Image reduction method based on the F-transform

We present a new method of (color) image reduction based on the F-transform technique with a generalized fuzzy partition. This technique successfully combines approximation (when reduction is performed) and interpolation (when reconstruction is produced). The efficiency of the proposed method is theoretically justified by its linear complexity and by comparison with interpolation, and aggregation-based reductions. We also analyze the measures (MSE\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{MSE}$$\end{document}, PEN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{PEN}$$\end{document}, and SSIM\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{SSIM}$$\end{document}) that are commonly used to estimate the quality of reduced images and show that these measures have better values using the newly proposed method.