Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Bücher
Zeitschriften
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
MTZ-Fachkongress

Antriebe und Energiesysteme von morgen


Austausch von Automobil- und Energiewirtschaft

Am 14./15. Mai geht es in Chemnitz um die Mobilitätswende durch Elektro- und Wasserstofffahrzeuge.
Erweiterte Suche
Anmelden
nach oben
3D Research
Erschienen in: 3D Research 3/2018

01.09.2018 | 3DR Express

Mixed Finite Element Approximation for Bivariate Perona–Malik Model Arising in 2D and 3D Image Denoising

verfasst von: Amal Hjouji, Mostafa Jourhmane, Jaouad EL-Mekkaoui, Mohammed Es-sabry

Erschienen in: 3D Research | Ausgabe 3/2018

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this paper, we present a new model of nonlinear diffusion arising in image processing field based on the Perona–Malik equation which we call the bivariate Perona–Malik model. The aim of this model is to remove image noise while preserving edges, boundaries, and textures. To solve this model we use a new algorithm based on mixed finite element method. In this context we prove mathematically the existence and uniqueness of the solution of the proposed model in a well chosen space. At last, we present the experimental results in 2D and 3D images filtering, which demonstrate the efficiency and effectiveness of our algorithm and finally, we compare it with other well known methods such as the finite difference method presented by Perona et al. (IEEE Trans Pattern Anal Mach Intell 12:629–639, 1990), the finite element method and the finite volume method studied by Handlovičová et al. (J Vis Commun Image Represent 13:217–237, 2002).
Vorheriger Artikel A Mamdani Fuzzy Logic System to Enhance Solar Cell Micro-Cracks Image Processing
Nächster Artikel Pixel Overlapping Image Steganography Using PVD and Modulus Function

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Literatur
1.
Perona, P., & Malik, J. (1990). Scale space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12, 629–639.CrossRef
2.
Catte, F., Lions, P. L., Morel, J. M., & Coll, T. (1992). Image selective smoothing and edge detection by nonlinear diffusion. SIAM Journal on Numerical Analysis, 29, 182–193.MathSciNetCrossRef
3.
Handlovicova, A., Mikula, K., & Sgallari, F. (2002). Variational numerical methods for solving nonlinear diffusion equations arising in image processing. Journal of Visual Communication and Image Representation, 13, 217–237.CrossRef
4.
Alvarez, L., Lions, P. L., & Morel, J. M. (1992). Image selective smoothing and edge detection by nonlinear diffusion II, SIAM. Journal of Numerical Analysis, 29, 845–866.CrossRef
5.
Brezzi, E., & Fortin, M. (1991). Mixed and hybrid finite element methods. New York: Springer.CrossRef
6.
Stenberg, R. (1990). A technique for analysing finite element methods for viscous incompressible flow. International Journal for Numerical Methods in Fluids, 11, 935–948.MathSciNetCrossRef
7.
Aboulaicha, R., Meskine, D., & Souissi, A. (2008). New diffusion models in image processing. Computers and Mathematics with Applications, 56, 874–882.MathSciNetCrossRef
8.
Mikula, K., & Ramarosy, N. (2001). Semi-implicit finite volume scheme for solving nonlinear diffusion equations in image processing. Numerische Mathematik, 89, 561–590.MathSciNetCrossRef
9.
Alvarez, L., & Morel, J. M. (1994). Formalization and computational aspects of image analysis. Acta Numerica, 3, 1–59.MathSciNetCrossRef
10.
Preusser, T., & Rumpf, M. (1999). An adaptive finite element method for large scale image processing. In M. Nielsen, P. Johansen, O. F. Olsen, & J. Weickert (Eds.), Proceedings of ScaleSpace-99 (pp. 223–234). Berlin: Springer.
11.
Osher, S., & Sethian, J. (1988). Front propagating with curvature dependent speed: Algorithms based on the Hamilton–Jacobi formulation. Journal of Computational Physics, 79, 12–49.MathSciNetCrossRef
12.
Sethian, J. A. (1990). Numerical algotithm for propagating interfaces: Hamilton–Jacobi equations and conservation laws. Journal of Differential Geometry, 31, 131–161.MathSciNetCrossRef
13.
Dziuk, G. (1994). Convergence of a semidiscrete scheme for the curve shortening flow. Mathematical Models and Methods in Applied Sciences, 4, 589–606.MathSciNetCrossRef
14.
15.
Sapiro, G., & Tannenbaum, A. (1994). On affine plane curve evolution. Journal of Functional Analysis, 119, 79–120.MathSciNetCrossRef
16.
Walkington, N. J. (1996). Algorithms for computing motion by mean curvature, SIAM. Journal of Numerical Analysis, 33, 2215–2238.CrossRef
17.
Brezzi, F., & Falk, R. (1991). Stability of higher order Taylor-Hood methods. SIAM Journal on Numerical Analysis, 28(3), 581–590.MathSciNetCrossRef
18.
Brenner, S. C., & Scott, L. R. (2002). The mathematical theory of finite element methods, of Texts in Applied Mathematics (2nd ed., p. 15). New York: Springer.CrossRef
19.
Wieners, C. (2003). Taylor-Hood elements in 3D, analysis and simulation of multifield problems (pp. 189–196). Berlin, Heidelberg: Springer.CrossRef
20.
Handlovičová, A., Mikula, K., & Sarti, A. (1999). Numerical solution of parabolic equations related to level set formulation of mean curvature flow. Computing and Visualization in Science, 1, 179–182.MATH
21.
Kačur, J., & Mikula, K. (1995). Solution of nonlinear diffusion appearing in image smoothing and edge detection. Applied Numerical Mathematics, 17, 47–59.MathSciNetCrossRef
22.
Eymard, R., Gallouet, T., & Herbin, R. (2000). The finite volume method. In P. Ciarlet & P. L. Lions (Eds.), Handbook for numerical analysis (Vol. 7, pp. 715–1022). Amsterdam: Elsevier.
23.
Bansch, E., & Mikula, K. (1999). Adaptivity in 3D image processing, Preprint 99–14. Zentrum fur Technomathematik: Universitat Bremen.
24.
Sarti, A., Mikula, K., & Sgallari, F. (1999). Nonlinear multiscale analysis of 3D echocardiographic sequences. IEEE Transactions on Medical Imaging, 18, 453–466.CrossRef
25.
John, F. (1991). Partial differential equations (4th edn). Springer. ISBN 978-0-387-90609-6.
26.
Farhloul, M., & Fortin, M. (1993). A new mixed finite element for the stokes and elasticity problems. SIAM Journal on Numerical Analysis, 30(4), 971.MathSciNetCrossRef
Metadaten
Titel
Mixed Finite Element Approximation for Bivariate Perona–Malik Model Arising in 2D and 3D Image Denoising
verfasst von
Amal Hjouji
Mostafa Jourhmane
Jaouad EL-Mekkaoui
Mohammed Es-sabry
Publikationsdatum
01.09.2018
Verlag
3D Display Research Center
Erschienen in
3D Research / Ausgabe 3/2018
Elektronische ISSN: 2092-6731
DOI
https://doi.org/10.1007/s13319-018-0187-6

Weitere Artikel der Ausgabe 3/2018

3D Research 3/2018 Zur Ausgabe

3DR Express

Pixel Overlapping Image Steganography Using PVD and Modulus Function

3DR Express

A New Objective Image Quality Assessment Metric: For Color and Grayscale Images

3DR Express

Impact of Video File Format on Quality of Experience (QoE) of Multimedia Content

3DR Express

3D Point Cloud Initial Registration Using Surface Curvature and SURF Matching

3DR Express

Automatic Depth Prediction from 2D Videos Based on Non-parametric Learning and Bi-directional Depth Propagation

3DR Express

Asymmetric Optical Image Triple Masking Encryption Based on Gyrator and Fresnel Transforms to Remove Silhouette Problem

Premium Partner

    Bildnachweise