Non-uniform to uniform image resampling utilizing a 2D Farrow structure
Harish Essaky Sankaran, Mihail Georgiev, Atanas P. Gotchev, Karen Egiazarian · 2007
We consider the problem of non-uniform to uniform re-sampling 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. ten-sor-product splines. A classical approach is to find the corresponding spline coefficients (coordinates with re-spect to the basis) through a least squares (LS) proce-dure. In order to achieve a higher computational effi-ciency we suggest a compromise leading to a near least squares solution. It allows substituting the matrix inver-sion in the traditional least squares with recursive digi-tal 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 recon-struction from registered images and by reconstruction of randomly sampled images. Compared with two state-of-the-art resampling methods, our technique gives competitive results while having low computational complexity. Furthermore, it is quite robust to registra-tion errors. 1.