On the Role of Exponential Splines in Image Interpolation
Hagai Kirshner and Moshe Porat,
Department of Electrical Engineering,
Technion - Israel Institute of Technology
Haifa 32000, Israel
A Sobolev reproducing-kernel Hilbert space approach to image
interpolation is introduced. The underlying kernels are exponential
functions and are related to stochastic autoregressive image modeling.
The corresponding image interpolants can be implemented effectively
using compactly-supported exponential B-splines. A tight $\lebesgue$
upper-bound on the interpolation error is then derived, suggesting
that the proposed exponential functions are optimal in this regard.
Experimental results indicate that the proposed interpolation approach
with properly-tuned, signal-dependent weights outperforms currently
available polynomial B-spline models of comparable order. Furthermore,
a unified approach to image interpolation by ideal and non-ideal
sampling procedures is derived, suggesting that the proposed exponential
kernels may have a significant role in image modeling as well.
Our conclusion is that the proposed Sobolev-based approach could be
instrumental and a preferred alternative in many interpolation tasks.
IEEE Trans. on Image Processing,
vol. 18, no.10, pp. 2198-2208 (2009).
Moshe Porat's Homepage (http://vision.technion.ac.il/mp)