Lagrange-Chebyshev Interpolation for image resizing

TL;DR

This paper introduces a novel image resizing method using Lagrange-Chebyshev interpolation, which performs well in both upscaling and downscaling, especially excelling in downscaling scenarios compared to existing methods.

Contribution

The paper applies Lagrange-Chebyshev interpolation to image resizing, providing a theoretically grounded approach that improves downscaling performance and offers error estimates for odd scale factors.

Findings

High performance in downscaling compared to Bicubic methods

Comparable results to Bicubic in upscaling with slightly better metrics

Theoretical null mean squared error in noise-free, artifact-free images for odd scale factors

Abstract

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.