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A New Formulation for Discrete Box Splines Reducing Computational Cost and Its Evaluation
Takeshi ASAHI Koichi ICHIGE Rokuya ISHII
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2001/03/01
Print ISSN: 0916-8508
Type of Manuscript: PAPER
box spline, B-spline, interpolation, truncated power,
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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.