Research Article

A Phase Field Model for Image Decomposition and Smoothing

Volume: 14 September 16, 2026
EN TR

A Phase Field Model for Image Decomposition and Smoothing

Abstract

In this paper we propose a new phase field model for image decomposition and smoothing based on a modification of the Cahn-Hilliard equation. The Cahn-Hilliard equation was first formulated as the minimization of a free energy that reflects the topological events, phase coarsening and separation processes. We replaced the energy density in this equation with the derivative of a new convex energy which allows only the decomposition of phase values into multiple layers. This system, although based on a variational formulation does not require the solution of an optimization problem and its main advantage is the flexibility it provides in designing decomposition algorithms. Within this framework, we developed several algorithms based on order statistics for image smoothing and decomposition.

Keywords

References

  1. [1] Perona, P. and Malik, J. Scale-space and edge detection using anisotropic diffusion. Pattern Analysis and Machine Intelligence, vol. 12, pp. 629–639, july 1990.
  2. [2] Tomasi, C. and Manduchi, R. Bilateral filtering for gray and color images. In IEEE International Conference on Computer Vision, 1998, pp. 839–846.
  3. [3] Comaniciu, D. Image smoothing via l0 gradient minimization. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 24, pp. 603–619, August 2002.
  4. [4] Farbman, Z., Fattal, R., and Lischinski, D. Edge-preserving decompositions for multi-scale tone and detail manipulation. ACM Transactions on Graphics (TOG), Proceedings of ACM SIGGRAPH, vol. 27, August 2008.
  5. [5] Subr, K., Soler, C. and Durand, F. Edge-preserving multiscale image decomposition based on local extrema. ACM Transactions on Graphics (TOG), Proceedings of ACM SIGGRAPH, vol. 28, december 2009.
  6. [6] Karacan, L., Erdem, E., and Erdem, A. Structure-preserving image smoothing via region covariances. ACM Transactions on Graphics (TOG),Proceedings of ACM SIGGRAPH, vol. 32, November 2013.
  7. [7] Xu, L., Lu, C., Xu, Y. and Jia, J. Image smoothing via l0 gradient minimization. ACM Transactions on Graphics (TOG), Proceedings of ACM SIGGRAPH, vol. 30, december 2011.
  8. [8] Samson, C., Blanc-Feraud, L., Aubert, G. and Zerubia, J. Image classification using a variational approach. Inria report-00073161, 1998.

Details

Primary Language

English

Subjects

Computer Software

Journal Section

Research Article

Publication Date

September 16, 2026

Submission Date

March 30, 2025

Acceptance Date

May 1, 2026

Published in Issue

Year 2026 Volume: 14

APA
Ruyam, A. (2026). A Phase Field Model for Image Decomposition and Smoothing. Balkan Journal of Electrical and Computer Engineering, 14. https://doi.org/10.17694/bajece.1668312
AMA
1.Ruyam A. A Phase Field Model for Image Decomposition and Smoothing. Balkan Journal of Electrical and Computer Engineering. 2026;14. doi:10.17694/bajece.1668312
Chicago
Ruyam, Acar. 2026. “A Phase Field Model for Image Decomposition and Smoothing”. Balkan Journal of Electrical and Computer Engineering 14 (September). https://doi.org/10.17694/bajece.1668312.
EndNote
Ruyam A (September 1, 2026) A Phase Field Model for Image Decomposition and Smoothing. Balkan Journal of Electrical and Computer Engineering 14
IEEE
[1]A. Ruyam, “A Phase Field Model for Image Decomposition and Smoothing”, Balkan Journal of Electrical and Computer Engineering, vol. 14, Sept. 2026, doi: 10.17694/bajece.1668312.
ISNAD
Ruyam, Acar. “A Phase Field Model for Image Decomposition and Smoothing”. Balkan Journal of Electrical and Computer Engineering 14 (September 1, 2026). https://doi.org/10.17694/bajece.1668312.
JAMA
1.Ruyam A. A Phase Field Model for Image Decomposition and Smoothing. Balkan Journal of Electrical and Computer Engineering. 2026;14. doi:10.17694/bajece.1668312.
MLA
Ruyam, Acar. “A Phase Field Model for Image Decomposition and Smoothing”. Balkan Journal of Electrical and Computer Engineering, vol. 14, Sept. 2026, doi:10.17694/bajece.1668312.
Vancouver
1.Acar Ruyam. A Phase Field Model for Image Decomposition and Smoothing. Balkan Journal of Electrical and Computer Engineering. 2026 Sep. 1;14. doi:10.17694/bajece.1668312

All articles published by BAJECE are licensed under the Creative Commons Attribution 4.0 International License. This permits anyone to copy, redistribute, remix, transmit and adapt the work provided the original work and source is appropriately cited.Creative Commons Lisansı