ative Evaluation of Variational PDE Approaches for Binary Image Inpainting

Abstract

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.