Image scaling by de la Vall\'ee-Poussin filtered interpolation

TL;DR

This paper introduces a novel image scaling technique using Chebyshev-based sampling and de la Vallée-Poussin filtered interpolation, achieving high-quality results with low artifacts and computational efficiency.

Contribution

The method uniquely combines Chebyshev zeros sampling with a de la Vallée-Poussin filter for polynomial interpolation, enhancing image scaling quality and efficiency.

Findings

High-quality scaled images with preserved details

Low artifact presence in results

Competitive performance with limited computational resources

Abstract

We present a new image scaling method both for downscaling and upscaling, running with any scale factor or desired size. The resized image is achieved by sampling a bivariate polynomial which globally interpolates the data at the new scale. The method's particularities lay in both the sampling model and the interpolation polynomial we use. Rather than classical uniform grids, we consider an unusual sampling system based on Chebyshev zeros of the first kind. Such optimal distribution of nodes permits to consider near--best interpolation polynomials defined by a filter of de la Vall\'ee Poussin type. The action ray of this filter provides an additional parameter that can be suitably regulated to improve the approximation. The method has been tested on a significant number of different image datasets. The results are evaluated in qualitative and quantitative terms and compared with other available competitive methods. The perceived quality of the resulting scaled images is such that important details are preserved, and the appearance of artifacts is low. Competitive quality measurement values, good visual quality, limited computational effort, and moderate memory demand make the method suitable for real-world applications.