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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