 정확하게 분할할 수 있음을 알 수 있었다.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2002년도 추계학술대회 논문집
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• pp.570-575
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• 2002

This paper presents a new circular curve fitting approach of articulated manipulators, based on pseudoinverses. The paper aims at gaining the interpolation of circle from n data points, under the condition that the fitted circle should pass both a start point and an end point. In this paper, two algorithms of circular interpolation are presented. Prior to circular interpolation, are a spherical fitting should be performed, using least squares. In the first algorithm, the relationship between point data and normal vector on the sphere is used. In the second algorithm. the equation of plane which can be obtained from 3 points, i.e., a start point, an end point, and center of a sphere. The proposed algorithms are show to be efficient by using MATLAB-based simulation.

• Coupled systems mechanics
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• 제7권4호
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• pp.407-420
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• 2018

In solid-liquid two phase flow, the knowledge of how descending solid particles affected by the presence of downstream wall is important. This work studies at what interstitial distance the velocity of a vertically descending sphere is affected by a downstream wall as a consequence of wall-modified hydrodynamic forces through a validated dynamic model. This interstitial distance-the hydrodynamic coupling distance ${\delta}_c-is$ found to decay monotonically with the approach Stokes number St which compares the particle inertia to viscous drag characterized by the quasi-steady Stokes' drag. The scaling relation ${\delta}_c-St-1$ decays monotonically as literature below the value of St equal to 10. However, the faster diminishing rate is found above the threshold value from St=10-40. Furthermore, an empirical relation of ${\delta}_c-St$ shows dependence on the drop height which clearly indicates the non-negligible effect of unsteady hydrodynamic force components, namely the added mass force and the history force. Finally, we attempt a fitting relation which embedded the particle acceleration effect in the dependence of fitting constants on the diameter-scaled drop height.

• 센서학회지
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• 제26권6호
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• pp.371-378
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• 2017

An accurate and robust estimation of center of rotation (CoR) using optical marker trajectory is crucial in human biomechanics. In this regard, the performances of the two prevailing least-squares methods, the Gamage and Lasenby (GL) method, and the Chang and Pollard (CP) method, are verified in this paper. While both methods are sphere-fitting approaches in closed form and require no tuning parameters, they have not been thoroughly verified by comparison of their estimation accuracies. Furthermore, while for both methods, results for stationary CoR locations are presented, cases for perturbed CoR locations have not been investigated for any of them. In this paper, the estimation performances of the GL method and CP method are investigated by varying the range of motion (RoM) and noise amount, for both stationary and perturbed CoR locations. The difference in the estimation performance according to the variation in the amount of noise and RoM was clearly shown for both methods. However, the CP method outperformed the GL method, as seen in results from both the simulated and the experimental data. Particularly, when the RoM is small, the GL method failed to estimate the appropriate CoR while the CP method reasonably maintained the accuracy. In addition, the CP method showed a considerably better predictability in CoR estimation for the perturbed CoR location data than the GL method. Accordingly, it may be concluded that the CP method is more suitable than the GL method for CoR estimation when RoM is limited and CoR location is perturbed.

• 한국정보처리학회논문지
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• 제3권6호
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• pp.1553-1567
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• 1996

표면 보간법을 응용하는 분야에는 모델링 자연현상 가시화 등을 비롯하여 여러 가지를 들 수 있다. 사면체 분할법은 사차원적 표면 형성을 위한 전 처리 단계 중의 하나이다. 사차원 공간상에서 피스와이즈(piecewise) 선형보간법의 질은 삼차원에서 의 자료 점의 분포에 영향을 받을 뿐 아니라 자료 값에도 영향을 받는다. 자료 값을 고려한 사면체 분할법이 추정의 질을 개선시킬 있음을 사차원 공간의 가시화를 통하 여 보여준다. 본 논문에서는 Delaunay 사면분할법의 구 기준(Sphere criterion)과 자 료 의존형 사면체 분할법 중의 하나인 최소 제공제곱 근사기준(least squares fitting criterion)을 논의하였다. 본 논문은 또한 새로운 자료 값을 고려한 기준인 gradient difference와 jump in normal direction derivative들을 논의하였다.

• 대한치과기공학회지
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• 제38권3호
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• pp.217-224
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• 2016

Purpose: This study aimed to generate 3-D occlusal curvatures and evaluate the relationship between the occlusal curvatures and mandibular occlusal morphology factors. Methods: Mandibular dental casts from 25 young adult Korean were scanned as a virtual dental models with a 3-D scanner(Scanner S600, Zirkonzahn, Italy). The curve of Spee, curve of Wilson, and Monson's sphere were generated by fitting a circle/sphere to the cusp tips using a least-squares method. The mandibular mesiodistal cusp inclination, buccolingual cusp inclination, and tooth wear parameters were measured on the prepared virtual models using RapidForm2004(INUS technology INC, Seoul, Korea). Wilcoxon signed-rank test was performed to test side difference, and Spearman's rank correlation coefficients were investigated to verify the correlation between occlusal curvatures and correlated factors (a=0.05). Results: The mean radii of curve of Spee were $83.09{\pm}33.94$ in the left side and $79.00{\pm}28.12mm$ in the right side. The mean radii of curve of Wilson were $66.82{\pm}15.87mm$ in the mesial side and $47.87{\pm}9.40mm$ in the distal side with significantly difference between mesiodistal sides(p<0.001). The mean radius of Monson's sphere was $121.85{\pm}47.11mm$. Most of the cusp inclination parameters showed negative correlation for the radius of Monson' sphere(p<0.05). Especially, the buccolingual cusp inclinations in mesial side of molar showed high correlation coefficients among the factors(p<0.05). Conclusion: The radius of Monson's sphere was greater than the classical 4-inch values, and the buccolingual cusp inclinations in mesial side of molar can be considered as one of the main factors correlating with the radius of Monson's sphere.

• 한국멀티미디어학회논문지
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• 제17권3호
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• pp.342-352
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• 2014

본 논문에서는 마이크로 CT 영상에서 치밀뼈와 해면뼈의 자동 분할 방법을 제안하고 분할된 해면뼈의 형태학적 분석 방법의 구현에 대해 기술한다. 제안된 분할 방법에서는 임계값을 이용하여 뼈 영역을 추출한다. 그 다음에는, 뼈의 바깥 경계선부터 안쪽 방향으로 인접한 경계선을 찾아 치밀뼈 후보 영역을 설정한다. 치밀뼈 후보 영역들 중에서 평균 픽셀값이 최대가 되는 지점을 후보 영역을 탐색하여 치밀뼈를 제거한다. 분할된 해면뼈에 BV/TV, Tb.Th, Tb.Sp, Tb.N의 네 가지 형태학적 지표자들을 계산하는 방법을 VTK(Visualization ToolKit)와 구 정합 알고리즘을 이용하여 구현하였다. 구현된 방법을 쥐의 20개 대퇴골 근위부 영상에 적용하였으며 사람이 수작업으로 분할하는 방법과 비교 실험을 수행하였다. 실험 결과 네 가지 형태학적 지표자 모두 수작업으로 분할한 경우와 자동으로 분할한 경우 3% 이내의 평균 오차율을 보여 제안된 방법은 번거로운 수작업 분할 대신 사용될 수 있음을 알 수 있었다.

• Journal of Information Processing Systems
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• 제10권1호
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• pp.23-35
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• 2014

Recently, novel application areas in digital geometry processing, such as simulation, dynamics, and medical surgery simulations, have necessitated the representation of not only the surface data but also the interior volume data of a given 3D object. In this paper, we present an efficient framework for the shape approximations of spherical solid objects based on trivariate B-splines. To do this, we first constructed a smooth correspondence between a given object and a unit solid cube by computing their harmonic mapping. We set the unit solid cube as a rectilinear parametric domain for trivariate B-splines and utilized the mapping to approximate the given object with B-splines in a coarse-to-fine manner. Specifically, our framework provides user-controllability of shape approximations, based on the control of the boundary condition of the harmonic parameterization and the level of B-spline fitting. Experimental results showed that our method is efficient enough to compute trivariate B-splines for several models, each of whose topology is identical to a solid sphere.