  Image resizing is a basic tool in image processing and in literature we have
many methods, based on different approaches, which are often specialized in
only upscaling or downscaling. In this paper, independently of the (reduced or
enhanced) size we aim to get, we approach the problem at a continuous scale
where the underlying continuous image is globally approximated by the tensor
product Lagrange polynomial interpolating at a suitable grid of first kind
Chebyshev zeros. This is a well-known approximation tool that is widely used in
many applicative yields, due to the optimal behavior of the related Lebesgue
constants. Here we show how Lagrange-Chebyshev interpolation can be fruitfully
applied also for resizing an arbitrary digital image in both downscaling and
upscaling. The performance of the proposed method has been tested in terms of
the standard SSIM and PSNR metrics. The results indicate that, in upscaling, it
is almost comparable with the classical Bicubic resizing method with slightly
better metrics, but in downscaling a much higher performance has been observed
in comparison with Bicubic and other recent methods too. Moreover, in
downscaling cases with an odd scale factor, we give an estimate of the mean
squared error produced by our method and prove it is theoretically null (hence
PSNR equals to infinite and SSIM equals to one) in absence of noise or initial
artifacts on the input image.

Numerical Analysis;Numerical Analysis