Mathematics in Computer Science
A Scratch Covering Algorithm Using Afﬁne
Irina Maria Artinescu ·
Liviu Octavian Mafteiu-Scai
Received: 27 October 2017 / Revised: 27 April 2018 / Accepted: 7 May 2018
© Springer International Publishing AG, part of Springer Nature 2018
Abstract The restoration process attempts to recover an image that has been degraded and for this many approaches
were used in time, but the ﬁlling-in with its two variants, apriori pattern and undamaged near border pattern are widely
used. In this paper a new algorithm for “inpainting” a scratch of an image is proposed. The proposed algorithm uses
a transfer of the information from the unaffected area to the damaged area by the bias of a dynamic pondered afﬁne
projection algorithm. The theoretical link between image recovery problem and the convex feasibility problem is
discussed in this paper. More, the convergence of the proposed algorithm is proved.
Keywords Image recovery · Convex feasibility problem · Inpainting · Afﬁne projection
Mathematics Subject Classiﬁcation 68U10 · 68T10
The restoration of a damaged image affected by inpainting is a very important topic in images processing, the proof
being the large number of scientiﬁc papers about it that have appeared lately. There are many approaches to recover
images, but the ﬁlling-in with its two variants apriori pattern and undamaged near border pattern are widely used.
In work  an algorithm is proposed for digital inpainting images that ﬁlls-in the areas selected by the user with
information surrounding these areas. The novelty element of this algorithm is that it does not require the user to
specify where the novel information comes from.
A similar faster algorithm was proposed in , based on the fast matching method to propagate the image
information near the boundary of the damaged area.
In  the Poisson equation to improve the performance of the structure inpainting is introduced. The image is
decomposed in its structure and texture.
A general method for adapting image reconstruction methods to the hyper-spectral imagery is presented in .
I. M. Artinescu (
) · L. O. Mafteiu-Scai
West University of Timi¸soara, Bd. V. Parvan 4, 300223 Timisoara, Romania
L. O. Mafteiu-Scai