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Directional difference-summation approach to discrete box splines and its applications

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. Furthermore, this method is applied to the reconstruction of enlarged digital images. Although similar results are obtained for images with low frequency components, a better visual result is obtained for images containing text characters.