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Relevant bibliographies by topics / Non-Stationary subdivision scheme

Academic literature on the topic 'Non-Stationary subdivision scheme'

Author: Grafiati

Published: 8 June 2024

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Contents

Journal articles
Dissertations / Theses
Book chapters
Conference papers

Journal articles on the topic "Non-Stationary subdivision scheme":

1

Siddiqi, S. S., and M. Younis. "A symmetric non-stationary subdivision scheme." LMS Journal of Computation and Mathematics 17, no. 1 (2014): 259–72. http://dx.doi.org/10.1112/s1461157013000375.

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AbstractThis paper proposes a new family of symmetric $4$-point ternary non-stationary subdivision schemes that can generate the limit curves of $C^3$ continuity. The continuity of this scheme is higher than the existing 4-point ternary approximating schemes. The proposed scheme has been developed using trigonometric B-spline basis functions and analyzed using the theory of asymptotic equivalence. It has the ability to reproduce or regenerate the conic sections, trigonometric polynomials and trigonometric splines as well. Some graphical and numerical examples are being considered, by choosing an appropriate tension parameter $0<\alpha <\pi /3 $, to show the usefulness of the proposed scheme. Moreover, the Hölder regularity and the reproduction property are also being calculated.

2

Daniel, Sunita, and P. Shunmugaraj. "An approximating non-stationary subdivision scheme." Computer Aided Geometric Design 26, no. 7 (October 2009): 810–21. http://dx.doi.org/10.1016/j.cagd.2009.02.007.

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Lamnii, Abdellah, Mohamed Yassir Nour, and Ahmed Zidna. "A Reverse Non-Stationary Generalized B-Splines Subdivision Scheme." Mathematics 9, no. 20 (October 18, 2021): 2628. http://dx.doi.org/10.3390/math9202628.

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In this paper, two new families of non-stationary subdivision schemes are introduced. The schemes are constructed from uniform generalized B-splines with multiple knots of orders 3 and 4, respectively. Then, we construct a third-order reverse subdivision framework. For that, we derive a generalized multi-resolution mask based on their third-order subdivision filters. For the reverse of the fourth-order scheme, two methods are used; the first one is based on least-squares formulation and the second one is based on solving a linear optimization problem. Numerical examples are given to show the performance of the new schemes in reproducing different shapes of initial control polygons.

4

Zhang, Baoxing, Yunkun Zhang, and Hongchan Zheng. "A Symmetric Non-Stationary Loop Subdivision with Applications in Initial Point Interpolation." Symmetry 16, no. 3 (March 21, 2024): 379. http://dx.doi.org/10.3390/sym16030379.

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Loop subdivision is a significant surface scheme with wide applications in fields like computer graphics and wavelet. As a type of stationary scheme, Loop subdivision cannot adjust the limit surface directly. In this paper, we present a new way to solve this problem by proposing a symmetric non-stationary Loop subdivision based on a suitable iteration. This new scheme can be used to adjust the limit surfaces freely and thus can generate surfaces with different shapes. For this new scheme, we show that it is C2 convergent in the regular part of mesh and is at least tangent plane continuous at the limit positions of the extraordinary points. Additionally, we present a non-uniform generalization of this new symmetric non-stationary subdivision so as to locally control the shape of the limit surfaces. More interestingly, we present the limit positions of the initial points, both for the symmetric non-stationary Loop subdivision and its non-uniform generalization. Such limit positions can be used to interpolate the initial points with different valences, generalizing the existing result. Several numerical examples are given to illustrate the performance of the new schemes.

5

Jena, M. K., P. Shunmugaraj, and P. C. Das. "A non-stationary subdivision scheme for curve interpolation." ANZIAM Journal 44 (January 13, 2008): 216. http://dx.doi.org/10.21914/anziamj.v44i0.494.

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Salam, Wardat us, Shahid S. Siddiqi, and Kashif Rehan. "Chaikin’s perturbation subdivision scheme in non-stationary forms." Alexandria Engineering Journal 55, no. 3 (September 2016): 2855–62. http://dx.doi.org/10.1016/j.aej.2016.07.002.

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Zhang, Zeze, Hongchan Zheng, and Lulu Pan. "Construction of a family of non-stationary combined ternary subdivision schemes reproducing exponential polynomials." Open Mathematics 19, no. 1 (January 1, 2021): 909–26. http://dx.doi.org/10.1515/math-2021-0058.

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Abstract In this paper, we propose a family of non-stationary combined ternary ( 2 m + 3 ) \left(2m+3) -point subdivision schemes, which possesses the property of generating/reproducing high-order exponential polynomials. This scheme is obtained by adding variable parameters on the generalized ternary subdivision scheme of order 4. For such a scheme, we investigate its support and exponential polynomial generation/reproduction and get that it can generate/reproduce certain exponential polynomials with suitable choices of the parameters and reach 2 m + 3 2m+3 approximation order. Moreover, we discuss its smoothness and show that it can produce C 2 m + 2 {C}^{2m+2} limit curves. Several numerical examples are given to show the performance of the schemes.

8

Daniel, Sunita, and P. Shunmugaraj. "An interpolating 6-point C2 non-stationary subdivision scheme." Journal of Computational and Applied Mathematics 230, no. 1 (August 2009): 164–72. http://dx.doi.org/10.1016/j.cam.2008.11.006.

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9

Tan, Jieqing, Jiaze Sun, and Guangyue Tong. "A non-stationary binary three-point approximating subdivision scheme." Applied Mathematics and Computation 276 (March 2016): 37–43. http://dx.doi.org/10.1016/j.amc.2015.12.002.

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Zheng, Hongchan, and Baoxing Zhang. "A non-stationary combined subdivision scheme generating exponential polynomials." Applied Mathematics and Computation 313 (November 2017): 209–21. http://dx.doi.org/10.1016/j.amc.2017.05.066.

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More sources

Dissertations / Theses on the topic "Non-Stationary subdivision scheme":

1

Nour, Mohamed-Yassir. "Schéma de subdivision non-stationnaire avec un paramètre de forme et applications en imagerie médicale." Electronic Thesis or Diss., Université de Lorraine, 2023. http://www.theses.fr/2023LORR0004.

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Les schémas de subdivision constituent un outil efficace pour la génération des courbes et surfaces. Ils sont à présent largement répandus dans de nombreux domaines de l'informatique graphique. Cette thèse est consacrée à l'étude et à la construction des schémas de subdivision non-stationnaires (uniforme ou non uniforme) basés sur la combinaison des fonctions splines trigonométriques et hyperboliques avec des paramètres de tension. Dans un premier temps, nous rappelons les différentes techniques mathématiques nécessaires à une meilleure compréhension des schémas subdivision non-stationnaires étudiés dans cette thèse. Puis, nous proposons deux nouveaux schémas de subdivision uni-variés basés sur un mélange entre les fonctions trigonométrique et hyperbolique avec des paramètres de tension. Une étude théorique et pratique est portée aussi sur la convergence de ces deux schémas, ainsi que sur leur régularité. Dans un deuxième temps, nous étendons les schémas proposés dans le chapitre précédent au cas surfacique. Plus précisément, nous proposons des règles de subdivisions pour le cas de maillage de topologie quelconque. Nous établissons la convergence et la régularité de ces schémas en se basant des outils analytiques et algébriques. Enfin, nous proposons ensuite des algorithmes dans le but d'appliquer numériquement les règles proposées afin de reconstruire des surfaces provenant de l'imagerie médicale. Dans un troisième temps, nous nous sommes intéressés à la construction de deux nouvelles approches de subdivision inverse. La première approche est basée sur un calcul direct alors que la deuxième exploite une méthode de résolution d'optimisation. Enfin, nous présentons des tests numériques qui démontrent l'efficacité des schémas proposés
In this thesis, we study and construct non-stationary subdivision schemes (uniform or non- uniform), using a combination of trigonometric and hyperbolic functions with tension parameters. These new subdivision schemes have the ability to generate more flexible curves and surfaces. In the first step, we recall the various mathematical techniques required to understand the non-stationary subdivision schemes studied in this thesis. Following that, we propose two new uni-variate subdivision schemes using a mixture of trigonometric and hyperbolic functions. In addition, we examine the convergence of these two schemes, as well as their regularity, in both theoretical and practical context. The second step aims to extend the previous chapter schemes to the surface case. Specifically, we suggest subdivision rules for meshes with arbitrary topology. We then establish the convergence and regularity of these schemes based on analytical and algebraic tools. Then, we propose several algorithms to numerically reconstruct surfaces from medical images using the proposed rules. In the third step, we are interested in the construction of two new approaches for reverse subdivision. The first approach is based on direct computation and the second one consist in solving an optimization problem. We also present numerical tests that show the efficiency of the proposed schemes

Book chapters on the topic "Non-Stationary subdivision scheme":

1

Dyn, Nira, and David LevinAriel Luzzatto. "Refining Oscillatory Signals by Non—Stationary Subdivision Schemes." In International Series of Numerical Mathematics, 125–42. Basel: Birkhäuser Basel, 2003. http://dx.doi.org/10.1007/978-3-0348-8067-1_6.

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Conti, Costanza, and Nira Dyn. "Non-stationary Subdivision Schemes: State of the Art and Perspectives." In Springer Proceedings in Mathematics & Statistics, 39–71. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-57464-2_4.

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Choi, Yoo-Joo, Yeon-Ju Lee, Jungho Yoon, Byung-Gook Lee, and Young J. Kim. "A New Class of Non-stationary Interpolatory Subdivision Schemes Based on Exponential Polynomials." In Geometric Modeling and Processing - GMP 2006, 563–70. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11802914_41.

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4

Dyn, Nira, and David Levin. "Stationary and Non-Stationary Binary Subdivision Schemes." In Mathematical Methods in Computer Aided Geometric Design II, 209–16. Elsevier, 1992. http://dx.doi.org/10.1016/b978-0-12-460510-7.50019-7.

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Conference papers on the topic "Non-Stationary subdivision scheme":

1

Daniel, Sunita, and P. Shunmugaraj. "Some Non-Stationary Subdivision Schemes." In Geometric Modeling and Imaging (GMAI '07). IEEE, 2007. http://dx.doi.org/10.1109/gmai.2007.30.

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Daniel, Sunita, and P. Shunmugaraj. "Some Interpolating Non-stationary Subdivision Schemes." In 2011 International Symposium on Computer Science and Society (ISCCS). IEEE, 2011. http://dx.doi.org/10.1109/isccs.2011.110.

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Daniel, Sunita, and P. Shunmugaraj. "Chapter 1: Three Point Stationary and Non-stationary Subdivision Schemes." In 2008 3rd International Conference on Geometric Modeling and Imaging GMAI. IEEE, 2008. http://dx.doi.org/10.1109/gmai.2008.13.

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4

Conti, Costanza, Lucia Romani, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "A New Family of Interpolatory Non-Stationary Subdivision Schemes for Curve Design in Geometric Modeling." In ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP, 2010. http://dx.doi.org/10.1063/1.3498528.

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