Least-squares image resizing using finite differences

We present an optimal spline-based algorithm for the enlargement or reducti on of digital images with arbitrary (noninteger) scaling factors. This proj ection-based approach can be realized thanks to a new finite difference met hod that allows the computation of inner products with analysis functions t hat are B-splines of any degree n. A noteworthy property of the algorithm i s that the computational complexity per pixel does not depend on the scalin g factor a. For a given choice of basis functions, the results of our metho d are consistently better than those of the standard interpolation procedur e; the present scheme achieves a reduction of artifacts such as aliasing an d blocking and a significant improvement of the signal-to-noise ratio. The method can be generalized to include other classes of piecewise polynomial functions, expressed as linear combinations of B-splines and their derivati ves.