• Structural Engineering and Mechanics
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• v.11 no.2
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• pp.221-236
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• 2001

A local point interpolation method (LPIM) is presented for the stress analysis of two-dimensional solids. A local weak form is developed using the weighted residual method locally in two-dimensional solids. The polynomial interpolation, which is based only on a group of arbitrarily distributed nodes, is used to obtain shape functions. The LPIM equations are derived, based on the local weak form and point interpolation. Since the shape functions possess the Kronecker delta function property, the essential boundary condition can be implemented with ease as in the conventional finite element method (FEM). The presented LPIM method is a truly meshless method, as it does not need any element or mesh for both field interpolation and background integration. The implementation procedure is as simple as strong form formulation methods. The LPIM has been coded in FORTRAN. The validity and efficiency of the present LPIM formulation are demonstrated through example problems. It is found that the present LPIM is very easy to implement, and very robust for obtaining displacements and stresses of desired accuracy in solids.

• Journal of Korea Society of Digital Industry and Information Management
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• v.16 no.3
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• pp.49-58
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• 2020

Image interpolation, a technology that converts low resolution images into high resolution images, has been widely used in various image processing fields such as CCTV, web-cam, and medical imaging. This technique is based on the fact that the statistical distributions of the white Gaussian noise and the difference between the interpolated image and the original image is similar to each other. The proposed algorithm is composed of three steps. In first, the interpolated image is derived by random image interpolation. In second, we derive weighting functions that are used to apply non-local mean filtering. In the final step, the prediction error is corrected by performing non-local mean filtering by applying the selected weighting function. It can be considered as a post-processing algorithm to further reduce the prediction error after applying an arbitrary image interpolation algorithm. Simulation results show that the proposed method yields reasonable performance.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2002.10a
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• pp.181-185
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• 2002

The modeling of realistic water-jet geometry is needed in order to facilitate the design modifications. The present paper proposes a method of generating inlet geometry. Inlet duct was represented by NURBS method which utilized the skinning and local cubic interpolation scheme. Three test examples are presented demonstrating the effectiveness of the methods of skinning and local cubic interpolation. Computational examples associated with practical configurations have shown the usefulness of the present method.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.5 no.11
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• pp.2068-2086
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• 2011

Based on the quincunx sub-sampling grid, the New Interleaved Hierarchical INTerpolation (NIHINT) method is recognized as a superior pyramid data structure for the lossless and progressive coding of natural images. In this paper, we propose a new image interpolation algorithm, Edge Adaptive Hierarchical INTerpolation (EAHINT), for a further reduction in the entropy of interpolation errors. We compute the local variance of the causal context to model the strength of a local edge around a target pixel and then apply three statistical decision rules to classify the local edge into a strong edge, a weak edge, or a medium edge. According to these local edge types, we apply an interpolation method to the target pixel using a one-directional interpolator for a strong edge, a multi-directional adaptive weighting interpolator for a medium edge, or a non-directional static weighting linear interpolator for a weak edge. Experimental results show that the proposed algorithm achieves a better compression bit rate than the NIHINT method for lossless image coding. It is shown that the compression bit rate is much better for images that are rich in directional edges and textures. Our algorithm also shows better rate-distortion performance and visual quality for progressive image transmission.

• Structural Engineering and Mechanics
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• v.14 no.6
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• pp.713-732
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• 2002

A local radial point interpolation method (LRPIM) based on local residual formulation is presented and applied to solid mechanics in this paper. In LRPIM, the trial function is constructed by the radial point interpolation method (PIM) and establishes discrete equations through a local residual formulation, which can be carried out nodes by nodes. Therefore, element connectivity for trial function and background mesh for integration is not necessary. Radial PIM is used for interpolation so that singularity in polynomial PIM may be avoided. Essential boundary conditions can be imposed by a straightforward and effective manner due to its Delta properties. Moreover, the approximation quality of the radial PIM is evaluated by the surface fitting of given functions. Numerical performance for this LRPIM method is further studied through several numerical examples of solid mechanics.

• The KIPS Transactions:PartA
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• v.8A no.4
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• pp.489-498
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• 2001

A new method for local control of arbitrary scattered data interpolation in the hyperbolic plane is developed in this paper. The issue associated with local control is very critical in the interactive in the interactive design field. Especially the suggested method in this paper could be effectively applied to the interactive shape modeling of genus-N objects, which are constructed on the hyperbolic plane. Since the effects of the changed data affects only the limited area around itself, it is more convenient for end-users to design a genus-N object interactively. Therefore, by improving the global interpolation on the hyperbolic plane where the genus-N object is constructed, this research is aiming at the development and implementation of the local interpolation on the hyperbolic plane. It is implemented using the following process. First, for localizing the interpolating functions, the hyperbolic domain is tessellated into arbitrary triangle patches and the group of adjacent triangle patches of each data point is defined as a sub-domain. On each sub-domain, a weight function is defined. Last, by blending of three weight functions on the overlapped triangles, local MQ interpolation is completed. Consequently, it is compared with the global MQ interpolation using several sample data and functions.

• The Korean Journal of Applied Statistics
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• v.20 no.3
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• pp.561-571
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• 2007

Local linear regression estimator is the most widely used nonparametric regression estimator which has a number of advantages over the traditional kernel estimators. It is well known that local linear estimator can produce erratic result in sparse regions in the realization of the design and the interpolation method of Hall and Turlach (1997) is the very efficient way to resolve this problem. However, it has been never pointed out that Hall and Turlach's interpolation method is very sensitive to outliers. In this paper, we propose the robust version of the interpolation method for adapting to sparse design. The finite sample properties of the method is compared with Hall and Turlach's method by the simulation study.

• Journal of the Korean Mathematical Society
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• v.38 no.3
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• pp.657-667
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• 2001

We propose a statistical interpolation approximate solution for a nonlinear stochastic integral equation of a stock price process. The proposed method has the order O(h$^2$) of local error under the weaker conditions of $\mu$ and $\sigma$ than those of Milstein' scheme.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.47 no.1
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• pp.120-127
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• 2010

This paper presents a SR method using adaptive interpolation based on local gradient features to obtain a high quality SR image. In this method, the distance between the interpolated pixel and the neighboring valid pixel is considered by using local gradient properties. The interpolation coefficients take the local gradient of the LR images into account. The smaller the local gradient of a pixel is, the more influence it should have on the interpolated pixel. And the median filter is finally applied to reduce the blurring and noise of the interpolated HR image. Experiment results show the effectiveness of the proposed method in comparison with other methods, especially in the edge areas of the images.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.10C
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• pp.1000-1009
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• 2007

This paper presents a content adaptive interpolation (CAI) for intra deinterlacing. The CAI consists of three steps: pre-processing, content classification, and adaptive interpolation. There are also three main interpolation methods in our proposed CAI, i.e. modified edge-based line averaging (M-ELA), gradient directed interpolation (GDI), and window matching method (WMM). Each proposed method shows different performances according to spatial local features. Therefore, we analyze the local region feature using the gradient detection and classify each missing pixel into four categories. And then, based on the classification result, a different do-interlacing algorithm is activated in order to obtain the best performance. Experimental results demonstrate that the CAI method performs better than previous techniques.