Non-uniform to Uniform Image Resampling Utilizing a 2d Farrow Structure

We consider the problem of non-uniform to uniform resampling of images as a problem of reconstruction of 2D continuous function out of non-uniformly distributed samples and its subsequent sampling at the desired grid. The function is assumed to belong to a shift-invariant space with a suitable space-generating basis, e.g. tensor-product splines. A classical approach is to find the corresponding spline coefficients (coordinates with respect to the basis) through a least squares (LS) procedure. In order to achieve a higher computational efficiency we suggest a compromise leading to a near least squares solution. It allows substituting the matrix inversion in the traditional least squares with recursive digital filtering and leads to a 2D form of the so-called transposed Farrow structure, utilized earlier for efficient computations with 1D piecewise-polynomial functions. The performance of the newly-derived filtering structure is demonstrated by applying it to superresolution reconstruction from registered images and by reconstruction of randomly sampled images. Compared with two stateof-the-art resampling methods, our technique gives competitive results while having low computational complexity. Furthermore, it is quite robust to registration errors.