An important task in image processing is the process of filling in missing parts of damaged images based on the information obtained from the surrounding areas. It is called inpainting. The goals of inpainting are numerous such as removing scratches in old photographic image, removing text and logos, restoration of damaged paintings. In this paper we present a nonlinear diffusion model for image inpainting based on a nonlinear partial differential equation as first proposed by Perona and Malik in [8]. In our previous work [3] the existence, uniqueness and regularity of the solution for the proposed mathematical model are established in an Hilbert space. The discretization of the partial differential equation of the proposed model is performed using finite elements method and finite differences method. For finite differences method our model is very simple to implement, fast, and produces nearly identical results to more complex, and usually slower, known methods. However for finite elements method we observe that it requires large computational cost, especially for high-resolution images. To avoid this slowing problem, domain decomposition algorithm has been proposed, aiming to split one large problem into many smaller problems. To illustrate the effective performance of our method, we present some experimental results on several images.
Abstract. The image's restoration is an essential step in medical imaging. Several Filters are developped to remove noise, the most interesting are filters who permits to denoise the image preserving semantically important structures. One class of recent adaptive denoising methods is the nonlinear Partial Differential Equations who knows currently a significant success. This work deals with mathematical study for a proposed nonlinear evolution partial differential equation for image processing. The existence and the uniqueness of the solution are established. Using a finite differences method we experiment the validity of the proposed model and we illustrate the efficiently of the method using some medical images. The Signal to Noise Ration (SNR) number is used to estimate the quality of the restored images.
Abstract:The generation process of medical images is inevitably accompanied by a certain noise which degrades the quality of the image and assigns the final clinical diagnosis. Therefore, the denoising step plays an important role in the treatment of medical images in order to prepare the steps of diagnosis and therapy. In this paper, we propose a nonlinear diffusion model for denoising of large size images. The numerical approach to this problem is based on an algorithm combining the methods of finite element and of domain decomposition. Numerical simulations show that the proposed algorithm is a useful alternative for the treatment of degraded images large size.
Due to advanced sensor technology, satellites and unmanned aerial vehicles (UAV) are producing a huge amount of data allowing advancement in all different kinds of earth observation applications. Thanks to this source of information, and driven by climate change concerns, renewable energy assessment became an increasing necessity among researchers and companies. Solar power, going from household rooftops to utility-scale farms, is reshaping the energy markets around the globe. However, the automatic identification of photovoltaic (PV) panels and solar farms' status is still an open question that, if answered properly, will help gauge solar power development and fulfill energy demands. Recently deep learning (DL) methods proved to be suitable to deal with remotely sensed data, hence allowing many opportunities to push further research regarding solar energy assessment. The coordination between the availability of remotely sensed data and the computer vision capabilities of deep learning has enabled researchers to provide possible solutions to the global mapping of solar farms and residential photovoltaic panels. However, the scores obtained by previous studies are questionable when it comes to dealing with the scarcity of photovoltaic systems. In this paper, we closely highlight and investigate the potential of remote sensing-driven DL approaches to cope with solar energy assessment. Given that many works have been recently released addressing such a challenge, reviewing and discussing them, it is highly motivated to keep its sustainable progress in future contributions. Then, we present a quick study highlighting how semantic segmentation models can be biased and yield significantly higher scores when inference is not sufficient. We provide a simulation of a leading semantic segmentation architecture U-Net and achieve performance scores as high as 99.78%. Nevertheless, further improvements should be made to increase the model's capability to achieve real photovoltaic units.
Abstract. We present in this work a numerical study of a problem governed by Navier-Stokes equations and heat equation. The mathematical problem under consideration is obtained by modelling the natural convection of an incompressible fluid, in laminar flow between two horizontal concentric coaxial cylinders, the temperature of the inner cylinder is supposed to be greater than the outer one. The numerical simulation of the flow is carried out by collocation-Legendre method. The influence of Prandtl and Rayleigh numbers is investigated.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.