Cubic splines for image interpolation and digital filtering

This paper presents the use of B-splines as a tool in various digital signal processing applications. The theory of B-splines is briefly reviewed, followed by discussions on B-spline interpolation and B-spline filtering. Computer implementation using both an efficient software viewpoint and a hardware method are discussed. Finally, experimental results are presented for illustrative purposes in two-dimensional image format. Applications to image and signal processing include interpolation, smoothing, filtering, enlargement, and reduction.

[1]  Ming-Lei Liou,et al.  Spline Fit Made Easy , 1976, IEEE Trans. Computers.

[2]  Carl de Boor,et al.  On uniform approximation by splines , 1968 .

[3]  A. Caprihan Finite-duration digital filter design by use of cubic splines , 1975 .

[4]  A. K. Cline Scalar- and planar-valued curve fitting using splines under tension , 1974, Commun. ACM.

[5]  G. Wahba Interpolating Spline Methods for Density Estimation I. Equi-Spaced Knots , 1975 .

[6]  Bernard Friedland,et al.  Linear Systems , 1965 .

[7]  Grace Wahba,et al.  A Polynomial Algorithm for Density Estimation , 1971 .

[8]  G. Golub MATRIX DECOMPOSITIONS AND STATISTICAL CALCULATIONS , 1969 .

[9]  L. Schumaker,et al.  Some multidimensional spline approximation methods , 1974 .

[10]  Edmund Taylor Whittaker XVIII.—On the Functions which are represented by the Expansions of the Interpolation-Theory , 1915 .

[11]  I J Schoenberg,et al.  SPLINE FUNCTIONS AND THE PROBLEM OF GRADUATION. , 1964, Proceedings of the National Academy of Sciences of the United States of America.

[12]  L. Horowitz,et al.  The effects of spline interpolation on power spectral density , 1974 .

[13]  D. G. Watts,et al.  Spectral analysis and its applications , 1968 .

[14]  Hiroshi Akima,et al.  A method of bivariate interpolation and smooth surface fitting based on local procedures , 1974, Commun. ACM.

[15]  Bede Liu,et al.  A new hardware realization of digital filters , 1974 .

[16]  L. Ostrander The Fourier transform of spline-function approximations to continuous data , 1971 .

[17]  L. Schumaker,et al.  Computation of Smoothing and Interpolating Natural Splines via Local Bases , 1973 .

[18]  Theodosios Pavlidis,et al.  Optimal Piecewise Polynomial L2Approximation of Functions of One and Two Variables , 1975, IEEE Transactions on Computers.

[19]  J. L. Walsh,et al.  The theory of splines and their applications , 1969 .

[20]  Edmund Taylor Whittaker On a New Method of Graduation , 1922, Proceedings of the Edinburgh Mathematical Society.

[21]  L. Rabiner,et al.  A digital signal processing approach to interpolation , 1973 .

[22]  Robert Todd Gregory,et al.  A collection of matrices for testing computational algorithms , 1969 .

[23]  Harry C. Andrews,et al.  Least Squares Image Restoration Using Spline Basis Functions , 1977, IEEE Transactions on Computers.