Theory and Practice of Image B-Spline Interpolation

We explain how the B-spline interpolation of signals and, in particular, of images can be efficiently performed by linear filtering. Based on the seminal two-step method proposed by Unser et al. in 1991, we propose two slightly different prefiltering algorithms whose precisions are proven to be controlled thanks to a rigorous boundary handling. This paper contains all the information, theoretical and practical, required to perform efficiently B-spline interpolation for any order and any boundary extension. We describe precisely how to evaluate the kernel and to compute the B-spline interpolator parameters. We show experimentally that increasing the order improves the interpolation quality. As a fundamental application we also provide an implementation of homographic transformation of images using B-spline interpolation.