• Journal of the Optical Society of Korea
• /
• v.13 no.3
• /
• pp.379-385
• /
• 2009

The vergence control of binocular stereoscopic camera is the most essential factor for acquiring high quality stereoscopic images. In this paper, we proposed a binocular stereoscopic camera vergence control method using disparity information by the simple image processing and estimate the quantity of vergence control using the Lagrange interpolation equation. The method of extracting disparity information through image processing is as follows: first the key-object in left & right images was extracted through labeling of the central area of the image, and then a simple method was used for calculating the disparity value of the same key-object in the labeled left and right images. The vergence control method uses disparity information and keeps the convergence distance of left & right cameras and the distance of the key-object the same. According to the proposed method, variance in the distance of the key-object and application of calculated disparity information of obtained left & right images to the quadratic Lagrange interpolation equation could estimate the quantity of vergence control, which confirmed that the method of stereoscopic camera vergence control can be simplified through experiments on various key-objects and other convergence distance.

• Journal of Institute of Control, Robotics and Systems
• /
• v.17 no.10
• /
• pp.967-982
• /
• 2011

This paper presents a FTNCS (Fault-Tolerant Networked Control System) that can tolerate control surface failure and packet delay/loss in an UAV (Unmanned Aerial Vehicle). The proposed method utilizes the benefits of self-diagnosis by smart actuators along with the control allocation technique. A smart actuator is an intelligent actuation system combined with microprocessors to perform self-diagnosis and bi-directional communications. In the event of failure, the smart actuator provides the system supervisor with a set of actuator condition data. The system supervisor then compensate for the effect of faulty actuators by re-allocating redundant control surfaces based on the provided actuator condition data. In addition to the compensation of faulty actuators, the proposed FTNCS also includes an efficient algorithm to deal with network induced delay/packet loss. The proposed algorithm is based on a Lagrange polynomial interpolation method without any mathematical model of the system. Computer simulations with an UAV show that the proposed FTNCS can achieve a fast and accurate tracking performance even in the presence of actuator faults and network induced delays.

• The Transactions of the Korea Information Processing Society
• /
• v.13 no.2
• /
• pp.34-40
• /
• 2024

Secret sharing is a cryptographic technique that involves dividing a secret or a piece of sensitive information into multiple shares or parts, which can significantly increase the confidentiality of a secret. There has been a lot of research on secret sharing for different contexts or situations. Tassa's conjunctive secret sharing method employs polynomial derivatives to facilitate hierarchical secret sharing. However, the use of derivatives introduces several limitations in hierarchical secret sharing. Firstly, only a single group of participants can be created at each level due to the shares being generated from a sole derivative. Secondly, the method can only reconstruct a secret through conjunction, thereby restricting the specification of arbitrary secret reconstruction conditions. Thirdly, Birkhoff interpolation is required, adding complexity compared to the more accessible Lagrange interpolation used in polynomial-based secret sharing. This paper introduces the multi-compartment secret sharing method as a generalization of the conjunctive hierarchical secret sharing. Our proposed method first encrypts a secret using external groups' shares and then generates internal shares for each group by embedding the encrypted secret value in a polynomial. While the polynomial can be reconstructed with the internal shares, the polynomial just provides the encrypted secret, requiring external shares for decryption. This approach enables the creation of multiple participant groups at a single level. It supports the implementation of arbitrary secret reconstruction conditions, as well as conjunction. Furthermore, the use of polynomials allows the application of Lagrange interpolation.

• The Transactions of the Korean Institute of Electrical Engineers A
• /
• v.48 no.6
• /
• pp.753-759
• /
• 1999

BPF(block pulse function) has been used widely in the system analysis and controller design. The integral operational matrix of BPF converts the system represented in the form of the differential equation into the algebraic problem. Therefore, it is important to reduce the error caused by the integral operational matrix. In this paper, a new integral operational matrix is derived from the approximating function using Lagrange's interpolation formula. Comparing the proposed integral operational matrix with another, the result by proposed matrix is closer to the real value than that by the conventional matrix. The usefulness of th proposed method is also verified by numerical examples.

• 한국가시화정보학회:학술대회논문집
• /
• 2006.12a
• /
• pp.25-35
• /
• 2006

We have evaluated the performances of the following six interpolation schemes used for window deformation in particle image velocimetry (PIV): the linear, quadratic, B-spline, cubic, sinc, Lagrange interpolations. Artificially generated images comprised of particles of diameter in a range $1.1{\leq}d_p\leq10.0$ pixel were investigated. Three particle diameters were selected for detailed evaluation: $d_p$=2.2, 3.3, 4.4 pixel with a constant particle concentration 0.02 $particle/pixel^2$. Two flow patterns were considered: uniform and shear flows. The mean and random errors, and the computation times of the interpolation schemes were determined and compared.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
• /
• v.27 no.4
• /
• pp.411-420
• /
• 2009

To plan a GPS survey, they have to decide if a survey can be conducted at a specific point and time based on the predicted GPS ephemeris. In this study, to predict ephemeris, we used the repeat time of a GPS satellite. The GPS satellite repeat time was determined by analysing correlation among three-dimensional satellite coordinates provided by the 48-hour GPS ephemeris in the ultra-rapid orbits. By using the calculated repeat time and Lagrange interpolation polynomials, we predicted GPS orbits f3r seven days. As a result, the RMS of the maximum errors in the X, Y, and Z coordinates were 39.8 km 39.7 km and 19.6 km, respectively. And the maximum and average three-dimensional positional errors were 119.5 km and 48.9 km, respectively. When the maximum 3-D positioning error of 119.5 km was translated into the view angle error, the azimuth and elevation angle errors were 9.7'and 14.9', respectively.

• Structural Engineering and Mechanics
• /
• v.75 no.4
• /
• pp.519-527
• /
• 2020

Dynamic analysis of a vehicle-track coupling system is important to structural design, damage detection and condition assessment of the structural system. Deterministic analysis of the vehicle-track coupling system has been extensively studied in the past, however, the structural parameters of the coupling system have uncertainties in engineering practices. It is essential to treat the parameters of the vehicle-track coupling system with consideration of uncertainties. In this paper, a method for predicting the bounds of the vehicle-track coupling system responses with uncertain parameters is presented. The uncertain system parameters are modeled as fuzzy variables instead of conventional random variables with known probability distributions. Then, the dynamic response functions of the coupling system are transformed into a component function based on the high dimensional representation approximation. The Lagrange interpolation method is used to approximate the component function. Finally, the bounds of the system's dynamic responses can be predicted by using Monte Carlo method for the interpolation polynomials of the Lagrange interpolation function. A numerical example is introduced to illustrate the ability of the proposed method to predict the bounds of the system's dynamic responses, and the results are compared with the direct Monte Carlo method. The results show that the proposed method is effective and efficient to predict the bounds of the system's dynamic responses with fuzzy variables.

• Structural Engineering and Mechanics
• /
• v.23 no.3
• /
• pp.263-278
• /
• 2006

This work presents a time-truncation scheme, based on the Lagrange interpolation polynomial, for the solution of the two-dimensional scalar wave problem by the time-domain boundary element method. The aim is to reduce the number of stored matrices, due to the convolution integral performed from the initial time to the current time, and to keep a compromise between computational economy and efficiency and the numerical accuracy. In order to verify the accuracy of the proposed formulation, three examples are presented and discussed at the end of the article.

• Korean Journal of Hydrosciences
• /
• v.6
• /
• pp.51-66
• /
• 1995

Various Eulerian-Lagerangian numerical models for the one-dimensional longtudinal dispersion equation are studied comparatively. In the models studied, the transport equation is decoupled into two component parts by the operator-splitting approach ; one part governing advection and the other dispersion. The advection equation has been solved using the method of characteristics following flud particles along the characteristic line and the result are interpolated onto an Eulerian grid on which the dispersion equation is solved by Crank-Nicholson type finite difference method. In solving the advection equation, various interpolation schemes are tested. Among those, Hermite interpo;ation po;ynomials are superor to Lagrange interpolation polynomials in reducing both dissipation and dispersion errors.

• Journal of applied mathematics & informatics
• /
• v.34 no.3_4
• /
• pp.207-220
• /
• 2016

Our goal is to construct a two-frequency-dependent formula $I_N$ which interpolates a product f of two functions with different frequencies at some N points. In the beginning, it is not clear to us that the formula $I_N$ satisfies $I_N=f$ at the points. However, it is later shown that $I_N$ satisfies the above equation. For this theoretical development, a one-frequency-dependent formula is introduced, and some of its characteristics are explained. Finally, our newly constructed formula $I_N$ is compared to the classical Lagrange interpolating polynomial and the one-frequency-dependent formula in order to show the advantage that is obtained by generating the formula depending on two frequencies.