This paper presents a fast algorithm for calculating box splines sampled at regular intervals. This algorithm is based on the representation by directional summations, while splines are often represented by convolutions. The summation-based representation leads less computational complexity: the proposed algorithm requires fewer additions and much fewer multiplications than the algorithm based on convolutions. The proposed algorithm is evaluated in the sense of the number of additions and multiplications for three- and four-directional box splines to see how much those operations are reduced.
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Takeshi ASAHI, Koichi ICHIGE, Rokuya ISHII, "A New Formulation for Discrete Box Splines Reducing Computational Cost and Its Evaluation" in IEICE TRANSACTIONS on Fundamentals,
vol. E84-A, no. 3, pp. 884-892, March 2001, doi: .
Abstract: This paper presents a fast algorithm for calculating box splines sampled at regular intervals. This algorithm is based on the representation by directional summations, while splines are often represented by convolutions. The summation-based representation leads less computational complexity: the proposed algorithm requires fewer additions and much fewer multiplications than the algorithm based on convolutions. The proposed algorithm is evaluated in the sense of the number of additions and multiplications for three- and four-directional box splines to see how much those operations are reduced.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e84-a_3_884/_p
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@ARTICLE{e84-a_3_884,
author={Takeshi ASAHI, Koichi ICHIGE, Rokuya ISHII, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A New Formulation for Discrete Box Splines Reducing Computational Cost and Its Evaluation},
year={2001},
volume={E84-A},
number={3},
pages={884-892},
abstract={This paper presents a fast algorithm for calculating box splines sampled at regular intervals. This algorithm is based on the representation by directional summations, while splines are often represented by convolutions. The summation-based representation leads less computational complexity: the proposed algorithm requires fewer additions and much fewer multiplications than the algorithm based on convolutions. The proposed algorithm is evaluated in the sense of the number of additions and multiplications for three- and four-directional box splines to see how much those operations are reduced.},
keywords={},
doi={},
ISSN={},
month={March},}
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TY - JOUR
TI - A New Formulation for Discrete Box Splines Reducing Computational Cost and Its Evaluation
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 884
EP - 892
AU - Takeshi ASAHI
AU - Koichi ICHIGE
AU - Rokuya ISHII
PY - 2001
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E84-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 2001
AB - This paper presents a fast algorithm for calculating box splines sampled at regular intervals. This algorithm is based on the representation by directional summations, while splines are often represented by convolutions. The summation-based representation leads less computational complexity: the proposed algorithm requires fewer additions and much fewer multiplications than the algorithm based on convolutions. The proposed algorithm is evaluated in the sense of the number of additions and multiplications for three- and four-directional box splines to see how much those operations are reduced.
ER -