Improvement of the digital radiographic images of old paintings on wooden support through the anisotropic diffusion method

[EN] The main defect types of historic-artistic paintings on wood are ruptures, scratches, twisting and suchwhich may be inflicted by environment conditions, insects, dust, and dirt as well as by physical damage.The exact localization of the defects and determination of their extent may be achieved using industrialradiography as a non-destructive testing method. The radiographs thus produced may suffer from blurri-ness mainly due to the inherent scattering of X-rays especially in the case of paintings on a wooden baseand hindering therefore accurate detection of the size and shape of such defects. Image processing meth-ods have been employed to reduce the blurriness of images leading to improved analysis of the images. Inthis study, an image processing method based on anisotropic diffusion with an automatic threshold levelwas applied to achieve improved outcomes. The reconstructed images of the implemented algorithmyielded sharper edges. Defects such as those due to xylophagous attack, the effect of the brushstrokes,superficial fissures, oxidation of the nails, and the different types of construction woods were bettervisualized than from the original image. The algorithm was shown to be useful by operators includingpainting conservators for their procedures.Madrid García, JA.; Yahaghi, E.; Movafeghi, A. (2021). Improvement of the digital radiographic images of old paintings on wooden support through the anisotropic diffusion method. Journal of Cultural Heritage. (49):115-122. https://doi.org/10.1016/j.culher.2021.02.008S1151224

A PDE-based Mathematical Method in Image Processing: Digital-Discrete Method for Perona-Malik Equation

In this study, we propose a new and effective algorithm for image processing. The method based on the combination of digital topology, partial differential equations and finite difference scheme is called the digital-discrete method. We try to solve the Perona-Malik equation using the digital-discrete method. We use the MATLAB package program when analyzing images. The analyzes we make on the images show how the algorithm is useful, effective and open to development

Perona-Malik equation: properties of explicit finite volume scheme

summary:The Perona–Malik nonlinear parabolic problem, which is widely used in image processing, is investigated in this paper from the numerical point of view. An explicit finite volume numerical scheme for this problem is presented and consistency property is proved

Parallel algorithms for solution of nonlinear diffusion problems in image smoothing

In this work we consider parallel algorithms for solution of nonlinear parabolic PDEs. First mathematical models describing nonlinear diffusion filters are presented. The finite‐volume method is used to approximate differential equations. Parallel algorithms are based on the domain decomposition method. The algorithms are implemented by using ParSol parallelization tool and a brief description of this tool is also presented. The efficiency of proposed parallel algorithms is investigated and results of the scalability analysis are given. Theoretical predictions are compared with results of computational experiments. Application of nonlinear diffusion filters for analysis of computer tomography images is discussed in the last section of the paper. Šiame darbe nagrinejami lygiagretieji algoritmai, kurie skirti netiesiniu nestacionariu difuzijos lygčiu sprendimui. Pirmiausia yra suformuluoti netiesiniu filtru matematiniai modeliai. Šie uždaviniai aproksimuoti baigtiniu tūriu schemomis. Lygiagretieji algoritmai konstruojami duomenu lygiagretumo metodu. Jie realizuoti autoriu sukurtu ParSolprogramavimo irankiu. Pateiktas trumpas šio irankio aprašymas. Ištirtas lygiagrečiuju algoritmu efektyvumas ir pateikti algoritmu išplečiamumo analizes rezultatai. Teorines išvados palygintos su skaičiavimo rezultatais. Netiesiniai difuziniai filtrai pritaikyti galvos kompiuteriniu tomogramu filtravimui. First Published Online: 14 Oct 201