• The Pure and Applied Mathematics
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• v.17 no.4
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• pp.321-332
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• 2010

In this paper, we experiment image warping and morphing. In image warping, we use radial basis functions : Thin Plate Spline, Multi-quadratic and Gaussian. Then we obtain the fact that Thin Plate Spline interpolation of the displacement with reverse mapping is the efficient means of image warping. Reflecting the result of image warping, we generate two examples of image morphing.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.7
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• pp.205-215
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• 2013

In digital imaging system, Bayer pattern is widely used and the observed image is degraded by optical blur during image acquisition process. Generally, demosaicing and deblurring process are separately performed in order to convert a blurred Bayer image to a high resolution color image. However, the demosaicing process often generates visible artifacts such as zipper effect and Moire artifacts when performing interpolation across edge direction in Bayer pattern image. These artifacts are emphasized by the deblurring process. In order to solve this problem, this paper proposes a deblurring algorithm combined with edge directional color demosaicing method. The proposed method is consisted of interpolation step and region classification step. Interpolation and deblurring are simultaneously performed according to horizontal and vertical directions, respectively during the interpolation step. In the region classification step, characteristics of local regions are determined at each pixel position and the directionally obtained values are region adaptively fused. Also, the proposed method uses blur model based on wave optics and deblurring filter is calculated by using estimated characteristics of local regions. The simulation results show that the proposed deblurring algorithm prevents the boosting of artifacts and outperforms conventional approaches in both objective and subjective terms.

• Korean Journal of Agricultural and Forest Meteorology
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• v.2 no.4
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• pp.175-182
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• 2000

Spatial interpolation of daily temperature forecasts and observations issued by public weather services is frequently required to make them applicable to agricultural activities and modeling tasks. In contrast to the long term averages like monthly normals, terrain effects are not considered in most spatial interpolations for short term temperatures. This may cause erroneous results in mountainous regions where the observation network hardly covers full features of the complicated terrain. We developed a spatial interpolation model for daily minimum temperature which combines inverse distance squared weighting and elevation difference correction. This model uses a time dependent function for 'mountain slope lapse rate', which can be derived from regression analyses of the station observations with respect to the geographical and topographical features of the surroundings including the station elevation. We applied this model to interpolation of daily minimum temperature over the mountainous Korean Peninsula using 63 standard weather station data. For the first step, a primitive temperature surface was interpolated by inverse distance squared weighting of the 63 point data. Next, a virtual elevation surface was reconstructed by spatially interpolating the 63 station elevation data and subtracted from the elevation surface of a digital elevation model with 1 km grid spacing to obtain the elevation difference at each grid cell. Final estimates of daily minimum temperature at all the grid cells were obtained by applying the calculated daily lapse rate to the elevation difference and adjusting the inverse distance weighted estimates. Independent, measured data sets from 267 automated weather station locations were used to calculate the estimation errors on 12 dates, randomly selected one for each month in 1999. Analysis of 3 terms of estimation errors (mean error, mean absolute error, and root mean squared error) indicates a substantial improvement over the inverse distance squared weighting.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.435-453
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• 2008

In this paper, by using q-deformed bosonic p-adic integral, we give $\lambda$-Bernoulli numbers and polynomials, we prove Witt's type formula of $\lambda$-Bernoulli polynomials and Gauss multiplicative formula for $\lambda$-Bernoulli polynomials. By using derivative operator to the generating functions of $\lambda$-Bernoulli polynomials and generalized $\lambda$-Bernoulli numbers, we give Hurwitz type $\lambda$-zeta functions and Dirichlet's type $\lambda$-L-functions; which are interpolated $\lambda$-Bernoulli polynomials and generalized $\lambda$-Bernoulli numbers, respectively. We give generating function of $\lambda$-Bernoulli numbers with order r. By using Mellin transforms to their function, we prove relations between multiply zeta function and $\lambda$-Bernoulli polynomials and ordinary Bernoulli numbers of order r and $\lambda$-Bernoulli numbers, respectively. We also study on $\lambda$-Bernoulli numbers and polynomials in the space of locally constant. Moreover, we define $\lambda$-partial zeta function and interpolation function.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.2C
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• pp.238-246
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• 2004

In this paper, an estimator that take advantages of time and frequency correlation within an OFDM symbol is investigated. OFDM systems using the proposed estimator can be very effective in detecting signals under non-sampled space and time-varying channels. Also, under same complexity, the proposed estimator outperforms the previously proposed estimator. Since even if there are no assumption about channel correlation, the linear interpolation method instead of optimal interpolation using correct channel correlation is proposed in case the receiver does not know the channel correlation function in time domain. Therefore the proposed channel estimator help improving the performance of OFDM systems under non-sampled spaced and fast time-varying channels.

• Journal of the Korea Institute of Military Science and Technology
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• v.22 no.3
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• pp.311-319
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• 2019

This paper proposes an acceleration of the multi-level fast multipole algorithm(MLFMA) by using a double interpolation method. The MLFMA has been primarily used to conduct scattering analysis of electrically large targets, e.g. stealth aircraft. In the MLFMA, radiation functions of each basis functions are first precomputed, and then aggregated. After transfer calculations for the aggregations, each interaction is disaggregated, and then received in the testing function. The key idea of the proposed method is to decrease the sampling rates of the radiation and receiving functions. The computational complexity of the unit sphere integration in terms of the testing functions is thus highly alleviated. The remaining insufficient sampling rate is then complemented by using additional interpolation. We demonstrate the performance of the proposed method through radar cross-section(RCS) calculations for realistic aircraft.

• Journal of Auto-vehicle Safety Association
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• v.13 no.2
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• pp.35-41
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• 2021

In this study, improved path tracking control algorithm based on pure pursuit algorithm is newly proposed by using improved lane detection algorithm through real time post-processing with interpolation methodology. Since the original pure pursuit works well only at speeds below 20 km/h, the look-ahead distance is implemented as a sigmoid function to work well at an average speed of 45 km/h to improve tracking performance. In addition, a smoothing filter was added to reduce the steering angle vibration of the original algorithm, and the stability of the steering angle was improved. The post-processing algorithm presented has implemented more robust lane recognition system using real-time pre/post processing method with deep learning and estimated interpolation. Real time processing is more cost-effective than the method using lots of computing resources and building abundant datasets for improving the performance of deep learning networks. Therefore, this paper also presents improved lane detection performance by using the final results with naive computer vision codes and pre/post processing. Firstly, the pre-processing was newly designed for real-time processing and robust recognition performance of augmentation. Secondly, the post-processing was designed to detect lanes by receiving the segmentation results based on the estimated interpolation in consideration of the properties of the continuous lanes. Consequently, experimental results by utilizing driving guidance line information from processing parts show that the improved lane detection algorithm is effective to minimize the lateral offset error in the diverse maneuvering roads.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.35 no.12C
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• pp.1004-1009
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• 2010

ost digital cameras use single sensor array with color filter array to reduce size and cost. However images taken by single sensor array have only one color component per pixel, to obtain a color image missing two color components need to be reconstructed. This reconstructing process is called as demosaicking. This paper propose a new directional demosaicking method and proposed method achieves better image quality with enhanced weighting function. With comparing objective and subjective performance, we show proposed method achieves better performance than the conventional methods.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.1 s.178
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• pp.113-120
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• 2006

This paper proposed the control algorithm fur aspheric surface grinding and was verified by the experiment. The functions of the algorithm were simultaneous control of the position and interpolation of the aspheric curve. The non-linear formula of the tool position was derived from the aspheric equations and the shape of the tool. The function was partitioned by an certain interval and the control parameters were calculated at each control section. The movement in a session was interpolated with acceleration and velocity. The position error was feed-backed by rotary encorder. The concept of feedback algorithm was correcting position error by increasing or decreasing the speed. In the experiment, two-axis machine was controlled to track the aspheric surface by the proposed algorithm. The effect of the control and process parameters was monitored. The result showed that the maximum tracking error was under sub-micro level for the concave and convex surfaces.

• Structural Engineering and Mechanics
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• v.56 no.4
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• pp.589-603
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• 2015

The mixed-mode stress intensity factors of 2-D angled cracks are evaluated by Petrov-Galerkin natural element (PG-NE) method in which Voronoi polygon-based Laplace interpolation functions and CS-FE basis functions are used for the trial and test functions respectively. The interaction integral is implemented in a frame of PG-NE method in which the weighting function defined over a crack-tip integral domain is interpolated by Laplace interpolation functions. Two Cartesian coordinate systems are employed and the displacement, strains and stresses which are solved in the grid-oriented coordinate system are transformed to the other coordinate system aligned to the angled crack. The present method is validated through the numerical experiments with the angled edge and center cracks, and the numerical accuracy is examined with respect to the grid density, crack length and angle. Also, the stress intensity factors obtained by the present method are compared with other numerical methods and the exact solution. It is observed from the numerical results that the present method successfully and accurately evaluates the mixed-mode stress intensity factors of 2-D angled cracks for various crack lengths and crack angles.