TY - JOUR
T1 - Improving smoothness and accuracy of Modified Butterfly subdivision scheme
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
UR - http://www.scopus.com/inward/record.url?scp=84947487519&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2015.07.065
DO - 10.1016/j.amc.2015.07.065
M3 - Article
AN - SCOPUS:84947487519
SN - 0096-3003
VL - 272
SP - 64
EP - 79
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
ER -