• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.305-334
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• 2005

The objective of this study is to analyze the decay characteristics of the hat interpolation wavelet coefficients of some smooth functions defined in a two-dimensional space. The motivation of this research is to establish some fundamental mathematical foundations needed in justifying the adaptive multiresolution analysis of the hat-interpolation wavelet-Galerkin method. Though the hat-interpolation wavelet-Galerkin method has been successful in some classes of problems, no complete error analysis has been given yet. As an effort towards this direction, we give estimates on the decaying ratios of the wavelet coefficients at children interpolation points to the wavelet coefficient at the parent interpolation point. We also give an estimate for the difference between non-adaptively and adaptively interpolated representations.

• Journal of Korea Society of Digital Industry and Information Management
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• v.16 no.1
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• pp.55-65
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• 2020

With the development of display hardware, image interpolation techniques have been used in various fields such as image zooming and medical imaging. Traditional image interpolation methods, such as bi-linear interpolation, bi-cubic interpolation and edge direction-based interpolation, perform interpolation in the spatial domain. Recently, interpolation techniques in the discrete cosine transform or wavelet domain are also proposed. Using these various existing interpolation methods and machine learning, we propose decision tree classification-based image interpolation methods. In other words, this paper is about the method of adaptively applying various existing interpolation methods, not the interpolation method itself. To obtain the decision model, we used Weka's J48 library with the C4.5 decision tree algorithm. The proposed method first constructs attribute set and select classes that means interpolation methods for classification model. And after training, interpolation is performed using different interpolation methods according to attributes characteristics. Simulation results show that the proposed method yields reasonable performance.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.46 no.5
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• pp.111-119
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• 2009

This paper presents an adaptive image interpolation algorithm using local characteristics. An input image is classified into edge region and flat low frequency region. And then, the edge region is further partitioned into directive edge region and high frequency texture region. A bilinear interpolation is applied to flat low frequency region, cubic convolution is applied to texture region, and new edge directed interpolation to directive edge region, respectively. Simulation results show that the proposed algorithm outperforms the existing interpolation methods in terms of visual quality as well as PSNR.

• Proceedings of the Korean Information Science Society Conference
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• 2005.11b
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• pp.952-954
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• 2005

The objective of this paper is to propose the image interpolation method with pseudomedian filter for Field warping and morphing, and to evaluate and analyze its subjective image quality. The Field warping relatively gives rise to more computing overhead, but it can use the control line to control the warping result with more elaboration. Due to the working characteristics of the image warping and morphing process, various complex geometrical transformations occur and a image interpolation technique is needed to effectively process them. Of the various interpolation techniques, bilinear interpolation which shows above average performance is the most widely used. However, this technology has its limits in the reconstructivity of diagonal edges. The proposed interpolation method is to efficiently combine the bilinear interpolation and the pseudomedian filter0based interpolation which shows good performance in the reconstructivity of diagonal edges. According to the proposed interpolation method, we could get more natural warping and morphing results than other interpolation methods.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.22 no.4
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• pp.37-41
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• 2021

This paper presents a study to implement a touch screen capable of real-time response processing in a low-end embedded system. This was done by introducing an algorithm using an interpolation method to represent real-time response characteristics when a touch input is performed. In this experiment, we applied a linear interpolation algorithm that estimates random data by deriving a first-order polynomial from 2-point data. We also applied a Lagrange interpolation algorithm that estimates random data by deriving a quadratic polynomial from 3-point data. As a result of the experiment, it was found that the Lagrange interpolation method was more complicated than the linear interpolation method, and the processing speed was slow, so the text was not smooth. When using the linear interpolation method, it was confirmed that the speed displayed on a screen is 2.4 times faster than when using the Lagrange interpolation method. For real-time response characteristics, it was confirmed that smaller size of the executable file of the algorithm is more advantageous than the superiority of the algorithm itself. In conclusion, in order to secure real-time response characteristics in a low-end embedded system, it was confirmed that a relatively simple linear interpolation algorithm performs touch operations with better real-time response characteristics than the Lagrange interpolation method.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.10 no.1
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• pp.95-101
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• 2017

In natural images, there is generally locality, and the values of adjacent pixels are similar. It is possible to estimate the curved surface characteristics of the original image using adjacent pixels having similar pixel values. In this paper, after precisely estimating the characteristics of the curved surface existing in the image, interpolation values are obtained so as to faithfully reflect the estimated characteristics of the curved surface, We propose an effective image enlarging method that generates an enlarged image using the obtained interpolation values. The image enlarged by the proposed method maintains the curved surface characteristics of the original image, and thus the image quality of the enlarged image is improved. Experimental results show that the image quality of the proposed method is superior to that of the conventional techniques.

• Water for future
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• v.29 no.1
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• pp.203-212
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• 1996

The subject research attempts to develop a new temporal interpolation scheme for the method of characteristics. The proposed three-point time-line Lagrange interpolation Reachback (3PR) method is a temporal quadratic interpolation scheme using the three grid points near the intersection between a characteristic line and a previous time-line. The accuracy of the 3PR method is compared with those of temporal and spatial interpolation schemes such as Reachback, Upwind, and quandratic spatial interpolation methods for two pure advection problems. The results show that on the aspects of the numerical damping and/or oscillation the temporal interpolation schemes are better than the spatial ones under the same interpolation order conditions. In addition, the spatial ones under the same interpolation order conditions. In addition, the proposed 3PR method improves the accuracy of Reachback method as well as it contains the merits of time-line interpolation schemes.

• Journal of the Korea Society of Computer and Information
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• v.20 no.1
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• pp.63-73
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• 2015

In this paper, a quality improvement scheme is proposed for magnified image using the various curved surface characteristics of image. After testing horizontal and vertical directional surface characteristics of source image, interpolation value is calculated to have the surface characteristics such as simple convex surface, simple concave surface, and compound surface. The calculated interpolation value become the value of the interpolated pixel of magnified image. The calculated interpolation value is closer to the pixel value of real image. So, the quality of the magnified image is improved. The PSNR value of the magnified image using the proposed scheme is larger than the PSNR values of the magnified image using the existing techniques.

• Journal of the Korean association of regional geographers
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• v.10 no.2
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• pp.389-406
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• 2004

with the increasing popularity of regional studies, the importance of regional data has been recognized dramatically in recent years. However, due to potential problems from the intrinsic characteristics of aggregate regional data for the research, and incompatible regional units between source and target regional data units, the method for reorganizing the regional data units for a given research analysis should be required. In this regard, the purpose of this research is to review the significant interpolation methods for reorganizing the data units and, based on it, to propose the population weighted interpolation method. For the first purpose, areal weighted interpolation method, pycnophylactic method, dasymetric method, area-to-point method were reviewed. The proposed population-weighted interpolation method was applied to the case study of population census regional data in Erie County, NY, compared with areal weighted interpolation method, pycnophylactic method in terms of several statistical characteristics.

• Journal of the Korean association of regional geographers
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• v.14 no.6
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• pp.736-751
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• 2008

Although a growing number of studies have commonly used a simple areal weighting interpolation method to quantify demographic characteristics of impacted areas in environmental equity analysis, the results obtained are inevitably imprecise because of the method's unrealistic assumption that population is evenly distributed within a census enumeration unit. Two alternative areal interpolation methods such as intelligent areal weighting and regression methods can account for the distributional biases in the estimation of impacted populations by making use of additional information about the geographic distribution of population. This research explores five areal interpolation methods for estimating the population characteristics of impacted areas in environmental equity analysis and evaluates the sensitivity of the outcomes of environmental equity analysis to areal interpolation methods. This study used GIS techniques to allow areal interpolation to be informed by the distribution of land cover types, as inferred from a satellite image. in both the source and target units. Independent samples t-test statistics were measured to verify the environmental equity hypothesis while coefficients of variation were calculated to compare the relative variability and consistency in the socioeconomic characteristics of populations at risk over different areal interpolation methods. Results show that the outcomes of environmental equity analysis in the study area are not sensitive to the areal interpolation methods used in estimating affected populations, but the population estimates within the impacted areas are largely variable as different areal interpolation methods are used. This implies that the use of different areal interpolation methods may to some degree alter the statistical results of environmental equity analysis.