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Complete Parametrization of Piecewise-Polynomial Interpolators According to Degree, Support, Regularity, and Order

P. Thévenaz, T. Blu, M. Unser

Proceedings of the 2000 IEEE International Conference on Image Processing (ICIP'00), Vancouver BC, Canada, September 10-13, 2000, vol. II, pp. 335-338.



The most essential ingredient of interpolation is its basis function. We have shown in previous papers that this basis need not be necessarily interpolating to achieve good results. On the contrary, several recent studies have confirmed that non-interpolating bases, such as B-splines and O-moms, perform best. This opens up a much wider choice of basis functions. In this paper, we give to the designer the tools that will allow him to characterize this enlarged space of functions. In particular, he will be able to specify up-front the four most important parameters for image processing: degree, support, regularity, and order. The theorems presented here will then allow him to refine his design by dealing with additional coefficients that can be selected freely, without interfering with the main design parameters.

Errata

The following erratum applies to the printed proceedings (the version that you can download below is amended):

  • pp. 1, definition of the degree of a Dirac distribution: printed version is δ ∈ {-n, 0, -2 - n, 0}, correct version should be δ ∈ {-n - 1, 0, -2 - n, 0}.

  • pp. 2, definition of γ, second line: a factor (1/n!) is missing in the printed version. See the downloadable version for corrections.


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