EPFL | Biomedical Imaging Group | Polynomial Pictures

Polynomial Representation of Pictures

M. Eden, M. Unser, R. Leonardi

Signal Processing, vol. 10, no. 4, pp. 385–393, June 1986.

In many image processing applications, the discrete values of an image can be embedded in a continuous function. This type of representation can be useful for interpolation, geometrical transformations or special features extraction. Given a rectangular M × N discrete image (or sub-image), it is shown how to compute a continuous polynomial function that guarantees an exact fit at the considered pixel locations. The polynomials coefficients can be expressed as a linear one-to-one separable transform of the pixels. The transform matrices can be computed using a fast recursive algorithm which enables efficient inversion of a Vandermonde matrix. It is also shown that the least square polynomial approximation with M' × M' coefficients, in separable formulation, involves the inversion of two M' × M' and N' × N' Hankel matrices.

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AUTHOR="Eden, M. and Unser, M. and Leonardi, R.",
TITLE="Polynomial Representation of Pictures",
JOURNAL="Signal Processing",
YEAR="1986",
volume="10",
number="4",
pages="385--393",
month="June",
note="")

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