Image Segmentation Based on Modified Fractional Allen–Cahn Equation
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-01-30
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
We present the image segmentation model using the modified Allen–Cahn equation with a fractional Laplacian.
The motion of the interface for the classical Allen–Cahn equation is known as the mean curvature flows, whereas its dynamics is changed to the macroscopic limit of Lévy process by replacing the Laplacian operator with the fractional one.
To numerical implementation, we prove the unconditionally unique solvability and energy stability of the numerical scheme for the proposed model.
The effect of a fractional Laplacian operator in our own and in the Allen–Cahn equation is checked by numerical simulations.
Finally, we give some image segmentation results with different fractional order, including the standard Laplacian operator.
American Psychological Association (APA)
Lee, Dongsun& Lee, Seunggyu. 2019. Image Segmentation Based on Modified Fractional Allen–Cahn Equation. Mathematical Problems in Engineering،Vol. 2019, no. 2019, pp.1-6.
https://search.emarefa.net/detail/BIM-1195370
Modern Language Association (MLA)
Lee, Dongsun& Lee, Seunggyu. Image Segmentation Based on Modified Fractional Allen–Cahn Equation. Mathematical Problems in Engineering No. 2019 (2019), pp.1-6.
https://search.emarefa.net/detail/BIM-1195370
American Medical Association (AMA)
Lee, Dongsun& Lee, Seunggyu. Image Segmentation Based on Modified Fractional Allen–Cahn Equation. Mathematical Problems in Engineering. 2019. Vol. 2019, no. 2019, pp.1-6.
https://search.emarefa.net/detail/BIM-1195370
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1195370