• 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.

• The Journal of the Acoustical Society of Korea
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• v.39 no.3
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• pp.191-199
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• 2020

Currently, studies on the estimation algorithm based on compressive sensing are actively underway, but to the best of our knowledge, no study on the performance of the Sparse Spectrum Fitting (SpSF) algorithm in nonuniform sensor arrays has been made. This paper deals with the derivation of the compressive sensing based covariance fitting algorithm extended to the frequency domain. In addition, it shows the performance of directon-of-arrival estimation of the frequency domain SpSF algorithm in non-uniform linear sensor array system and the sensor array failure situation.

• Journal of the Korean Magnetic Resonance Society
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• v.9 no.2
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• pp.93-102
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• 2005

Purpose: To develop an advanced non-linear curve fitting (NLCF) algorithm for dynamic susceptibility contrast study of brain. Materials and Methods: The first pass effects give rise to spuriously high estimates of $K^{trans}$ in voxels with large vascular components. An explicit threshold value has been used to reject voxels. Results: By using this non-linear curve fitting algorithm, the blood perfusion and the volume estimation were accurately evaluated in T2*-weighted dynamic contrast enhanced (DCE)-MR images. From the recalculated each parameters, perfusion weighted image were outlined by using modified non-linear curve fitting algorithm. This results were improved estimation of T2*-weighted dynamic series. Conclusion: The present study demonstrated an improvement of an estimation of kinetic parameters from dynamic contrast-enhanced (DCE) T2*-weighted magnetic resonance imaging data, using contrast agents. The advanced kinetic models include the relation of volume transfer constant $K^{trans}\;(min^{-1})$ and the volume of extravascular extracellular space (EES) per unit volume of tissue $\nu_e$.

• Journal of Biomedical Engineering Research
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• v.42 no.4
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• pp.159-166
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• 2021

In order to analyze cell images, accurate segmentation of each cell is indispensable. However, the reality is that accurate cell image segmentation is not easy due to various noises, dense cells, and inconsistent shape of cells. Therefore, in this paper, we propose an algorithm that combines marker-based watershed segmentation and ellipse fitting method for glioblastoma cell segmentation. In the proposed algorithm, in order to solve the over-segmentation problem of the existing watershed method, the marker-based watershed technique is primarily performed through "seeding using local minima". In addition, as a second process, the concave point search using ellipse fitting for final segmentation based on the connection line between the concave points has been performed. To evaluate the performance of the proposed algorithm, we compared three algorithms with other algorithms along with the calculation of segmentation accuracy, and we applied the algorithm to other cell image data to check the generalization and propose a solution.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.1029-1047
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• 2019

We are interested in the problem of determining the best fitted circle to a set of data points in space. This can be usually obtained by minimizing the geometric distances or various approximate algebraic distances from the fitted circle to the given data points. In this paper, we propose an algorithm in such a way that the sum of the squares of the geometric distances is minimized in ${\mathbb{R}}^3$. Our algorithm is mainly based on the steepest descent method with a view of ensuring the convergence of the corresponding objective function Q(u) to a local minimum. Numerical examples are given.

• Journal of Information Processing Systems
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• v.4 no.4
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• pp.153-158
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• 2008

This paper deals with the geometric fitting algorithms for parametric curves and surfaces in 2-D/3-D space, which estimate the curve/surface parameters by minimizing the square sum of the shortest distances between the curve/surface and the given points. We identify three algorithmic approaches for solving the nonlinear problem of geometric fitting. As their general implementation we describe a new algorithm for geometric fitting of parametric curves and surfaces. The curve/surface parameters are estimated in terms of form, position, and rotation parameters. We test and evaluate the performances of the algorithms with fitting examples.

• Journal of the Korean Society for Precision Engineering
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• v.25 no.2
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• pp.43-48
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• 2008

This paper proposes a new method for measuring the power of spherical and cylindrical lens with 6 points light source, which is composed of a LED and six holes, and magnification ellipse fitting algorithm. Each measured diagonal length of 6 points light source is determined by the target lens power. After finding the center position of each light point with threshold method, 3 axis-diagonal lengths were calculated. The long axis and short axis power of cylindrical lens can be calculated by using magnification ellipse fitting algorithm with the magnification relationships between the initial diagonal lengths and the measured diagonal lengths changed by lens power.

• Korean Journal of Optics and Photonics
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• v.18 no.3
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• pp.179-184
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• 2007

In order to extract more accurate skin parameters, this study was focused on the improvement of the efficiency of a previous inverse fitting algorithm based on genetic algorithms. The algorithm provides the best fitting result of the diffusion approximation model to a VRS (visual reflectance spectroscopy) curve of skin. Simplex and wavelength selection methods were applied to the previous algorithm. Nine skin parameters were inversely extracted from the modeling studies. The revised inverse fitting algorithm was determined to produce an 83% reduction of computation time and a 0.64% reduction of sum of square error, compared to the previous algorithm. In conclusion, we confirmed that the new algorithm provides faster and more accurate solutions for the diffusion approximation model.

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.7
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• pp.507-514
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• 2003

Inspection and shape measurement of three-dimensional objects are widely needed in industries for quality monitoring and control. Recently the shape measurement using interferometric principle is found to be a successful methodology among other visual or optical technologies. Especially, the measuring method using wavelength scanning interferometer(WSI) has a great advantage in comparison with other conventional jnterferometric methods in that the absolute distance from the reference surface can be directly obtained from the amount of jnterferometric phase change. However, the measurement methods using WSI proposed by other researchers have low measurement resolution so far because they can't measure fractional phase change. To avoid this shortcoming we propose a new algorithm in this paper, which can obtain a small amount of even fractional phase change by sinusoidal function fitting. To evaluate the effectiveness of the proposed sinusoidal function fitting algorithm, a series of measuring experiments are conducted for discontinuously shaped specimens which have various height. The proposed algorithm shows much more enhanced measurement resolution than other existing conventional algorithms such as zero crossing algorithm and Fourier transform algorithm.

• Journal of Information Processing Systems
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• v.16 no.3
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• pp.557-571
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• 2020

The existing methods for detection of fire smoke in a video easily lead to misjudgment of cloud, fog and moving distractors, such as a moving person, a moving vehicle and other non-smoke moving objects. Therefore, an algorithm for detection of fire smoke in a video based on wavelet energy slope fitting is proposed in this paper. The change in wavelet energy of the moving target foreground is used as the basis, and a time window of 40 continuous frames is set to fit the wavelet energy slope of the suspected area in every 20 frames, thus establishing a wavelet-energy-based smoke judgment criterion. The experimental data show that the algorithm described in this paper not only can detect smoke more quickly and more accurately, but also can effectively avoid the distraction of cloud, fog and moving object and prevent false alarm.