• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.575-584
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• 2006

In this paper we introduce a discrete tangent vector of a polygon defined on each vertex by a linear combination of forward difference and backward difference, and show that if the polygon is originated from a smooth curve then direction of the discrete tangent vector is a second order approximation of the direction of the tangent vector of the original curve. Using this discrete tangent vector, we also introduced the geometric cubic Hermite interpolation of a polygon with controlled initial and terminal speed of the curve segments proportional to the edge length. In this case the whole interpolation is $C^1$. Experiments suggest that about $90\%$ of the edge length is the best fit for the initial and terminal speeds.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.2
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• pp.433-442
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• 1995

For the line search of a multi-variable optimization, an efficient algorithm is presented. The algorithm sequentially employs several polynomial approximations such as 2-point quadratic interpolation, 3-point cubic interpolation/extrapolation and 4-point cubic interpolation/extrapolation. The order of polynomial function is automatically increased for improving the accuracy of approximation. The method of approximation (interpolation or extrapolation) is automatically switched by checking the slope information of the sample points. Also, for selecting the initial step length along the descent vector, a new approach is presented. The performance of the proposed method is examined by solving typical test problems such as mathematical problems, mechanical design problems and dynamic response problems.

• Proceedings of the IEEK Conference
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• 2000.11b
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• pp.71-74
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• 2000

The purpose of format conversion is to convert a wide range of personal computer video formats into a target format. Circuits for the conversion have been developed by means of interpolation techniques, such as zero-order interpolation, bilinear interpolation, and bisigmoidal interpolation. This paper proposes a scan converter using cubic splines. The converter was modeled in VHDL on Max+PlusII and implemented with an FPGA chip. The circuit gives much better conversion performance than a scan converter with zero-order or linear interpolation.

• Journal of the Korea Society for Simulation
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• v.9 no.4
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• pp.11-23
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• 2000

The purpose of format conversion is to convert a wide range of personal computer video formats into a target format. Circuits for the conversion have been developed by means of interpolation techniques, such as zero-order interpolation, bilinear interpolation, and bisigmoidal interpolation. This paper proposes a scan converter using cubic splines. The converter was modeled in VHDL, simulated on Max+plus Ⅱ , and implemented with an FPGA chip. The circuit gives much better conversion performance than a scan converter with zero-order or linear interpolation techniques according to simulation results and implementation.

• Proceedings of the Korea Society for Simulation Conference
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• 2000.04a
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• pp.91-95
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• 2000

The purpose of format conversion is to convert a wide range of personal computer video formats to a target format. Circuits for the conversion has been developed by means of interpolation techniques, such as zero-order interpolation, bilinear interpolation, and bisigmoidal interpolation. This paper proposes a scan converter using cubic splines. The converter was modeled in VHDL on Max+Plus II and implemented with an FPGA cpip. The circuit gives much better conversion performance than a scan converter with zero-order or linear interpolation.

• Journal of the Korean Data and Information Science Society
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• v.17 no.4
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• pp.1289-1297
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• 2006

Before other statistical data analysis the preprocessing steps should be performed adequately to have meaningful results. These steps include processes such as baseline correction, normalization, denoising, and multiple alignment. In this paper an algorithm for baseline correction is proposed with using the piecewise cubic Hermite interpolation with block-selected points and local minima after denoising for SELDI or MALDI mass spectrometry data.

• Journal of Korea Multimedia Society
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• v.10 no.7
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• pp.838-845
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• 2007

In this paper, we propose a modified cubic convolution scaler for the enlargement or reduction of digital images. The proposed method has less computational complexity than the cubic convolution method. In order to reduce the computational complexity, we use the linear function of the cubic convolution and the difference value of adjacent pixels for selecting interpolation methods. We employ adders and barrel shifts to calculate weights of the proposed method. The proposed method is compared with the conventional one for the computational complexity and the image quality. It has been designed and verified by HDL(Hardware Description Language), and synthesized using Xilinx Virtex FPGA.

• 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 Korean Academy of Oral and Maxillofacial Radiology
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• v.29 no.1
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• pp.65-85
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• 1999

Objectives: To determine the effect of interpolation functions when processing the digital periapical images. Material and Methods: The digital images were obtained by Digora and CDR system on the dry skull and human subject. 3 oral radiologists evaluated the 3 portions of each processed image using 7 interpolation methods, and ROC curves were obtained by trapezoidal methods. Results: The heighest Az value(0.96) was obtained with cubic spline method and the lowest Az value(0.03) was obtained with facet model method in Digora system. The heighest Az value (0.79) was obtained with gray segment expansion method and the lowest Az value(0.07) was obtained with facet model method in CDR system. There was significant difference of Az value in original image between Digora and CDR system at a=0.05 level. There were significant differences of Az values between Digora and CDR images with cubic spline method, facet model method, linear interpolation method and non-linear interpolation method at α=0.1 level.

• Journal of KIISE:Databases
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• v.31 no.5
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• pp.479-491
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• 2004

Location information of mobile objects is applied to vehicle tracking, digital battlefields, location based services, and telematics. Their location coordinates are periodically measured and stored in the application systems. The linear function is mainly used to estimate the location information that is not in the system at the query time point. However, a new method is needed to improve uncertainties of the location representation, because the location estimation by linear function induces the estimation error. This paper proposes an application method of the cubic spline interpolation in order to reduce deviation of the location estimation by linear function. First, we define location information of the mobile object moving on the two-dimensional space. Next, we apply the cubic spline interpolation to location estimation of the proposed data model and describe algorithm of the estimation operation. Finally, the precision of this estimation operation model is experimented. The experimentation comes out more accurate results than the method by linear function, although the proposed location estimation function uses the small amount of information. The proposed method has an advantage that drops the cost of data storage space and communication for the management of location information of the mobile objects.