IFS-Based Image Reconstruction of Binary Images with Functional Networks

Akemi Gálvez, Iztok Fister, Andrés Iglesias, Iztok Fister, Valentín Gómez-Jauregui, Cristina Manchado and César Otero
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Akemi Gálvez: Department of Applied Mathematics and Computational Sciences, Universidad de Cantabria, 39005 Santander, Spain
Iztok Fister: Department of Applied Mathematics and Computational Sciences, Universidad de Cantabria, 39005 Santander, Spain
Andrés Iglesias: Department of Applied Mathematics and Computational Sciences, Universidad de Cantabria, 39005 Santander, Spain
Iztok Fister: Faculty of Electrical Engineering and Computer Science, University of Maribor, 2000 Maribor, Slovenia
Valentín Gómez-Jauregui: R&D EgiCAD, School of Civil Engineering, Universidad de Cantabria, Avda. de los Castros 44, 39005 Santander, Spain
Cristina Manchado: R&D EgiCAD, School of Civil Engineering, Universidad de Cantabria, Avda. de los Castros 44, 39005 Santander, Spain
César Otero: R&D EgiCAD, School of Civil Engineering, Universidad de Cantabria, Avda. de los Castros 44, 39005 Santander, Spain

Mathematics, 2022, vol. 10, issue 7, 1-26

Abstract: This work addresses the IFS-based image reconstruction problem for binary images. Given a binary image as the input, the goal is to obtain all the parameters of an iterated function system whose attractor approximates the input image accurately; the quality of this approximation is measured according to a similarity function between the original and the reconstructed images. This paper introduces a new method to tackle this issue. The method is based on functional networks, a powerful extension of neural networks that uses functions instead of the scalar weights typically found in standard neural networks. The method relies on an artificial network comprised of several functional networks, one for each of the contractive affine maps forming the IFS. The method is applied to an illustrative and challenging example of a fractal binary image exhibiting a complicated shape. The graphical and numerical results show that the method performs very well and is able to reconstruct the input image using IFS with high accuracy. The results also show that the method is not yet optimal and offers room for further improvement.

Keywords: functional networks; artificial neural networks; binary images; iterated function systems; collage theorem; image reconstruction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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