• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.713-719
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• 2011

The problem of approximation from a set of scattered data arises in a wide range of applied mathematics and scientific applications. In this study, we present a quasi-interpolatory approximation scheme for scattered data approximation problem, which reproduces a certain space of polynomials. The proposed scheme is local in the sense that for an evaluation point, the contribution of a data value to the approximating value is decreasing rapidly as the distance between two data points is increasing.

• Journal of Korean Society for Geospatial Information Science
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• v.4 no.2 s.8
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• pp.173-180
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• 1996

In a grid based data transformation, the different gridding methods provide different interpretations of scattered data because each method calculate grid node values using a different weighted mathematical algorithms. Therefore, it is necessary to review the interpolated characteristics of some gridding methods according to search distance, search area and search options before determing the best method with a data set. For this, in this paper, six different gridding methods with the same search conditions are applied to a scattered data obtained from sterro-plotter. The interpolated characteristics of the scattered geographic data considered through comparison of coincidence between the data point and the grid node being interpolated. And also, shows the real application of gridding methods through calculating volumes and creating cross sections.

• The KIPS Transactions:PartA
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• v.10A no.1
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• pp.59-68
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• 2003

3-D data modeling of a volumetric scattered data is highly demanded for geological structure inspection, environment visualization and supersonic testing. The data used in these area are generally irregularly scattered in a volume data space, which are much different from the structured points data (cuberille data) used in Marching cube algorithm. In this paper, first we explore a volume modeling method for the scattered data based on tetrahedral domain. Next we propose a method for solving the ambiguity of tetrahedral domain decision using asymptotic decider criterion. Last we implement a simple visualization system based on the proposed asymptotic decider criterion and compare it with a system based on sphere criterion. In deciding tetrahedral domain, sphere criterion considers only positional values but asymptotic decider criterion considers not only positional values but also functional values, so asymptotic decider criterion is more accurate on deciding tetrahedral domain than sphere criterion.

• The Transactions of the Korea Information Processing Society
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• v.6 no.9
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• pp.2504-2511
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• 1999

This paper proposes the scattered data interpolation as an efficient method that is designed for free-form surface. Data interpolation is an essential method of designing for various objects. For the generating free-form surface of complexity construction, the existing method had problems to represent flat area and sharp corner edge, in presenting objects with computing the weight of control points. For solving this problem, we proposes the generating method of new approximation surfaces, using scattered data interpolation. This method obtains B-Spline basis function which calculates main curvature, having optimized value in variable area, on given control points and changed objects, and then computes the changing rate the approximating data, using it's value. We also present this method that generates smoother free-form surface, using the scattered data interpolation with minimum weight.

• Journal of radiological science and technology
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• v.47 no.1
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• pp.13-19
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• 2024

Control of scattered radiation is one of very important factors in the use of medical radiation. In general X-ray exam, the causes, measurement methods, and the kind of detectors of scattered rays within the radiation area are diverse. In this study, the dose of scattered ray was measured by changing the thickness of the polycarbonate phantom and the tube voltage. As a result of measurement of scattered radiation, the results show that the scattered dose significantly(p<.05) increased with growing of thickness of phantom in the tube voltage 40, 50 and 60 kVp(F(p)<.05, R²>64%). As tube voltage increased at all phantom thicknesses, the scattered dose also significantly(p<.05) increased(F(p)<.05, R²>69%). In cases where a significant correlation was shown, the coefficient of determination of more than 60% was shown in regression analysis. The results of this study can be used as data on scattered radiation dose according to the tube voltage and the object thickness in general X-ray imaging exam.

• Korean Journal of Computational Design and Engineering
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• v.12 no.1
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• pp.27-38
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• 2007

This paper describes a multiresidual approximation method for scattered volumetric data modeling. The approximation method employs a volumetric NURBS or VNURBS as a data interpolating function and proposes two multiresidual methods as a data modeling algorithm. One is called as the residual series method that constructs a sequence of VNURBS functions and their algebraic summation produces the desired approximation. The other is the residual merging method that merges all the VNURBS functions mentioned above into one equivalent function. The first one is designed to construct wavelet-type multiresolution models and also to achieve more accurate approximation. And the second is focused on its improvement of computational performance with the save fitting accuracy for more practical applications. The performance results of numerical examples demonstrate the usefulness of VNURBS approximation and the effectiveness of multiresidual methods. In addition, several graphical examples suggest that the VNURBS approximation is applicable to various applications such as surface modeling and fitting problems.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1087-1095
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• 2009

In this paper, we study approximation method from scattered data to the derivatives of a function f by a radial basis function $\phi$. For a given function f, we define a nearly interpolating function and discuss its accuracy. In particular, we are interested in using smooth functions $\phi$ which are (conditionally) positive definite. We estimate accuracy of approximation for the Sobolev space while the classical radial basis function interpolation applies to the so-called native space. We observe that our approximant provides spectral convergence order, as the density of the given data is getting smaller.

• Korean Journal of Digital Imaging in Medicine
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• v.13 no.1
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• pp.21-26
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• 2011

A radiation imaging system used in a surgery room is mainly using C-arm which is purposed to fluoroscope. C-arm is often use to watch an operation's accuracy and progress, but not only being bombed to this first beam but also affected to this scattered beam, so now we are look for the way to reduce bombed amount of doctor, nurses and radiological technologists. We measured the exposure dose in $0^{\circ}$ spot according to the distance to find out frequency distribution of scattered ray in an operation room and found the spot which has the same exposure dose from $30^{\circ}$ distance of all directions and wrote isodose curve. We analyzed the data and found out the sudden reduction of scattered ray according to the long direction also found out that scattered ray was not related to the directions. Operators must recognize the reduction of exposure dose. Because reducing scattered ray from all directions in an operation room is really difficult. So every operators must use shelters to reduce the exposure dose and notice the safety.

• The KIPS Transactions:PartA
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• v.13A no.3 s.100
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• pp.267-274
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• 2006

This paper describes a method to achieve different level of detail for the given volumetric data by assigning weight for the given data points. The relation between wavelet transformation and alpha shape was investigated to define the different level of resolution. Scattered data are defined as a collection of data that have little specified connectivity between data points. The quality of interpolant in volumetric trivariate space depends not only on the distribution of the data points in ${\Re}^3$, but also on the data value (intensity). We can improve the quality of an approximation by using wavelet coefficient as weight for the corresponding data points.

• Journal of the Korean Statistical Society
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• v.36 no.2
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• pp.209-228
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• 2007

Given scattered surface air temperatures observed by a network of weather stations, it is an important problem to estimate the entire temperature field for every location on the globe. Recently, a multi-scale spherical basis function (SBF) representation was proposed by Li (1999) for representing scattered data on the sphere. However, for a successful application of Li (1999)'s method, some practical issues such as network design, bandwidth selection of SBFs and initial coefficients are to be resolved. This paper proposes automatic procedures to design network and to select bandwidths. This paper also considers a preprocessing problem to obtain a stable initial coefficients from scattered data. Experiments with real temperature data demonstrate the promising empirical properties of the proposed approaches.