Volume 59, pp. 295-318, 2023.

Filtered polynomial interpolation for scaling 3D images

Donatella Occorsio, Giuliana Ramella, and Woula Themistoclakis

Abstract

Image scaling methods allow us to obtain a given image at a different, higher (upscaling) or lower (downscaling), resolution to preserve as much as possible the original content and the quality of the image. In this paper, we focus on interpolation methods for scaling three-dimensional grayscale images. Within a unified framework, we introduce two different scaling methods, respectively based on the Lagrange and filtered de la Vallée Poussin type interpolation at the zeros of Chebyshev polynomials of the first kind. In both cases, using a non-standard sampling model, we take (via tensor product) the associated trivariate polynomial interpolating the input image. It represents a continuous approximate 3D image to resample at the desired resolution. Using discrete $\ell^\infty$ and $\ell^2$ norms, we theoretically estimate the error achieved in output, showing how it depends on the error in the input and on the smoothness of the specific image we are processing. Finally, taking the special case of medical images as a case study, we experimentally compare the performances of the proposed methods and with the classical multivariate cubic and Lanczos interpolation methods.

Full Text (PDF) [3.7 MB], BibTeX

Key words

Image resizing, image downscaling, image upscaling, Lagrange interpolation, filtered VP interpolation, de la Vallée Poussin means, Chebyshev nodes

AMS subject classifications

94A08, 68U10, 41A05, 62H35

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