• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.175-195
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• 2012

Representing planar Pythagorean hodograph (PH) curves by the complex roots of their hodographs, we standardize Farouki's double cubic method to become the undetermined junction point (UJP) method, and then prove the generic existence of solutions for general $C^1$ Hermite interpolation problems. We also extend the UJP method to solve $C^2$ Hermite interpolation problems with multiple PH cubics, and also prove the generic existence of solutions which consist of triple PH cubics with $C^1$ junction points. Further generalizing the UJP method, we go on to solve $C^2$ Hermite interpolation problems using two PH quintics with a $C^1$ junction point, and we also show the possibility of applying the modi e UJP method to $G^2[C^1]$ Hermite interpolation.

• Proceedings of the KSME Conference
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• 2007.05a
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• pp.1621-1625
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• 2007

This paper examines the interpolation algorithms and error criteria using stateline based control architectures that is proposed in the University of British Columbia. The main purpose of this paper is checking the influences of jerk in error criteria and judging several interpolation algorithms that are used for positioning. The performance of the extended error criteria and interpolation algorithm are demonstrated by simulation. It is found that a slight improvement was achieved by applying jerk in the error checking criteria and that spline interpolation yields stable result.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.129.1-129
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• 2001

In this paper, we present an approach for matching images from finding interesting points and applying new image interpolation algorithm. New algorithms are developed that automatically align the input images match them and reconstruct 3-D surfaces. The interpolation algorithm is designed to cope with simple shapes. The proposed image interpolation algorithm generate a rotation image about vertical axes by an any angle from 4 base images. Each base image that was obtained from CCD camera has an angle difference of 90$^{\circ}$ The proposed image interpolation algorithm use the geometric analysis of image and depth information.

• Proceedings of the Korean Society of Surveying, Geodesy, Photogrammetry, and Cartography Conference
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• 2004.11a
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• pp.129-133
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• 2004

9 GPS data with a 30 second sampling rate were extracted from the GPS raw data that recorded with 1 second interval for interpolation. 9 GPS data were interpolated using lagrange interpolation method and compared to the GPS raw data. Using a 9th-order interpolation, error of interpolated code data were within 0.5m.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.563-570
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• 2007

There has been a considerable research interest in medical communities for neuronal fiber tracking with magnetic resonance diffusion tensor imaging(DTI). DTI data have abundant structural boundaries that need to be preserved during interpolation to facilitate fiber tracking. Sigmoid function has been used in recent papers but the sigmoid function still is not good enough to be served as an positive interpolation in mathematical point of view. In this paper, we construct and provide two families positive cardinal interpolation functions.

• Honam Mathematical Journal
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• v.39 no.4
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• pp.617-635
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• 2017

By applying a classical approach for scalar rational interpolation problem, certain type of minimal interpolation problem for rational matrix functions is solved. It is shown that an appropriately defined matrix plays a key role in solving the minimal problem.

• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.771-771
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• 1999

• Journal of Astronomy and Space Sciences
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• v.37 no.3
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• pp.199-208
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• 2020

This paper presents a kinematic ephemeris generator for Korea Pathfinder Lunar Orbiter (KPLO) and its performance test results. The kinematic ephemeris generator consists of a ground ephemeris compressor and an onboard ephemeris calculator. The ground ephemeris compressor has to compress desired orbit propagation data by using an interpolation method in a ground system. The onboard ephemeris calculator can generate spacecraft ephemeris and the Sun/Moon ephemeris in onboard computer of the KPLO. Among many interpolation methods, polynomial interpolation with uniform node, Chebyshev interpolation, Hermite interpolation are tested for their performances. As a result of the test, it is shown that all the methods have some cases that meet requirements but there are some performance differences. It is also confirmed that, the Chebyshev interpolation shows better performance than other methods for spacecraft ephemeris generation, and the polynomial interpolation with uniform nodes yields good performance for the Sun/Moon ephemeris generation. Based on these results, a Kinematic ephemeris generator is developed for the KPLO mission. Then, the developed ephemeris generator can find an approximating function using interpolation method considering the size and accuracy of the data to be transmitted.

• Journal of the Institute of Electronics and Information Engineers
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• v.51 no.3
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• pp.112-118
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• 2014

As higher quality of image is required for digital image scaling, longer processing time is required. Therefore the technology that can make higher quality image quickly is needed. We propose the double linear-cubic convolution interpolation which creates the high quality image with low complexity and hardware resources. The proposed interpolation methods which are made up of four one-dimensional linear interpolations and one one-dimensional cubic convolution perform linear-cubic convolution interpolation in horizontal and vertical direction. When compared in aspects of peak signal-to-noise ratio(PSNR), performance time and amount of hardware resources, the proposed interpolation provided better PSNR, low complexity and less hardware resources than bicubic convolution interpolation.

• Journal of Korea Multimedia Society
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• v.5 no.5
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• pp.494-504
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• 2002

Volume rendering is a method of displaying volumetric data as a sequence two-dimensional image. Because this algorithm has an advantage of visualizing structures within objects, it has recently been used to analyze medical images i.e, MRI, PET, and SPECT. In this paper. we suggested a method for creating images easily from sampled volumetric data and applied the interpolation method to medical images. Additionally, we implemented and applied two kinds of interpolation methods to improve the image quality, linear interpolation and cubic interpolation at the sampling stage. Subsequently, we compared the results of volume rendered data using a transfer function. We anticipate a significant contribution to diagnosis through image reconstruction using a volumetric data set, because volume rendering techniques of medical images are the result of 3-dimensional data.