Relevant bibliographies by topics / Cubic spline interpolation

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Cubic spline interpolation'

Author: Grafiati
Published: 4 June 2021
Last updated: 27 April 2022

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Journal articles on the topic "Cubic spline interpolation"

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Xu, Weizhi. "Elements of Bi-cubic Polynomial Natural Spline Interpolation for Scattered Data: Boundary Conditions Meet Partition of Unity Technique." Statistics, Optimization & Information Computing 8, no. 4 (December 2, 2020): 994–1010. http://dx.doi.org/10.19139/soic-2310-5070-1083.

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This paper investigates one kind of interpolation for scattered data by bi-cubic polynomial natural spline, in which the integral of square of partial derivative of two orders to x and to y for the interpolating function is minimal (with natural boundary conditions). Firstly, bi-cubic polynomial natural spline interpolations with four kinds of boundary conditions are studied. By the spline function methods of Hilbert space, their solutions are constructed as the sum of bi-linear polynomials and piecewise bi-cubic polynomials. Some properties of the solutions are also studied. In fact, bi-cubic natural spline interpolation on a rectangular domain is a generalization of the cubic natural spline interpolation on an interval. Secondly, based on bi-cubic polynomial natural spline interpolations of four kinds of boundary conditions, and using partition of unity technique, a Partition of Unity Interpolation Element Method (PUIEM) for fitting scattered data is proposed. Numerical experiments show that the PUIEM is adaptive and outperforms state-of-the-art competitions, such as the thin plate spline interpolation and the bi-cubic polynomial natural spline interpolations for scattered data.
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Xie, Jin, and Xiaoyan Liu. "The EH Interpolation Spline and Its Approximation." Abstract and Applied Analysis 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/745765.

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A new interpolation spline with two parameters, called EH interpolation spline, is presented in this paper, which is the extension of the standard cubic Hermite interpolation spline, and inherits the same properties of the standard cubic Hermite interpolation spline. Given the fixed interpolation conditions, the shape of the proposed splines can be adjusted by changing the values of the parameters. Also, the introduced spline could approximate to the interpolated function better than the standard cubic Hermite interpolation spline and the quartic Hermite interpolation splines with single parameter by a new algorithm.
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Abdul Karim, Samsul Ariffin, and Kong Voon Pang. "Shape Preserving Interpolation UsingC2Rational Cubic Spline." Journal of Applied Mathematics 2016 (2016): 1–14. http://dx.doi.org/10.1155/2016/4875358.

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This paper discusses the construction of newC2rational cubic spline interpolant with cubic numerator and quadratic denominator. The idea has been extended to shape preserving interpolation for positive data using the constructed rational cubic spline interpolation. The rational cubic spline has three parametersαi,βi, andγi. The sufficient conditions for the positivity are derived on one parameterγiwhile the other two parametersαiandβiare free parameters that can be used to change the final shape of the resulting interpolating curves. This will enable the user to produce many varieties of the positive interpolating curves. Cubic spline interpolation withC2continuity is not able to preserve the shape of the positive data. Notably our scheme is easy to use and does not require knots insertion andC2continuity can be achieved by solving tridiagonal systems of linear equations for the unknown first derivativesdi,i=1,…,n-1. Comparisons with existing schemes also have been done in detail. From all presented numerical results the newC2rational cubic spline gives very smooth interpolating curves compared to some established rational cubic schemes. An error analysis when the function to be interpolated isft∈C3t0,tnis also investigated in detail.
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Kumar, Arun, and L. K. Govil. "Interpolation of natural cubic spline." International Journal of Mathematics and Mathematical Sciences 15, no. 2 (1992): 229–34. http://dx.doi.org/10.1155/s0161171292000292.

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From the result in [1] it follows that there is a unique quadratic spline which bounds the same area as that of the function. The matching of the area for the cubic spline does not follow from the corresponding result proved in [2]. We obtain cubic splines which preserve the area of the function.
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Rana, S. S., and M. Purohit. "Deficient cubic spline interpolation." Proceedings of the Japan Academy, Series A, Mathematical Sciences 64, no. 4 (1988): 111–14. http://dx.doi.org/10.3792/pjaa.64.111.

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Dyer, S. A., and J. S. Dyer. "Cubic-spline interpolation. 1." IEEE Instrumentation & Measurement Magazine 4, no. 1 (March 2001): 44–46. http://dx.doi.org/10.1109/5289.911175.

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Kim, Jung-Min, Eun-Kook Jung, and Sun-Shin Kim. "Simplification of Face Image using Cubic Spline Interpolation." Journal of Korean Institute of Intelligent Systems 20, no. 5 (October 25, 2010): 722–27. http://dx.doi.org/10.5391/jkiis.2010.20.5.722.

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Azizan, Irham, Samsul Ariffin Bin Abdul Karim, and S. Suresh Kumar Raju. "Fitting Rainfall Data by Using Cubic Spline Interpolation." MATEC Web of Conferences 225 (2018): 05001. http://dx.doi.org/10.1051/matecconf/201822505001.

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This study discusses the application of two cubic spline i.e. natural and not-a-knot end boundary conditions to visualize and predict the rainfall data. The interpolation and the analysis of the rainfall data will be done on a monthly basis by using the MATLAB software. The rainfall data is obtained from Malaysia Meteorology Department for Ipoh and Petaling Jaya in year 2014 and 2015. The interpolating curves are then being compared and if there is any negative value on the interpolating curve on some sub-interval, that part will be replaced by using the Piecewise Cubic Hermite Interpolating Polynomial (PCHIP). We discuss the missing data imputation by using both splines.
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Li, Jie, Yaoyao Tu, and Shilong Fei. "C˜2 Continuous Cubic Hermite Interpolation Splines with Second-Order Elliptic Variation." Tobacco Regulatory Science 7, no. 6 (November 3, 2021): 6317–31. http://dx.doi.org/10.18001/trs.7.6.106.

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In order to solve the deficiency of Hermite interpolation spline with second-order elliptic variation in shape control and continuity, c-2 continuous cubic Hermite interpolation spline with second-order elliptic variation was designed. A set of cubic Hermite basis functions with two parameters was constructed. According to this set of basis functions, the three-order Hermite interpolation spline curves were defined in segments 02, and the parameter selection scheme was discussed. The corresponding cubic Hermite interpolation spline function was studied, and the method to determine the residual term and the best interpolation function was given. The results of an example show that when the interpolation conditions remain unchanged, the cubic Hermite interpolation spline curves not only reach 02 continuity, but also can use the parameters to control the shape of the curves locally or globally. By determining the best values of the parameters, the cubic Hermite interpolation spline function can get a better interpolation effect, and the smoothness of the interpolation spline curve is the best.
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Karim, Samsul Ariffin Bin Abdul, and S. Suresh Kumar Raju. "Wind Velocity Data Interpolation Using Rational Cubic Spline." MATEC Web of Conferences 225 (2018): 04006. http://dx.doi.org/10.1051/matecconf/201822504006.

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Wind velocity data is always having positive value and the minimum value approximately close to zero. The standard cubic spline interpolation (not-a-knot and natural) as well as cubic Hermite polynomial may be produces interpolating curve with negative values on some subintervals. To cater this problem, a new rational cubic spline with three parameters is constructed. This rational spline will be used to preserve the positivity of the wind velocity data. Numerical results shows that the proposed scheme work very well and give visually pleasing interpolating curve on the given domain.
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Dissertations / Theses on the topic "Cubic spline interpolation"

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Kaya, Hikmet Emre. "A comparative study between the cubic spline and b-spline interpolation methods in free energy calculations." Master's thesis, Faculty of Science, 2020. http://hdl.handle.net/11427/32228.

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Numerical methods are essential in computational science, as analytic calculations for large datasets are impractical. Using numerical methods, one can approximate the problem to solve it with basic arithmetic operations. Interpolation is a commonly-used method, inter alia, constructing the value of new data points within an interval of known data points. Furthermore, polynomial interpolation with a sufficiently high degree can make the data set differentiable. One consequence of using high-degree polynomials is the oscillatory behaviour towards the endpoints, also known as Runge's Phenomenon. Spline interpolation overcomes this obstacle by connecting the data points in a piecewise fashion. However, its complex formulation requires nested iterations in higher dimensions, which is time-consuming. In addition, the calculations have to be repeated for computing each partial derivative at the data point, leading to further slowdown. The B-spline interpolation is an alternative representation of the cubic spline method, where a spline interpolation at a point could be expressed as the linear combination of piecewise basis functions. It was proposed that implementing this new formulation can accelerate many scientific computing operations involving interpolation. Nevertheless, there is a lack of detailed comparison to back up this hypothesis, especially when it comes to computing the partial derivatives. Among many scientific research fields, free energy calculations particularly stand out for their use of interpolation methods. Numerical interpolation was implemented in free energy methods for many purposes, from calculating intermediate energy states to deriving forces from free energy surfaces. The results of these calculations can provide insight into reaction mechanisms and their thermodynamic properties. The free energy methods include biased flat histogram methods, which are especially promising due to their ability to accurately construct free energy profiles at the rarely-visited regions of reaction spaces. Free Energies from Adaptive Reaction Coordinates (FEARCF) that was developed by Professor Kevin J. Naidoo has many advantages over the other flat histogram methods. iii Because of its treatment of the atoms in reactions, FEARCF makes it easier to apply interpolation methods. It implements cubic spline interpolation to derive biasing forces from the free energy surface, driving the reaction towards regions with higher energy. A major drawback of the method is the slowdown experienced in higher dimensions due to the complicated nature of the cubic spline routine. If the routine is replaced by a more straightforward B-spline interpolation, sampling and generating free energy surfaces can be accelerated. The dissertation aims to perform a comparative study between the cubic spline interpolation and B-spline interpolation methods. At first, data sets of analytic functions were used instead of numerical data to compare the accuracy and compute the percentage errors of both methods by taking the functions themselves as reference. These functions were used to evaluate the performances of the two methods at the endpoints, inflections points and regions with a steep gradient. Both interpolation methods generated identically approximated values with a percentage error below the threshold of 1%, although they both performed poorly at the endpoints and the points of inflection. Increasing the number of interpolation knots reduced the errors, however, it caused overfitting in the other regions. Although significant speed-up was not observed in the univariate interpolation, cubic spline suffered from a drastic slowdown in higher dimensions with up to 103 in 3D and 105 in 4D interpolations. The same results applied to the classical molecular dynamics simulations with FEARCF with a speed-up of up to 103 when B-spline interpolation was implemented. To conclude, the B-spline interpolation method can enhance the efficiency of the free energy calculations where cubic spline interpolation has been the currently-used method.
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Fantoni, Anna. "Long-period oscillations in GPS Up time series. Study over the European/Mediterranean area." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2022. http://amslaurea.unibo.it/25586/.

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The surface of the Earth is subjected to vertical deformations caused by geophysical and geological processes which can be monitored by Global Positioning System (GPS) observations. The purpose of this work is to investigate GPS height time series to identify interannual signals affecting the Earth’s surface over the European and Mediterranean area, during the period 2001-2019. Thirty-six homogeneously distributed GPS stations were selected from the online dataset made available by the Nevada Geodetic Laboratory (NGL) on the basis of the length and quality of the data series. The Principal Component Analysis (PCA) is the technique applied to extract the main patterns of the space and time variability of the GPS Up coordinate. The time series were studied by means of a frequency analysis using a periodogram and the real-valued Morlet wavelet. The periodogram is used to identify the dominant frequencies and the spectral density of the investigated signals; the second one is applied to identify the signals in the time domain and the relevant periodicities. This study has identified, over European and Mediterranean area, the presence of interannual non-linear signals with a period of 2-to-4 years, possibly related to atmospheric and hydrological loading displacements and to climate phenomena, such as El Niño Southern Oscillation (ENSO). A clear signal with a period of about six years is present in the vertical component of the GPS time series, likely explainable by the gravitational coupling between the Earth’s mantle and the inner core. Moreover, signals with a period in the order of 8-9 years, might be explained by mantle-inner core gravity coupling and the cycle of the lunar perigee, and a signal of 18.6 years, likely associated to lunar nodal cycle, were identified through the wavelet spectrum. However, these last two signals need further confirmation because the present length of the GPS time series is still too short when compared to the periods involved.
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Subramanian, Harshavardhan. "Combining scientific computing and machine learning techniques to model longitudinal outcomes in clinical trials." Thesis, Linköpings universitet, Institutionen för datavetenskap, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-176427.

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Scientific machine learning (SciML) is a new branch of AI research at the edge of scientific computing (Sci) and machine learning (ML). It deals with efficient amalgamation of data-driven algorithms along with scientific computing to discover the dynamics of the time-evolving process. The output of such algorithms is represented in the form of a governing equation(s) (e.g., ordinary differential equation(s), ODE(s)), which one can solve then for any time point and, thus, obtain a rigorous prediction.  In this thesis, we present a methodology on how to incorporate the SciML approach in the context of clinical trials to predict IPF disease progression in the form of governing equation. Our proposed methodology also quantifies the uncertainties associated with the model by fitting 95\% high density interval (HDI) for the ODE parameters and 95\% posterior prediction interval for posterior predicted samples. We have also investigated the possibility of predicting later outcomes by using the observations collected at early phase of the study. We were successful in combining ML techniques, statistical methodologies and scientific computing tools such as bootstrap sampling, cubic spline interpolation, Bayesian inference and sparse identification of nonlinear dynamics (SINDy) to discover the dynamics behind the efficacy outcome as well as in quantifying the uncertainty of the parameters of the governing equation in the form of 95 \% HDI intervals. We compared the resulting model with the existed disease progression model described by the Weibull function. Based on the mean squared error (MSE) criterion between our ODE approximated values and population means of respective datasets, we achieved the least possible MSE of 0.133,0.089,0.213 and 0.057. After comparing these MSE values with the MSE values obtained after using Weibull function, for the third dataset and pooled dataset, our ODE model performed better in reducing error than the Weibull baseline model by 7.5\% and 8.1\%, respectively. Whereas for the first and second datasets, the Weibull model performed better in reducing errors by 1.5\% and 1.2\%, respectively. Comparing the overall performance in terms of MSE, our proposed model approximates the population means better in all the cases except for the first and second datasets, assuming the latter case's error margin is very small. Also, in terms of interpretation, our dynamical system model contains the mechanistic elements that can explain the decay/acceleration rate of the efficacy endpoint, which is missing in the Weibull model. However, our approach had a limitation in predicting final outcomes using a model derived from  24, 36, 48 weeks observations with good accuracy where as on the contrast, the Weibull model do not possess the predicting capability. However, the extrapolated trend based on 60 weeks of data was found to be close to population mean and the ODE model built on 72 weeks of data. Finally we highlight potential questions for the future work.
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Al-alam, Wagner Guimarães. "SisA3 : Sistema Automatizado de Auditoria de Armaz´ens de Gran´eis." Universidade Catolica de Pelotas, 2010. http://tede.ucpel.edu.br:8080/jspui/handle/tede/113.

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Made available in DSpace on 2016-03-22T17:26:24Z (GMT). No. of bitstreams: 1 Wagner Guimaraes Al-Alam.pdf: 2995290 bytes, checksum: 9902eafe02c0b5318a99f1e796dc399f (MD5) Previous issue date: 2010-01-15
Companies working with bulk materials have appropriate locations for storage during the development of the production and storage of the final product, known as warehouses or storehouses. The values of stocks need to be periodically validated by comparing the control of receipts the and the physical situation (removal of the volume stored in the company). In this context, the calculation of physical inventory as the volume of bulk present in the warehouses is usually done manually with low credibility and prone to errors. The current audit procedures on the contents of warehouses involve inaccurate estimates, and often require emptying the warehouse. Considering the use of technologies which enable the electronic measurement of distances, angles, and automatic controls on actuators enabling mechanical movements on the supporting structures, we sought to develop a system capable of providing both computing solutions, and technology for the problem of calculation of irregular relief (products stocked in warehouses). The Automated Auditing Warehouse SisA3 intends to make this process automatic, fast and precise, without the need for emptying warehouses or having contact the products. To achieve this goal, we developed an integrated system composed of: (i) a scanner equipment, consoling the hybrid prototype of hardware and software called DigSisA3, in order to the measurement of points of relief non-uniform, formed by the products in stock, and (ii) a method for calculating the volume iCone, which combines techniques of scientific visualization, numerical interpolation points and iterative calculation of volume. The parallelization of the prototype iCone was also developed in order to satisfy the test of agility and performance of the method iCone in the audit process. The development for multiprocessor, multi-core, and distributed architectures was done over the DGM (Geometric Distributed Machine), which provides the formalities to ensure creation, management and application processing parallel and / or distributed scientific computing, with emphasis on the exploitation of data parallelism and synchronization steps. The prototype of software iCone was functionally validated, including analysis of error in the method. The analysis of performance in the prototype p-iCone showed satisfactory results. The development of this work strengthens the system SisA3, enabling automatic and reliable measurement of inventories, including broad market application
Empresas que trabalham com produtos a granel possuem locais para estocagem, durante o desenvolvimento do processo produtivo e no armazenamento do produto final, denominados armaz´ens ou silos. Os valores dos estoques devem ser validados periodicamente atrav´es da comparac¸ ao dos estoques fiscal (controle das notas fiscais) e f´ısico (levantamento do volume estocado na empresa). Neste contexto, o c´alculo do estoque f´ısico, ou seja, o volume de gran´eis presentes nos armaz´ens, ´e geralmente efetuado de forma manual e com baixa credibilidade, desta forma com propens ao a erros. Os atuais processos de auditoria no conte´udo de silos, al´em de envolverem estimativas inexatas, est ao frequentemente baseados no esvaziamento do silo. Considerando o uso de tecnologias que viabilizam a medic¸ ao eletr onica de dist ancias, angulos, e controles autom´aticos sobre atuadores que possibilitam movimentos mec anicos sobre estruturas de suporte, buscou-se o desenvolvimento de um sistema capaz de prover tanto soluc¸ oes computacionais, quanto tecnol´ogicas para o problema de c´alculo do volume de relevos irregulares, no caso dos produtos estocados nos armaz´ens. O Sistema Automatizado de Auditoria em Armaz´ens (SisA3) pretende tornar este processo autom´atico, r´apido e preciso, sem a necessidade de esvaziamento ou contato com os produtos. Para alcanc¸ar este objetivo, tem-se um sistema integrado composto de: (i) um equipamento digitalizador, consolidando o prot´otipo h´ıbrido de hardware e software denominado Dig-SisA3 , para a medic¸ ao de pontos do relevo n ao-uniforme, formado pelos produtos estocados; e (ii) m´etodo para o c´alculo do volume (iCone), que combina t´ecnicas de visualizac¸ ao cient´ıfica, interpolac¸ ao num´erica de pontos e c´alculo iterativo de volume. Al´em disto, introduz-se a paralelizac¸ ao do prot´otipo iCone, para diminuir o tempo da obtenc¸ ao dos resultados do m´etodo iCone no processo de auditoria. A an´alise sobre as perspectivas em arquiteturas multiprocessadas, multi-core e paralela distribu´ıda, utiliza o ambiente D-GM (Distributed Geometric Machine), a qual prov e os formalismos para garantir criac¸ ao, gerenciamento e processamento de aplicac¸ oes paralelas e/ou distribu´ıdas da computac¸ ao cient´ıfica, com enfase na explorac¸ ao do paralelismo de dados e nas etapas de sincronizac¸ oes. O prot´otipo de software iCone apresenta-se funcionalmente validado, incluindo an´alise de erro na execuc¸ ao do m´etodo. As an´alises de desempenho no prot´otipo p-iCone apresentaram resultados satisfat´orios. O desenvolvimento deste trabalho consolida o sistema SisA3, viabilizando aferic¸ ao autom´atica e confi´avel de estoques, incluindo ampla aplicac¸ ao no mercado
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Soares, M. J. "A posteriori corrections for cubic and quintic interpolating splines with applications to the solution of two-point boundary value problems." Thesis, Brunel University, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.373087.

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Malina, Jakub. "Vytvoření interaktivních pomůcek z oblasti 2D počítačové grafiky." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2013. http://www.nusl.cz/ntk/nusl-219924.

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In this master’s thesis we focus on the basic properties of computer curves and their practical applicability. We explain how the curve can be understood in general, what are polynomial curves and their composing possibilities. Then we focus on the description of Bezier curves, especially the Bezier cubic. We discuss in more detail some of fundamental algorithms that are used for modelling these curves on computers and then we will show their practical interpretation. Then we explain non uniform rational B-spline curves and De Boor algorithm. In the end we discuss topic rasterization of segment, thick line, circle and ellipse. The aim of master’s thesis is the creation of the set of interactive applets, simulating some of the methods and algorithm we discussed in theoretical part. This applets will help facilitate understanding and will make the teaching more effective.
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Wang, Lung-Jen, and 王隆仁. "A Fast Cubic-Spline Interpolation and Its Applications." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/23129972138898368567.

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博士
國立中山大學
資訊工程學系研究所
89
In this dissertation, a new cubic-spline interpolation (CSI) for both one-dimensional and two-dimensional signals is developed to sub-sample signal, image and video compression data. This new interpolation scheme that is based on the least-squares method with a cubic-spline function can be implemented by the fast Fourier transform (FFT). The result is a simpler and faster interpolation scheme than can be obtained by other conventional means. It is shown by computer simulation that such a new CSI yields a very accurate algorithm for smoothing. Linear interpolation, linear-spline interpolation, cubic-convolution interpolation and cubic B-spline interpolation tend to be inferior in performance. In addition it is shown in this dissertation that the CSI scheme can be performed by a fast and efficient computation. The proposed method uses a simpler technique in the decimation process. It requires substantially fewer additions and multiplications than the original CSI algorithm. Moreover, a new type of overlap-save scheme is utilized to solve the boundary-condition problems that occur between two neighboring subimages in the actual image. It is also shown in this dissertation that a very efficient 9-point Winograd discrete Fourier transform (Winograd DFT) can be used to replace the FFT needed to implement the CSI scheme. Furthermore, the proposed fast new CSI scheme is used along with the Joint Photographic Experts Group (JPEG) standard to design a modified JPEG encoder- decoder for image data compression. As a consequence, for higher compression ratios the proposed modified JPEG encoder-decoder obtains a better quality of reconstructed image and also requires less computational time than both the conventional JPEG method and the America on Line (AOL) algorithm. Finally, the new fast CSI scheme is applied to the JPEG 2000, MPEG-1 and MPEG-2 algorithms, respectively. A computer simulation shows that in the encoding and decoding, the proposed modified JPEG 2000 encoder-decoder speeds up the JPEG 2000 standard, respectively, and still obtains a good quality of reconstructed image that is similar to JPEG 2000 standard for high compression ratios. Additionally, the reconstructed video using the modified MPEG encoder-decoder indicates a better quality than the conventional MPEG-1 and MPEG-2 algorithms for high compression ratios or low-bit rates.
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Tang, Ying-Lun, and 唐英倫. "A Study on Image Enhancement by Cubic-Spline Interpolation." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/53963800635618396623.

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碩士
國立屏東商業技術學院
資訊管理系
95
With the digital image processing technology growing up, the applications in this domain such as high definition television (HDTV) and video-phone, have already gone deep in our life. When the digital image enlargement, it causes a blur problem. To improve the quality of the blurred image, many digital image processing approaches have been developed. Image enhancement is an indispensable post-processing method. Among many image enhancement approaches, Nonlinear Image Enhancement method is not only a simple structure but also has better effect, this method uses a Low-Pass Filter with an image enhancement scheme to improve the blurred image. Cubic-Spline Interpolation (CSI) has been proposed based on the Least-Squares method with a Cubic-Spline function for the smoothing of image data. In this paper, it is shown that this CSI can be used to improve the nonlinear image enhancement method. In addition, the two important parameters c (Clipping) and s (Scaling) are discussed in the Nonlinear Image Enhancement scheme to improve the blurred image problem. Finally, experimental results show that the proposed method yields a better quality of the reconstructed image than other nonlinear enhancement methods.
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Chang, Tsai-Yen, and 張綵晏. "Information Hiding in Audio Using Cubic Spline Interpolation Technique." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/59058900260553750724.

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碩士
玄奘大學
資訊管理學系碩士班
98
Audio information hiding methods are widely discussed during this few years. WAVE or WAV is one of the most popular sound storage standard formats. In this thesis we use the spline interpolation technique to embed the secret data in the wave form of the original audio data. We set the control points, such as the odd number points to rebuild the spline curve to fit the original curve. We use the different between original and spline curve to embed the secret data to be a stego-audio. The extracting steps are simply to use the unchanged control points to compute the spline curve then find the different between spline curve and the stego-audio, to obtain the embedded secret data. The experiments show the sound is inaudible to be distinguished between stego-audio and original audio.
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Liu, Pin-hsiu, and 劉品秀. "Curve Design by C2 Cubic B-spline Curve''s Interpolation." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/62783732709493433975.

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碩士
國立中正大學
應用數學研究所
97
In there, we persent B-spline curves and C2 cubic B-spline interpolating curves. Next, we do curve design by C2 cubic B-spline interpolating curves to cover irregular shapes.
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Books on the topic "Cubic spline interpolation"

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Knott, Gary D. Interpolating Cubic Splines. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1320-8.

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Papamichael, Nicholas. An O(h6) cubic spline interpolating procedure for harmonic functions. Uxbridge, Middx: Department of Mathematics and Statistics, Brunel University, 1989.

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Soares, Maria Joana. A posteriori corrections for cubic and quintic interpolating splines with applications to the solution of two-point boundary value problems. Uxbridge: Brunel University, 1986.

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Interpolating Cubic Splines (Progress in Computer Science and Applied Logic (PCS)). Birkhäuser Boston, 1999.

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Boudreau, Joseph F., and Eric S. Swanson. Interpolation and extrapolation. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198708636.003.0004.

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This chapter deals with two related problems occurring frequently in the physical sciences: first, the problem of estimating the value of a function from a limited number of data points; and second, the problem of calculating its value from a series approximation. Numerical methods for interpolating and extrapolating data are presented. The famous Lagrange interpolating polynomial is introduced and applied to one-dimensional and multidimensional problems. Cubic spline interpolation is introduced and an implementation in terms of Eigen classes is given. Several techniques for improving the convergence of Taylor series are discussed, including Shank’s transformation, Richardson extrapolation, and the use of Padé approximants. Conversion between representations with the quotient-difference algorithm is discussed. The exercises explore public transportation, human vision, the wine market, and SU(2) lattice gauge theory, among other topics.
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Interpolating Cubic Splines. Birkhäuser, 2014.

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Knott, Gary D. Interpolating Cubic Splines. Birkhäuser, 2012.

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Interpolating Cubic Splines (Systems & Control). Birkhauser, 2000.

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Ford, Natalie. An example of the use of cubic B-splines for interpolation and structural analysis. 1996.

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Book chapters on the topic "Cubic spline interpolation"

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Sablonnière, P., D. Sbibih, and M. Tahrichi. "Chordal Cubic Spline Quasi Interpolation." In Curves and Surfaces, 603–11. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-27413-8_40.

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Wang, Zhijiang, Kaili Wang, and Shujiang An. "Cubic B-Spline Interpolation and Realization." In Communications in Computer and Information Science, 82–89. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-27503-6_12.

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Schmidt, Jochen W. "On the Convex Cubic C2-Spline Interpolation." In Numerical Methods of Approximation Theory/Numerische Methoden der Approximationstheorie, 213–28. Basel: Birkhäuser Basel, 1987. http://dx.doi.org/10.1007/978-3-0348-6656-9_19.

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Scardapane, Simone, Michele Scarpiniti, Danilo Comminiello, and Aurelio Uncini. "Learning Activation Functions from Data Using Cubic Spline Interpolation." In Neural Advances in Processing Nonlinear Dynamic Signals, 73–83. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-95098-3_7.

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Truong, T. K., and Lung-Jen Wang. "Medical Image Data Compression Using Cubic Convolution Spline Interpolation." In Central Auditory Processing and Neural Modeling, 175–88. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4615-5351-9_16.

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Yan, Tianfeng, and Yu Zhang. "TDOA Time Delay Estimation Algorithm Based on Cubic Spline Interpolation." In Advances in Intelligent Systems and Computing, 154–62. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-14680-1_18.

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Bellavia, Fabio, and Carlo Colombo. "Color Correction for Image Stitching by Monotone Cubic Spline Interpolation." In Pattern Recognition and Image Analysis, 165–72. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19390-8_19.

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de Boor, Carl. "Best Approximation Properties of Complete Cubic Spline Interpolation and Its Error." In Applied Mathematical Sciences, 51–58. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4612-6333-3_5.

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Ma, Lan, Shan Tian, Yang Song, Zhijun Wu, and Meng Yue. "An Approach of ACARS Trajectory Reconstruction Based on Adaptive Cubic Spline Interpolation." In Security, Privacy, and Anonymity in Computation, Communication, and Storage, 245–52. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-24900-7_20.

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Sablonnière, P. "Gradient Approximation on Uniform Meshes by Finite Differences and Cubic Spline Interpolation." In Mathematics of Surfaces XIII, 322–34. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-03596-8_19.

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Conference papers on the topic "Cubic spline interpolation"

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Wolber and Alfy. "Monotonic cubic spline interpolation." In Proceedings Computer Graphics International CGI-99. IEEE, 1999. http://dx.doi.org/10.1109/cgi.1999.777953.

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Chand, A. K. B., and P. Viswanathan. "Cubic hermite and cubic spline fractal interpolation functions." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756439.

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Li, Zhiwei, Min Zhang, and Jiechao Wang. "Improved cubic spline interpolation based on LAZ." In 2010 10th International Conference on Signal Processing (ICSP 2010). IEEE, 2010. http://dx.doi.org/10.1109/icosp.2010.5655895.

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Bharati, Nilashma, Arun Khosla, and Neetu Sood. "Image reconstruction using cubic B-Spline interpolation." In 2011 Annual IEEE India Conference (INDICON). IEEE, 2011. http://dx.doi.org/10.1109/indcon.2011.6139378.

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Meng Tian. "A shape preserving rational cubic interpolation spline." In 2010 2nd International Conference on Information Science and Engineering (ICISE). IEEE, 2010. http://dx.doi.org/10.1109/icise.2010.5689166.

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Li, J. S. Jimmy, and Sharmil Randhawa. "Colour Filter Array Demosaicking using Cubic Spline Interpolation." In 2007 IEEE International Conference on Acoustics, Speech, and Signal Processing. IEEE, 2007. http://dx.doi.org/10.1109/icassp.2007.366045.

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Sun, Ningping, Toru Ayabe, and Kentarou Okumura. "An Animation Engine with the Cubic Spline Interpolation." In 2008 Fourth International Conference on Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP). IEEE, 2008. http://dx.doi.org/10.1109/iih-msp.2008.321.

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Jiang, JianXing, Shao-Hua Hong, Tsung-Ching Lin, Lin Wang, and Trieu-Kien Truong. "Adaptive image coding based on cubic-spline interpolation." In SPIE Optical Engineering + Applications, edited by Andrew G. Tescher. SPIE, 2014. http://dx.doi.org/10.1117/12.2062984.

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Tian, Meng, and Qiuju Bian. "A Rational Cubic Spline Interpolation and Its Application." In 2010 International Conference on Digital Manufacturing and Automation (ICDMA). IEEE, 2010. http://dx.doi.org/10.1109/icdma.2010.90.

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Hong, Shao-Hua, Lin Wang, and Trieu-Kien Truong. "An Improved Approach to the Cubic-Spline Interpolation." In 2018 25th IEEE International Conference on Image Processing (ICIP). IEEE, 2018. http://dx.doi.org/10.1109/icip.2018.8451362.

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