ative Evaluation of Variational PDE Approaches for Binary Image Inpainting - Al Aliwi, Layth Hussein Abdul Hussein (University of Thi-Qar Journal, 2025)
This research aims to study and evaluate the effectiveness of methods based on partial differential equations (PDEs) in restoring binary images, which are widely used in document applications, optical character recognition (OCR), industrial scanning, and medical imaging. Binary images are a special case compared to grayscale or color images, as they consist of only two values (0 and 1), making them more sensitive to noise or pixel loss. The main problem is that many traditional PDE-based restoration methods, such as the thermal diffusion model or the Perona–Malik equation, fail to preserve fine edges and lead to significant geometric distortions? The research sought to achieve a set of objectives, most notably reviewing current methods for restoring binary images using PDEs, proposing a modified model that is compatible with the nature of these images, and conducting practical experiments to compare its performance with traditional models. The research also focused on adopting quantitative and qualitative evaluation indicators appropriate for the nature of binary images, such as PSNR, SSIM, and bit error ratio (BER), in addition to edge preservation indicators. The research is based on fundamental hypotheses, most notably that modified or specifically developed models for binary images will outperform conventional models, and that the use of higher-order equations, such as the Cahn–Hilliard equation, will contribute to improved restoration quality and better edge preservation. The discussion demonstrated that actual performance is significantly affected by the choice of numerical parameters, such as the diffusion coefficient and time step? The results confirm that binary image restoration using modified PDEs represents a promising approach that combines theoretical accuracy with practical utility. It provides practical solutions to challenges associated with binary images in multiple fields, opening the way for future studies that integrate mathematical models and deep learning algorithms.