• Title/Summary/Keyword: polynomial interpolation

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Assessment of Image Registration for Pressure-Sensitive Paint (Pressure Sensitive Paint를 이용한 압력장 측정기술의 이미지 등록에 관한 연구)

  • Chang, Young-Ki;Park, Sang-Hyun;Sung, Hyung-Jin
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.28 no.3
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    • pp.271-280
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    • 2004
  • Assessment of image registration for Pressure Sensitive Paint (PSP) was performed. A 16 bit camera and LED lamp were used with Uni-FIB paint (ISSI). Because of model displacement and deformation at 'wind-on' condition, a large error of the intensity ratio was induced between 'wind-on' and' wind-off images. To correct the error, many kinds of image registrations were tested. At first, control points were marked on the model surface to find the coefficients of polynomial transform functions between the 'wind-off' 'wind-on' images. The 2nd-order polynomial function was sufficient for representing the model displacement and deformation. An automatic detection scheme was introduced to find the exact coordinates of the control points. The present automatic detection algorithm showed more accurate and user-friendly than the manual detection algorithm. Since the coordinates of transformed pixel were not integer, five interpolation methods were applied to get the exact pixel intensity after transforming the 'wind-on' image. Among these methods, the cubic convolution interpolation scheme gave the best result.

Model-based subpixed motion estimation for image sequence compression (도영상 압축을 위한 모델 기반 부화소 단위 움직임 추정 기법)

  • 서정욱;정제창
    • Journal of the Korean Institute of Telematics and Electronics S
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    • v.35S no.1
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    • pp.130-140
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    • 1998
  • This paper presents a method to estimate subpixel accuracy motion vectors using a mathermatical model withoug interpolation. the proposed method decides the coefficients of mathematical model, which represents the motion vector which is achieved by full search. And then the proposed method estimates subpixel accuracy motion vector from achieved mathematical model. Step by step mathematical models such as type 1, type 2, type 3, modified bype 2, modified type 3, and Partial Interpolation type 3 are presented. In type 1, quadratic polynomial, which has 9 unknown coefficients and models the 3by 3 pixel plane, is used to get the subpixel accuracy motion vectors by inverse matrix solution. In type 2 and 3, each quadratic polynomial which is simplified from type 1 has 5 and 6 unknown coefficients and is used by least square solution. Modified type 2 and modified type 3 are enhanced models by weighting only 5 pixels out of 9. P.I. type 3 is more accurate method by partial interpolation around subpixel which isachieved by type 3. LThese simulation results show that the more delicate model has the better performance and modified models which are simplified have excellent performance with reduced computational complexity.

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Research on Touch Function capable of Real-time Response in Low-end Embedded System (저사양 임베디드 시스템에서의 실시간 응답이 가능한 터치 기능 연구)

  • Lee, Yong-Min;Han, Chang Ho
    • 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.

On the interpolation formula, Chao-ch'a-shu, applied to the Chinese Calendar, Shou-Shih-li (초차법(招差法)과 고대역법(古代曆法)에서의 그 응용(應用))

  • Lee, Eun-Sung
    • Journal of The Korean Astronomical Society
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    • v.7 no.1
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    • pp.19-23
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    • 1974
  • The interpolation formula Chao-ch'a-shn devised for the Chinese calendar, Shou-shih-li, has been shown as the one of the 3rd order polynomial. Its 3 coefficients have been determined from the table of the Sun in Shou-shih-li. Its applications to the moon and planets are also briefly mentioned.

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A 3-dimensional EEG topography based on the polygon technique (보간 알고리즘 비교와 폴리곤 테크닉에 기초한 3차원 EEG 맵핑)

  • 한이범;이용희;김선일
    • Proceedings of the IEEK Conference
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    • 1998.06a
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    • pp.581-584
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    • 1998
  • To obtain 3-D topography of EEG records, we propose a new method based on the polygon mapping technique. The method has the low complexity to calculate the interpolation of the EEG records on the scalp and maintains the high resolution topography because the polygon technique performs the interpolation at the only vertexes of each polygon. We implemented the topographic system with 3D barycentric, 3D polynomial and spherical spline algorithms in a personal computer.

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A Study on The Error Analysis of Integration Operational Metrices by The Lagrange Second Order Interpolation Polvnomial (Lagrange 이차 보간 다항식을 이용한 적분연산 행렬의 오차 해석에 관한 연구)

  • Lee, Hae-Ki;Kim, Tai-Hoon
    • Proceedings of the KIEE Conference
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    • 2003.07e
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    • pp.55-57
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    • 2003
  • This paper presents a new method for finding the Block Pulse series coefficients and deriving the Block Pulse integration operational matrices which are necessary for the control fields using the Block Pulse functions. In this paper, the accuracy of the Block Pulse series coefficients derived by using the Lagrange second order interpolation polynomial is approved by the mathematical method.

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Derivation of Galois Switching Functions by Lagrange's Interpolation Method (Lagrange 보간법에 의한 Galois 스윗칭함수 구성)

  • 김흥수
    • Journal of the Korean Institute of Telematics and Electronics
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    • v.15 no.5
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    • pp.29-33
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    • 1978
  • In this paper, the properties of Galois fields defined over any finite field are analysed to derive Galois switching functions and the arithmetic operation methods over any finite field are showed. The polynomial expansions over finite fields by Lagrange's interpolation method are derived and proved. The results are applied to multivalued single variable logic networks.

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The Use of The Spectral Properties of Basis Splines in Problems of Signal Processing

  • Nasiritdinovich, Zaynidinov Hakim;Egamberdievich, MirzayevAvaz;Panjievich, Khalilov Sirojiddin
    • Journal of Multimedia Information System
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    • v.5 no.1
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    • pp.63-66
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    • 2018
  • In this work, the smoothing and the interpolation basis splines are analyzed. As well as the possibility of using the spectral properties of the basis splines for digital signal processing are shown. This takes into account the fact that basic splines represent finite, piecewise polynomial functions defined on compact media.

Polynomials satisfying f(x-a)f(x)+c over finite fields

  • Park, Hong-Goo
    • Bulletin of the Korean Mathematical Society
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    • v.29 no.2
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    • pp.277-283
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    • 1992
  • Let GF(q) be a finite field with q elements where q=p$^{n}$ for a prime number p and a positive integer n. Consider an arbitrary function .phi. from GF(q) into GF(q). By using the Largrange's Interpolation formula for the given function .phi., .phi. can be represented by a polynomial which is congruent (mod x$^{q}$ -x) to a unique polynomial over GF(q) with the degree < q. In [3], Wells characterized all polynomial over a finite field which commute with translations. Mullen [2] generalized the characterization to linear polynomials over the finite fields, i.e., he characterized all polynomials f(x) over GF(q) for which deg(f) < q and f(bx+a)=b.f(x) + a for fixed elements a and b of GF(q) with a.neq.0. From those papers, a natural question (though difficult to answer to ask is: what are the explicit form of f(x) with zero terms\ulcorner In this paper we obtain the exact form (together with zero terms) of a polynomial f(x) over GF(q) for which satisfies deg(f) < p$^{2}$ and (1) f(x+a)=f(x)+c for the fixed nonzero elements a and c in GF(q).

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Correction of Antenna Position for Projection Center Coordinates by Kinematic DGPS-Positioning (동적 DGPS 측위에 의한 투영중심좌표 결정을 위한 수신기 위치의 보간)

  • 이종출;문두열;신상철
    • Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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    • v.15 no.2
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    • pp.165-173
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    • 1997
  • The combined bundle block adjustment with projection center coordinates determined by kinematic DGPS-positioning has reached a high level of accuracy. Standard deviations of the ground coordinates of $\pm{10cm}$ or even better can be reached. On this accuracy level also smaller error components are becoming more important. One major point of this is the interpolation of the projection centers as a function of time between the GPS-antenna locations. A just linear interpolation is not respecting the not linear movement of the aircraft. Based on a least squares polynomial fitting the aircraft maneuver can be estimated more accurate and blunders of the GPS-positions caused by loss of satellite and cycle slips are determinable. The interpolation with a time interval of 3sec in the study area RHEINKAMP is quite different to the interpolation with a time interval of 6-7sec in the study area MAAS. The GPS-positions of the study area are identified as blunders based on a local polynomial regression. This cannot be neglected for precise block adjustment.

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