Improving smoothness and accuracy of Modified Butterfly subdivision scheme

Paola Novara; Lucia Romani; Jungho Yoon

doi:10.1016/j.amc.2015.07.065

Improving smoothness and accuracy of Modified Butterfly subdivision scheme

Paola Novara, Lucia Romani, Jungho Yoon

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

Motivated by the increasing request of surface representation techniques suitable for biomedical imaging applications, we construct a non-stationary subdivision scheme for regular 3-directional grids, which enjoys the following properties: (i) interpolation, (ii) affine invariance, (iii) C² smoothness, (iv) approximation order 6 and (v) the capability of reproducing several trigonometric surfaces, especially ellipsoids. To study the smoothness properties of this new scheme via existing analysis tools, we also construct an auxiliary stationary subdivision scheme enjoying properties (i)-(iv). Taking into account that, when applied on regular 3-directional grids, the Modified Butterfly scheme is C¹ and has approximation order 4, the subdivision schemes derived in this paper can be considered improved variants of the Modified Butterfly scheme.

Original language	English
Pages (from-to)	64-79
Number of pages	16
Journal	Applied Mathematics and Computation
Volume	272
DOIs	https://doi.org/10.1016/j.amc.2015.07.065
State	Published - 1 Jan 2016

Bibliographical note

Funding Information:
Lucia Romani was partially supported by MIUR-PRIN 2012, grant no. 2012MTE38N. Jungho Yoon was supported by Priority Research Centers Program 2009-0093827 through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology.

Publisher Copyright:
© 2015 Elsevier Inc. All rights reserved.

Keywords

Approximation order
Exponential polynomial reproduction
Interpolation
Non-stationary subdivision
Smoothness

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10.1016/j.amc.2015.07.065

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title = "Improving smoothness and accuracy of Modified Butterfly subdivision scheme",

abstract = "Motivated by the increasing request of surface representation techniques suitable for biomedical imaging applications, we construct a non-stationary subdivision scheme for regular 3-directional grids, which enjoys the following properties: (i) interpolation, (ii) affine invariance, (iii) C2 smoothness, (iv) approximation order 6 and (v) the capability of reproducing several trigonometric surfaces, especially ellipsoids. To study the smoothness properties of this new scheme via existing analysis tools, we also construct an auxiliary stationary subdivision scheme enjoying properties (i)-(iv). Taking into account that, when applied on regular 3-directional grids, the Modified Butterfly scheme is C1 and has approximation order 4, the subdivision schemes derived in this paper can be considered improved variants of the Modified Butterfly scheme.",

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author = "Paola Novara and Lucia Romani and Jungho Yoon",

note = "Funding Information: Lucia Romani was partially supported by MIUR-PRIN 2012, grant no. 2012MTE38N. Jungho Yoon was supported by Priority Research Centers Program 2009-0093827 through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology. Publisher Copyright: {\textcopyright} 2015 Elsevier Inc. All rights reserved.",

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doi = "10.1016/j.amc.2015.07.065",

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AU - Novara, Paola

AU - Romani, Lucia

AU - Yoon, Jungho

N1 - Funding Information: Lucia Romani was partially supported by MIUR-PRIN 2012, grant no. 2012MTE38N. Jungho Yoon was supported by Priority Research Centers Program 2009-0093827 through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology. Publisher Copyright: © 2015 Elsevier Inc. All rights reserved.

PY - 2016/1/1

Y1 - 2016/1/1

N2 - Motivated by the increasing request of surface representation techniques suitable for biomedical imaging applications, we construct a non-stationary subdivision scheme for regular 3-directional grids, which enjoys the following properties: (i) interpolation, (ii) affine invariance, (iii) C2 smoothness, (iv) approximation order 6 and (v) the capability of reproducing several trigonometric surfaces, especially ellipsoids. To study the smoothness properties of this new scheme via existing analysis tools, we also construct an auxiliary stationary subdivision scheme enjoying properties (i)-(iv). Taking into account that, when applied on regular 3-directional grids, the Modified Butterfly scheme is C1 and has approximation order 4, the subdivision schemes derived in this paper can be considered improved variants of the Modified Butterfly scheme.

AB - Motivated by the increasing request of surface representation techniques suitable for biomedical imaging applications, we construct a non-stationary subdivision scheme for regular 3-directional grids, which enjoys the following properties: (i) interpolation, (ii) affine invariance, (iii) C2 smoothness, (iv) approximation order 6 and (v) the capability of reproducing several trigonometric surfaces, especially ellipsoids. To study the smoothness properties of this new scheme via existing analysis tools, we also construct an auxiliary stationary subdivision scheme enjoying properties (i)-(iv). Taking into account that, when applied on regular 3-directional grids, the Modified Butterfly scheme is C1 and has approximation order 4, the subdivision schemes derived in this paper can be considered improved variants of the Modified Butterfly scheme.

KW - Approximation order

KW - Exponential polynomial reproduction

KW - Interpolation

KW - Non-stationary subdivision

KW - Smoothness

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SP - 64

EP - 79

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

Improving smoothness and accuracy of Modified Butterfly subdivision scheme

Abstract

Bibliographical note

Keywords

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