Image inpainting is the process of recovering the damage areas in the images in an undetectable way, it is considered the important one of the subjects in image processing. There are many applications of image inpainting include the restoration of damaged images, paintings, and movies, to the removal of selected objects, such as text, lines, subtitles, publicity, and stamps. The main objective of inpainting is to reconstruct the missing region in such a way that the observer does not come to know that the image has been manipulated. Inpainting methods can be categorized into global and local methods, the global methods are applied to reconstruct the damaged areas in the image based on the information in the data of images that have the same content. While the local methods are used to reconstruct the missing regions based on the information in the rest parts of the image. There are several local methods proposed for image inpainting such as PDE-based inpainting (PDE-BI), exemplar-based inpainting (EBI), hybrid, and texture synthesis methods. In this paper, a review of different PDE and variational methods used for image inpainting is provided. Different PDE-BI methods like 2nd-and high-order of variational and PDE methods are discussed with its pros and cons.
The modeling of many phenomena in various fields such as mathematics, physics, chemistry, engineering, biology, and astronomy is done by the nonlinear partial differential equations (PDE). The hyperbolic telegraph equation is one of them, where it describes the vibrations of structures (e.g., buildings, beams, and machines) and are the basis for fundamental equations of atomic physics. There are several analytical and numerical methods are used to solve the telegraph equation. An analytical solution considers framing the problem in a well-understood form and calculating the exact resolution. It also helps to understand the answers to the problem in terms of accuracy and convergence. These analytic methods have limitations with accuracy and convergence. Therefore, a novel analytic approximate method is proposed to deal with constraints in this paper. This method uses the Taylors' series in its derivation. The proposed method has used for solving the secondorder, hyperbolic equation (Telegraph equation) with the initial condition. Three examples have presented to check the effectiveness, accuracy, and convergence of the method. The solutions of the proposed method also compared with those obtained by the Adomian decomposition method (ADM), and the Homotopy analysis method (HAM). The technique is easy to implement and produces accurate results. In particular, these results display that the proposed method is efficient and better than the other methods in terms of accuracy and convergence.
Photo-Optical Instrumentation Engineers (SPIE). One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this publication for a fee or for commercial purposes, and modification of the contents of the publication are prohibited.
Image denoising is process of removing the noise (i.e. artifacts) in digital image. Noise reduction is an essential process of image processing in order to improve, analyze and interpret important information in an image. Edges are important to the visual appearance of images, to preserve important features such as edges and corners during the noise reduction process. A class of fourth- and second-order partial differential equations (PDEs) are used to optimize the trade-off between noise removal and edge preservation. Image quality assessment plays an important role in various image processing applications. It is still an active field of research. Several techniques have been suggested for measuring image quality but none of them are ideal for measuring the quality. This paper presents a new assessment of image quality based on topological data analysis (TDA) which is used for evaluating noise removal from colour images and also for assessing the performance of PDE-based denoising models. The experimental results show that the proposed assessment model gives high correlation. Furthermore, the proposed method provides very low computational load and similar extraction of characteristics to human perceptional assessment.
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