Theory and Practice of Image B-Spline Interpolation
Thibaud Briand, Pascal Monasse
→ BibTeX
    title   = {{Theory and Practice of Image B-Spline Interpolation}},
    author  = {Briand, Thibaud and Monasse, Pascal},
    journal = {{Image Processing On Line}},
    volume  = {8},
    pages   = {99--141},
    year    = {2018},
    doi     = {10.5201/ipol.2018.221},
% if your bibliography style doesn't support doi fields:
    note    = {\url{}}
Thibaud Briand, and Pascal Monasse, Theory and Practice of Image B-Spline Interpolation, Image Processing On Line, 8 (2018), pp. 99–141.

Communicated by Mauricio Delbracio
Demo edited by Pascal Monasse, Thibaud Briand


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.