Fast exact area image upsampling with natural biquadratic histosplines

Abstract

Interpreting pixel values as averages over abutting squares mimics the image capture process. Average Matching (AM) exact area resampling involves the construction of a surface with averages given by the pixel values; the surface is then averaged over new pixel areas. AM resampling approximately preserves local averages (error bounds are given). Also, original images are recovered by box filtering when the magnification factor is an integer in both directions. Natural biquadratic histosplines, which satisfy a minimal norm property like bicubic splines, are used to construct the AM surface. Recurrence relations associated with tridiagonal systems allow the computation of tensor B-Spline coefficients at modest cost and their storage in reduced precision with little accuracy loss. Pixel values are then obtained by multiplication by narrow band matrices computed from B-Spline antiderivatives. Tests involving the re-enlargement of images downsampled with box filtering suggest that natural biquadratic histopolation is the best linear upsampling reconstructor. © 2008 Springer-Verlag Berlin Heidelberg.