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Relevant bibliographies by topics / Free Knot Spline

Academic literature on the topic 'Free Knot Spline'

Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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Dissertations / Theses
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Journal articles on the topic "Free Knot Spline"

1

Gervini, Daniel. "Free-knot spline smoothing for functional data." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 68, no. 4 (September 2006): 671–87. http://dx.doi.org/10.1111/j.1467-9868.2006.00561.x.

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Wang, Xiao. "Bayesian Free-Knot Monotone Cubic Spline Regression." Journal of Computational and Graphical Statistics 17, no. 2 (June 2008): 373–87. http://dx.doi.org/10.1198/106186008x321077.

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Creutzig, Jakob, Thomas Müller-Gronbach, and Klaus Ritter. "Free-knot spline approximation of stochastic processes." Journal of Complexity 23, no. 4-6 (August 2007): 867–89. http://dx.doi.org/10.1016/j.jco.2007.05.003.

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Ciarlini, Patrizia, and Daniela Ichim. "Free-knot cubic spline modelling in cryogenic thermometer calibration." Measurement 39, no. 9 (November 2006): 815–20. http://dx.doi.org/10.1016/j.measurement.2006.04.006.

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Bittner, Kai, and Hans Georg Brachtendorf. "Fast Algorithms for Adaptive Free Knot Spline Approximation Using Nonuniform Biorthogonal Spline Wavelets." SIAM Journal on Scientific Computing 37, no. 2 (January 2015): B283—B304. http://dx.doi.org/10.1137/14095354x.

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MAMIC, G., and M. BENNAMOUN. "AUTOMATED SPLINE SURFACE MODELING AND MATCHING FOR RECOGNITION OF FREE-FORM OBJECTS." International Journal of Image and Graphics 04, no. 01 (January 2004): 51–84. http://dx.doi.org/10.1142/s0219467804001294.

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Surface representations are utilized in a multitude of applications such as computer vision, medical imaging and computer graphics. B-spline surfaces have a number of desirable properties for representing surfaces, however, the complexity of knot placement strategies has prevented their widespread use in high-level vision environments. A solution to this problem is formulated within the reversible jump Markov chain Monte Carlo framework, whereby a derived posterior distribution may be sampled to calculate expected values for the number of knots required, their expected positions and a maximum likelihood estimate for the resulting control net of a given surface. Recognition of individual models may then be achieved using a hash table constructed using the principal components of the model control nets. Results of the fitting procedure, in terms of estimated knot vectors and spline surface errors, and the recognition of objects are provided for a set of free-form objects.

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Wang, Xin, Guo Wei, and Jinwei Sun. "Free knot recursive B-spline for compensation of nonlinear smart sensors." Measurement 44, no. 5 (June 2011): 888–94. http://dx.doi.org/10.1016/j.measurement.2011.02.009.

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Slassi, Mehdi. "A Milstein-based free knot spline approximation for stochastic differential equations." Journal of Complexity 28, no. 1 (February 2012): 37–47. http://dx.doi.org/10.1016/j.jco.2011.03.005.

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9

Kawasaki, H. "A Second-Order Property of Spline Functions with One Free Knot." Journal of Approximation Theory 78, no. 2 (August 1994): 293–97. http://dx.doi.org/10.1006/jath.1994.1079.

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Slassi, Mehdi. "The optimal free knot spline approximation of stochastic differential equations with additive noise." Journal of Computational and Applied Mathematics 261 (May 2014): 62–71. http://dx.doi.org/10.1016/j.cam.2013.09.034.

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Dissertations / Theses on the topic "Free Knot Spline"

1

Miyata, Satoshi. "Adaptive free-knot splines and inference /." The Ohio State University, 2001. http://rave.ohiolink.edu/etdc/view?acc_num=osu1486399451962014.

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Merleau, James. "Modélisation bayésienne avec des splines du comportement moyen d'un échantillon de courbes." Thèse, 2009. http://hdl.handle.net/1866/12816.

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Cette thèse porte sur l'analyse bayésienne de données fonctionnelles dans un contexte hydrologique. L'objectif principal est de modéliser des données d'écoulements d'eau d'une manière parcimonieuse tout en reproduisant adéquatement les caractéristiques statistiques de celles-ci. L'analyse de données fonctionnelles nous amène à considérer les séries chronologiques d'écoulements d'eau comme des fonctions à modéliser avec une méthode non paramétrique. Dans un premier temps, les fonctions sont rendues plus homogènes en les synchronisant. Ensuite, disposant d'un échantillon de courbes homogènes, nous procédons à la modélisation de leurs caractéristiques statistiques en faisant appel aux splines de régression bayésiennes dans un cadre probabiliste assez général. Plus spécifiquement, nous étudions une famille de distributions continues, qui inclut celles de la famille exponentielle, de laquelle les observations peuvent provenir. De plus, afin d'avoir un outil de modélisation non paramétrique flexible, nous traitons les noeuds intérieurs, qui définissent les éléments de la base des splines de régression, comme des quantités aléatoires. Nous utilisons alors le MCMC avec sauts réversibles afin d'explorer la distribution a posteriori des noeuds intérieurs. Afin de simplifier cette procédure dans notre contexte général de modélisation, nous considérons des approximations de la distribution marginale des observations, nommément une approximation basée sur le critère d'information de Schwarz et une autre qui fait appel à l'approximation de Laplace. En plus de modéliser la tendance centrale d'un échantillon de courbes, nous proposons aussi une méthodologie pour modéliser simultanément la tendance centrale et la dispersion de ces courbes, et ce dans notre cadre probabiliste général. Finalement, puisque nous étudions une diversité de distributions statistiques au niveau des observations, nous mettons de l'avant une approche afin de déterminer les distributions les plus adéquates pour un échantillon de courbes donné.
This thesis is about Bayesian functional data analysis in hydrology. The main objective is to model water flow data in a parsimonious fashion while still reproducing the statistical features of the data. Functional data analysis leads us to consider the water flow time series as functions to be modelled with a nonparametric method. First, the functions are registered in order to make them more homogeneous. With a more homogeneous sample of curves, we proceed to model their statistical features by relying on Bayesian regression splines in a fairly broad probabilistic framework. More specifically, we study a family of continuous distributions, which include those of the exponential family, from which the data might have arisen. Furthermore, to have a flexible nonparametric modeling tool, we treat the interior knots, which define the basis elements of the regression splines, as random quantities. We then use MCMC with reversible jumps in order to explore the posterior distribution of the interior knots. In order to simplify the procedure in our general modeling context, we consider some approximations for the marginal distribution of the observations, namely one based on the Schwarz information criterion and another which relies on Laplace's approximation. In addition to modeling the central tendency of a sample of curves, we also propose a methodology to simultaneously model the central tendency and the dispersion of the curves in our general probabilistic framework. Finally, since we study several statistical distributions for the observations, we put forward an approach to determine the most adequate distributions for a given sample of curves.

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Books on the topic "Free Knot Spline"

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Old, Oliver. Modeling Time-Varying Unconditional Variance by Means of a Free-Knot Spline-GARCH Model. Wiesbaden: Springer Fachmedien Wiesbaden, 2022. http://dx.doi.org/10.1007/978-3-658-38618-4.

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Old, Oliver. Modeling Time-Varying Unconditional Variance by Means of a Free-Knot Spline-GARCH Model. Springer Fachmedien Wiesbaden GmbH, 2023.

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3

Budworth, Geoffrey. 101 Step-By-Step Knots: Special stand-up design for hands-free practice. Lorenz Books, 2008.

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Book chapters on the topic "Free Knot Spline"

1

Old, Oliver. "Free-knot spline-GARCH model." In Modeling Time-Varying Unconditional Variance by Means of a Free-Knot Spline-GARCH Model, 50–103. Wiesbaden: Springer Fachmedien Wiesbaden, 2022. http://dx.doi.org/10.1007/978-3-658-38618-4_4.

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Creutzig, Jakob, and Mikhail Lifshits. "Free-Knot Spline Approximation of Fractional Brownian Motion." In Monte Carlo and Quasi-Monte Carlo Methods 2006, 195–204. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-74496-2_10.

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Banks, Michael J., Elaine Cohen, and Timothy I. Mueller. "Chapter 7: An Envelope Approach to a Sketching Editor for Hierarchical Free-form Curve Design and Modification." In Knot Insertion and Deletion Algorithms for B-Spline Curves and Surfaces, 179–93. Philadelphia, PA: Society for Industrial and Applied Mathematics, 1992. http://dx.doi.org/10.1137/1.9781611971583.ch7.

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Old, Oliver. "Introduction." In Modeling Time-Varying Unconditional Variance by Means of a Free-Knot Spline-GARCH Model, 1–12. Wiesbaden: Springer Fachmedien Wiesbaden, 2022. http://dx.doi.org/10.1007/978-3-658-38618-4_1.

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Old, Oliver. "Smoothing long term volatility." In Modeling Time-Varying Unconditional Variance by Means of a Free-Knot Spline-GARCH Model, 32–49. Wiesbaden: Springer Fachmedien Wiesbaden, 2022. http://dx.doi.org/10.1007/978-3-658-38618-4_3.

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Old, Oliver. "Conclusion." In Modeling Time-Varying Unconditional Variance by Means of a Free-Knot Spline-GARCH Model, 153–62. Wiesbaden: Springer Fachmedien Wiesbaden, 2022. http://dx.doi.org/10.1007/978-3-658-38618-4_7.

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Old, Oliver. "Financial time series." In Modeling Time-Varying Unconditional Variance by Means of a Free-Knot Spline-GARCH Model, 13–31. Wiesbaden: Springer Fachmedien Wiesbaden, 2022. http://dx.doi.org/10.1007/978-3-658-38618-4_2.

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Old, Oliver. "Simulation study." In Modeling Time-Varying Unconditional Variance by Means of a Free-Knot Spline-GARCH Model, 104–31. Wiesbaden: Springer Fachmedien Wiesbaden, 2022. http://dx.doi.org/10.1007/978-3-658-38618-4_5.

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Old, Oliver. "Empirical study." In Modeling Time-Varying Unconditional Variance by Means of a Free-Knot Spline-GARCH Model, 132–52. Wiesbaden: Springer Fachmedien Wiesbaden, 2022. http://dx.doi.org/10.1007/978-3-658-38618-4_6.

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Sonderegger, Derek L., and Jan Hannig. "Fiducial Theory for Free-Knot Splines." In Contemporary Developments in Statistical Theory, 155–89. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-02651-0_10.

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Conference papers on the topic "Free Knot Spline"

1

Lee, Y. W., Jongwon Lee, W. J. Yoo, H. S. Yoo, and W. J. Warwick. "Free-knot spline model for analysis of pulmonary function." In 2009 Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE, 2009. http://dx.doi.org/10.1109/iembs.2009.5333553.

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Barbot, N., Olivier Boëffard, and D. Lolive. "F0 stylisation with a free-knot b-spline model and simulated-annealing optimization." In Interspeech 2005. ISCA: ISCA, 2005. http://dx.doi.org/10.21437/interspeech.2005-175.

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3

Shalaby, Mohammed M., Ashraf O. Nassef, and Sayed M. Metwalli. "On the Classification of Fitting Problems for Single Patch Free-Form Surfaces in Reverse Engineering." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/dac-21105.

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Abstract The design and manufacture of free-form surfaces increased in industrial applications, especially for the re-manufacture of spare parts, or in the die and mold industry. Reverse engineering has become the status quo technique in reproducing parts whose original designs are no longer existing or for parts, which assume slightly different shapes after manufacturing as in the case of die and mold industry. Laser scanners have been used extensively in sampling points from parts surfaces. The sampled points are then fitted with a free-form surface using one of the geometric modeling techniques such as Bezier or B-Spline surfaces. Since Non-Uniform Rational B-Splines (NURBS) is the most general form of geometric modeling techniques, this paper presents the possible formulations of the fitting problem optimization and presents some guidelines of the choice of the independent NURBS parameters, once the control points are evaluated using least squares fitting. The work shows that the use of NURBS weights can provide better improvements for the significant reduction of the fitting error, rather than the widely used knot values. In addition the work shows that parts with semi planar surfaces do not need further refinement using non-linear optimization methods.

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Wen, Manhong, and Kwun-Lon Ting. "From NURBS to C-NURBS: I — C-NURBS Curves and Their Properties." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/cie-9106.

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Abstract This paper develops a new free-form model, called c-NURBS, which is a general model of NURBS. A c-NURBS curve or surface is the projection of a 6D B-spline curve from a 6D homogeneous space H6 into a 3D space R3. The construction procedure of a c-NURBS curve or surface is that using cubic curves or bicubic patches repeatedly and piecewisely interpolates the given control points. The distinct properties of c-NURBS include independent weight modification, super-convexity, strong c-convex hull, and hidden degrees and control points. These properties greatly enhance the shape control and modification capability. All techniques developed for NURBS, such as the de Boor-Cox algorithm, knot insertion, and degree elevation and reduction, can be applied to c-NURBS. The implementation of c-NURBS requires little improvement on the CAD/CAM systems based on NURBS.

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Yildirim, Yüksel, Chinyere Onwubiko, and Eugene F. Fichter. "Optimization of Polynomial Trajectories for Robotic Manipulators." In ASME 1991 International Computers in Engineering Conference and Exposition. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/cie1991-0161.

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Abstract This paper utilizes the modified pattern search method to solve the nonlinear optimization problem of design of minimum-time robot trajectories between given end states in a workspace containing obstacles. This method is applied to a collision-free path of a two-degree-of-freedom elbow manipulator. Bezier curves, B-spline curves, and parabolic blend curves are used to simplify end-effector path planning. Motion of the manipulator, represented by a sequence of Cartesian knots along the end-effector path, is first transformed into sets of joints displacements. Piecewise cubic spline functions are then fit to the sequence of joint displacements. The minimum-time trajectory planning problem is formulated as the problem of minimizing the total traveling time, taken as objective function, subject to constraints on joint positions, velocities, accelerations, jerks, motor torques, and end-effector acceleration. The computer program, ROBOPATH, has been developed to implement this algorithm for generating end-effector paths and joint trajectories for a manipulator with two links. The results show the modified pattern search method to be a very effective nonlinear optimization technique in design of minimum-time robot trajectories. Also, ROBOPATH can be a useful tool in the design of manipulators, robot tasks and workcells.

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Theodoracatos, Vassilios E., and Vasudeva Bobba. "NURBS Surface Reconstruction From a Large Set of Image and World Data Points." In ASME 1993 Design Technical Conferences. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/detc1993-0373.

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Abstract In this paper an approach is presented for the generation of a NURBS (Non-Uniform Rational B-splines) surface from a large set of 3D data points. The main advantage of NURBS surface representation is the ability to analytically describe both, precise quadratic primitives and free-form curves and surfaces. An existing three dimensional laser-based vision system is used to obtain the spatial point coordinates of an object surface with respect to a global coordinate system. The least-squares approximation technique is applied in both the image and world space of the digitized physical object to calculate the homogeneous vector and the control net of the NURBS surface. A new non-uniform knot vectorization process is developed based on five data parametrization techniques including four existing techniques, viz., uniform, chord length, centripetal, and affine invariant angle and a new technique based on surface area developed in this study. Least-squares error distribution and surface interrogation are used to evaluate the quality of surface fairness for a minimum number of NURBS control points.

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