• Journal of Mechanical Science and Technology
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• v.19 no.spc1
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• pp.452-460
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• 2005

Based on an introduced optimal trajectory planning method, this paper mainly deals with the accuracy analysis during the function approximation process of the optimal trajectory planning method. The basis functions are composed of Hermit polynomials and Fourier series to improve the approximation accuracy. Since the approximation accuracy is affected by the given orders of each basis function, the accuracy of the optimal solution is examined by changing the combinations of the orders of Hermit polynomials and Fourier series as the approximation basis functions. As a result, it is found that the proper approximation basis functions are the $5^{th}$ order Hermit polynomials and the $7^{th}-10^{th}$ order of Fourier series.

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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• pp.285-288
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• 1998

A least-squares identification method is studied that estimates a finite number of coefficients in the series expansion of a transfer function, where the expansion is in terms of recently introduced generalized basis functions, We will expand and generalize the orthogonal functions as basis functions for dynamical system representations. To this end, use is made of balanced realizations as inner transfer functions. The orthogonal functions can be considered as generalizations of, for example, the pulse functions, Laguerre functions, and Kautz functions, and give rise to an alternative series expansion of rational transfer functions. We show that the Laplace transform of the expansion for some sets$\Psi_{\kappa}(Z)$ is equivalent to a series expansion . Techniques based on this result are presented for obtaining the coefficients $c_{n}$ as those of a series. One of their important properties is that, if chosen properly, they can substantially increase the speed of convergence of the series expansion. This leads to accurate approximate models with only a few coefficients to be estimated. The set of Kautz functions is discussed in detail and, using the power-series equivalence, the truncation error is obtained.

• Proceedings of the KSRS Conference
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• 2003.11a
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• pp.1326-1328
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• 2003

An elliptical basis function (EBF) network is proposed in this study for the classification of remotely sensed images. Though similar in structure, the EBF network differs from the well-known radial basis function (RBF) network by incorporating full covariance matrices and uses the expectation-maximization (EM) algorithm to estimate the basis functions. Since remotely sensed data often take on mixture -density distributions in the feature space, the proposed network not only possesses the advantage of the RBF mechanism but also utilizes the EM algorithm to compute the maximum likelihood estimates of the mean vectors and covariance matrices of a Gaussian mixture distribution in the training phase. Experimental results show that the EM-based EBF network is faster in training, more accurate, and simpler in structure.

• The KIPS Transactions:PartB
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• v.11B no.3
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• pp.303-308
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• 2004

The Gabor cosine and sine transform can be applied to image and video compression algorithm by representing image frequency components locally The computational complexity of forward and inverse matrix transforms used in the compression and decompression requires O($N^3$)operations. In this paper, the length of basis functions is truncated to produce a sparse basis matrix, and the computational burden of transforms reduces to deal with image compression and reconstruction in a real-time processing. As the length of basis functions is decreased, the truncation effects to the energy of basis functions are examined and the change in various Qualify measures is evaluated. Experiment results show that 11 times fewer multiplication/addition operations are achieved with less than 1% performance change.

• Journal of Multimedia Information System
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• v.5 no.1
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• pp.63-66
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• 2018

In this work, the smoothing and the interpolation basis splines are analyzed. As well as the possibility of using the spectral properties of the basis splines for digital signal processing are shown. This takes into account the fact that basic splines represent finite, piecewise polynomial functions defined on compact media.

• The Pure and Applied Mathematics
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• v.17 no.4
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• pp.321-332
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• 2010

In this paper, we experiment image warping and morphing. In image warping, we use radial basis functions : Thin Plate Spline, Multi-quadratic and Gaussian. Then we obtain the fact that Thin Plate Spline interpolation of the displacement with reverse mapping is the efficient means of image warping. Reflecting the result of image warping, we generate two examples of image morphing.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.6
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• pp.1223-1229
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• 2009

The performance of Radial Basis Function Neural Networks depends on setting up the Radial Basis Functions over the input space which are the important design procedure of Radial Basis Function Neural Networks. The existing method to initialize the location of the radial basis functions over the input space is to use the conditional fuzzy C-means clustering. However, the researchers which are interested in the conditional fuzzy C-means clustering cannot get as good modeling performance as they expect because the conditional fuzzy C-means clustering cannot project the information which is extracted over the output space into the input space. To compensate the above mentioned drawback of the conditional fuzzy C-means clustering, we apply a fuzzy K-nearest neighbors approach to project the auxiliary information defined over the output space into the input space without lose of the information.

• Bulletin of the Korean Chemical Society
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• v.28 no.3
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• pp.386-390
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• 2007

By use of a simple two-point extrapolation scheme estimating the correlation energies of the molecules along with the basis sets specifically targeted for extrapolation, we have shown that the MP2 basis set limit binding energies of large hydrogen-bonded complexes can be accurately predicted with relatively small amount of computational cost. The basis sets employed for computation and extrapolation consist of the smallest correlation consistent basis set cc-pVDZ and another basis set made of the cc-pVDZ set plus highest angular momentum polarization functions from the cc-pVTZ set, both of which were then augmented by diffuse functions centered on the heavy atoms except hydrogen in the complex. The correlation energy extrapolation formula takes the (X+1)-3 form with X corresponding to 2.0 for the cc-pVDZ set and 2.3 for the other basis set. The estimated MP2 basis set limit binding energies for water hexamer, hydrogen fluoride pentamer, alaninewater, phenol-water, and guanine-cytosine base pair complexes of nucleic acid by this method are 45.2(45.9), 36.1(37.5), 10.9(10.7), 7.1(6.9), and 27.6(27.7) kcal/mol, respectively, with the values in parentheses representing the reference basis set limit values. A comparison with the DFT results by B3LYP method clearly manifests the effectiveness and accuracy of this method in the study of large hydrogen-bonded complexes.

• Journal of the Korean Data and Information Science Society
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• v.23 no.3
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• pp.487-494
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• 2012

This paper discusses a method for getting a basis set of estimable functions of model parameters in a two-way fixed effects model. Since the fixed effects model has more parameters than those that can be estimated, model parameters are not estimable. So it is not possible to make inferences for nonestimable functions of parameters. When the assumed model of matrix notation is reparameterized by the estimable functions in a basis set, it also discusses how to use projections for the estimation of estimable functions.

• Korean Journal of Computational Design and Engineering
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• v.5 no.3
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• pp.276-284
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• 2000

Usual practice of the transformation of a B-spline curve into a set of piecewise polynomial curves in a power form is done by either a knot refinement followed by basis conversions or applying a Taylor expansion on the B-spline curve for each knot span. Presented in this paper is a new algorithm, called a direct expansion algorithm, for the problem. The algorithm first locates the coefficients of all the linear terms that make up the basis functions in a knot span, and then the algorithm directly obtains the power form representation of basis functions by expanding the summation of products of appropriate linear terms. Then, a polynomial segment of a knot span can be easily obtained by the summation of products of the basis functions within the knot span with corresponding control points. Repeating this operation for each knot span, all of the polynomials of the B-spline curve can be transformed into a power form. The algorithm has been applied to both static and dynamic curves. It turns out that the proposed algorithm outperforms the existing algorithms for the conversion for both types of curves. Especially, the proposed algorithm shows significantly fast performance for the dynamic curves.