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Simple Algorithms and Architectures for B-spline Interpolation
March 1988 (vol. 10 no. 2)
pp. 271-276

It is proved that the Toeplitz binary value matrix inversion associated with mth-order B-spline interpolation can be implemented using only 2(m+1) additions. Pipelined architectures are developed for real-time B-spline interpolation based on simple running average filters. It is shown that an ideal interpolating function, which is approximated by a truncated sinc function with M half cycles, can be implemented using B-splines with M+2 multiplies. With insignificant loss of performance, the coefficients at the knots of the truncated sinc function can be approximated using coefficients which are powers of two. The resulting implementation requires only M+4m+6 additions. It is believed that the truncated sinc function approximated by zero-order B-spline functions actually achieves the best visual performance.

[1] H. S. Hou and H. C. Andrews, "Cubic splines for image interpolation and digital filtering,"IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-26, pp. 508-517, 1978.
[2] R. G. Keys, "Cubic convolution interpolation for digital image processing,"IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-29, pp. 1153-1160, 1981.
[3] S. K. Park and R. A. Schowemgerdt, "Image reconstruction by parametric convolution,"Comput. Vision, Graphics, Image Processing, vol. 23, pp. 258-272.
[4] T. C. Chen and R. J. P. deFigueiredo, "Two-dimensional interpolationby generalized spline filters based on partial differential equations,"IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-33, pp. 631-642, June 1985.
[5] J. A. Parker, R. V. Kenyon, and D. E. Troxel, "Comparison of interpolating methods for image resampling,"IEEE Trans. Med. Imaging, vol. MI-2, Mar. 1983.

Index Terms:
picture processing; pipelined architecture; B-spline interpolation; filters; truncated sinc function; visual performance; interpolation; parallel architectures; picture processing; splines (mathematics)
P.V. Sankar, L.A. Ferrari, "Simple Algorithms and Architectures for B-spline Interpolation," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 10, no. 2, pp. 271-276, March 1988, doi:10.1109/34.3889
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