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Mathematics
Special Issues
Applications of Partial Differential Equations in Image Analysis
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Applications of Partial Differential Equations in Image Analysis

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Difference and Differential Equations".

Deadline for manuscript submissions: closed (30 November 2020) | Viewed by 3577

Special Issue Editors

Prof. Dr. Costica Morosanu

E-Mail Website
Guest Editor
Department of Mathematics, Al. I. Cuza University of Iasi, Bdul Carol I 11, 700506 Iasi, Romania
Interests: numerical modeling; numerical analysis; mathematical modelling
Prof. Dr. Ovidiu Cârjă

E-Mail Website
Guest Editor
Department of Mathematics, Al. I. Cuza University of Iasi, Bdul Carol I 11, 700506 Iasi, Romania
Interests: controllability and time optimal control; viability and invariance for differential inclusions; Hamilton-Jacobi-Bellman equations
Prof. Dr. Mitica Craus

E-Mail Website
Guest Editor
Department of Computer Science and Engineering, “Gheorghe Asachi” Technical University of Iaşi, 27 Dimitrie Mangeron Street, 700050 Iasi, Romania
Interests: algorithm design; parallel and distributed computing; combinatorial optimization; data mining; Grid and Cloud computing
Prof. Dr. Gheorghiu Calin-Ioan

E-Mail Website
Guest Editor
“T. Popoviciu” Institute of Numerical Analysis, Romanian Academy, Cluj-Napoca, Romania
Interests: numerical analysis; differential equations; fluid mechanics; spectral methods

Special Issue Information

Dear Colleagues,

During the last number of years, there has been a significant increase in the level of interest in image morphology, full-color image processing, image data compression, image recognition, and knowledge-based image analysis systems.

Image analysis is the extraction of meaningful information from images; mainly from digital images by means of digital image processing techniques. Some techniques which are used in digital image processing include: partial differential equations (anisotropic diffusion), image restoration (denoising-deblurring), image filtering, image reconstruction, image segmentation, neural networks, etc.

The present Special Issue "Applications of Partial Differential Equations in Image Analysis" is dedicated to researchers working in the fields of qualitative and quantitative analysis of nonlinear evolution equations and their applications in image analysis. Both analytical studies as well as simulation-based studies will be considered.

Moreover, this Special Issue gives an opportunity for researchers and practitioners to communicate their ideas.

Prof. Costica Morosanu
Prof. Ovidiu Cârjă
Prof. Mitica Craus
Prof. Gheorghiu Calin-Ioan
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • well-posedness (existence, regularity, uniqueness) in the presence of different boundary conditions
  • numerical approximation schemes for solving nonlinear equation and systems (convergence, stability and consistency)
  • boundary and distributed optimal control problems
  • numerical simulations and possible industrial applications (medical imaging, autonomous driving, for example).

Published Papers (2 papers)

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Research

23 pages, 595 KiB  
Article
Rigorous Mathematical Investigation of a Nonlocal and Nonlinear Second-Order Anisotropic Reaction-Diffusion Model: Applications on Image Segmentation
by Costică Moroşanu and Silviu Pavăl
Mathematics 2021, 9(1), 91; https://doi.org/10.3390/math9010091 - 04 Jan 2021
Cited by 9 | Viewed by 1613
Abstract
In this paper we are addressing two main topics, as follows. First, a rigorous qualitative study is elaborated for a second-order parabolic problem, equipped with nonlinear anisotropic diffusion and cubic nonlinear reaction, as well as non-homogeneous Cauchy-Neumann boundary conditions. Under certain assumptions on [...] Read more.
In this paper we are addressing two main topics, as follows. First, a rigorous qualitative study is elaborated for a second-order parabolic problem, equipped with nonlinear anisotropic diffusion and cubic nonlinear reaction, as well as non-homogeneous Cauchy-Neumann boundary conditions. Under certain assumptions on the input data: f(t,x), w(t,x) and v0(x), we prove the well-posedness (the existence, a priori estimates, regularity, uniqueness) of a solution in the Sobolev space Wp1,2(Q), facilitating for the present model to be a more complete description of certain classes of physical phenomena. The second topic refers to the construction of two numerical schemes in order to approximate the solution of a particular mathematical model (local and nonlocal case). To illustrate the effectiveness of the new mathematical model, we present some numerical experiments by applying the model to image segmentation tasks. Full article
(This article belongs to the Special Issue Applications of Partial Differential Equations in Image Analysis)
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12 pages, 647 KiB  
Article
An Accelerating Numerical Computation of the Diffusion Term in a Nonlocal Reaction-Diffusion Equation
by Mitică CRAUS and Silviu-Dumitru PAVĂL
Mathematics 2020, 8(12), 2111; https://doi.org/10.3390/math8122111 - 26 Nov 2020
Cited by 5 | Viewed by 1349
Abstract
In this paper we propose and compare two methods to optimize the numerical computations for the diffusion term in a nonlocal formulation for a reaction-diffusion equation. The diffusion term is particularly computationally intensive due to the integral formulation, and thus finding a better [...] Read more.
In this paper we propose and compare two methods to optimize the numerical computations for the diffusion term in a nonlocal formulation for a reaction-diffusion equation. The diffusion term is particularly computationally intensive due to the integral formulation, and thus finding a better way of computing its numerical approximation could be of interest, given that the numerical analysis usually takes place on large input domains having more than one dimension. After introducing the general reaction-diffusion model, we discuss a numerical approximation scheme for the diffusion term, based on a finite difference method. In the next sections we propose two algorithms to solve the numerical approximation scheme, focusing on finding a way to improve the time performance. While the first algorithm (sequential) is used as a baseline for performance measurement, the second algorithm (parallel) is implemented using two different memory-sharing parallelization technologies: Open Multi-Processing (OpenMP) and CUDA. All the results were obtained by using the model in image processing applications such as image restoration and segmentation. Full article
(This article belongs to the Special Issue Applications of Partial Differential Equations in Image Analysis)
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