American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Second order estimates for boundary blow-up solutions of elliptic equations
  • PROC Home
  • This Issue
  • Next Article
    A necessary and sufficient condition for the existence of periodic solutions of linear impulsive differential equations with distributed delay
2007, 2007(Special): 44-53. doi: 10.3934/proc.2007.2007.44

Contour enhancement via a singular free boundary problem

Anna Lisa Amadori 1,

1. 

Dipartimento di Scienze Applicate - Università di Napoli "Parthenope", Via A. De Gasperi, 5 - 80133 Napoli, Italy

Received  September 2006 Revised  August 2007 Published  September 2007

We study a degenerate nonlinear parabolic equation with moving boundaries which describes the technique of contour enhancement in image processing. Such problem arises from the model by Malladi and Sethian after an asymptotic expansion suggested by Barenblatt: in order to recover the phenomenon of mass concentration, a singular data is imposed at the free boundary.
Keywords: Free boundary problems, image processing..
Mathematics Subject Classification: Primary: 35R35, 94A08; Secondary: 35K55, 35K65.
Citation: Anna Lisa Amadori. Contour enhancement via a singular free boundary problem. Conference Publications, 2007, 2007 (Special) : 44-53. doi: 10.3934/proc.2007.2007.44
[1]

Avner Friedman. Free boundary problems arising in biology. Discrete and Continuous Dynamical Systems - B, 2018, 23 (1) : 193-202. doi: 10.3934/dcdsb.2018013
[2]

Hong-Mei Chen, Hai-Wen Xu, Jun-Feng Yang. A hybrid alternating minimization algorithm for structured convex optimization problems with application in Poissonian image processing. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022163
[3]

Nam-Yong Lee, Bradley J. Lucier. Preconditioned conjugate gradient method for boundary artifact-free image deblurring. Inverse Problems and Imaging, 2016, 10 (1) : 195-225. doi: 10.3934/ipi.2016.10.195
[4]

Jianhong (Jackie) Shen, Sung Ha Kang. Quantum TV and applications in image processing. Inverse Problems and Imaging, 2007, 1 (3) : 557-575. doi: 10.3934/ipi.2007.1.557
[5]

Avner Friedman. Free boundary problems for systems of Stokes equations. Discrete and Continuous Dynamical Systems - B, 2016, 21 (5) : 1455-1468. doi: 10.3934/dcdsb.2016006
[6]

Serena Dipierro, Enrico Valdinoci. (Non)local and (non)linear free boundary problems. Discrete and Continuous Dynamical Systems - S, 2018, 11 (3) : 465-476. doi: 10.3934/dcdss.2018025
[7]

Noriaki Yamazaki. Almost periodicity of solutions to free boundary problems. Conference Publications, 2001, 2001 (Special) : 386-397. doi: 10.3934/proc.2001.2001.386
[8]

Lekbir Afraites, Abdelghafour Atlas, Fahd Karami, Driss Meskine. Some class of parabolic systems applied to image processing. Discrete and Continuous Dynamical Systems - B, 2016, 21 (6) : 1671-1687. doi: 10.3934/dcdsb.2016017
[9]

Yan Jin, Jürgen Jost, Guofang Wang. A new nonlocal variational setting for image processing. Inverse Problems and Imaging, 2015, 9 (2) : 415-430. doi: 10.3934/ipi.2015.9.415
[10]

Yong Zheng Ong, Haizhao Yang. Generative imaging and image processing via generative encoder. Inverse Problems and Imaging, 2022, 16 (3) : 525-545. doi: 10.3934/ipi.2021060
[11]

Avner Friedman, Xiulan Lai. Free boundary problems associated with cancer treatment by combination therapy. Discrete and Continuous Dynamical Systems, 2019, 39 (12) : 6825-6842. doi: 10.3934/dcds.2019233
[12]

Ugur G. Abdulla, Evan Cosgrove, Jonathan Goldfarb. On the Frechet differentiability in optimal control of coefficients in parabolic free boundary problems. Evolution Equations and Control Theory, 2017, 6 (3) : 319-344. doi: 10.3934/eect.2017017
[13]

Daniela De Silva, Fausto Ferrari, Sandro Salsa. On two phase free boundary problems governed by elliptic equations with distributed sources. Discrete and Continuous Dynamical Systems - S, 2014, 7 (4) : 673-693. doi: 10.3934/dcdss.2014.7.673
[14]

Daniela De Silva, Fausto Ferrari, Sandro Salsa. Recent progresses on elliptic two-phase free boundary problems. Discrete and Continuous Dynamical Systems, 2019, 39 (12) : 6961-6978. doi: 10.3934/dcds.2019239
[15]

Huiqiang Jiang. Regularity of a vector valued two phase free boundary problems. Conference Publications, 2013, 2013 (special) : 365-374. doi: 10.3934/proc.2013.2013.365
[16]

Mingxin Wang. Existence and uniqueness of solutions of free boundary problems in heterogeneous environments. Discrete and Continuous Dynamical Systems - B, 2019, 24 (2) : 415-421. doi: 10.3934/dcdsb.2018179
[17]

Jesús Ildefonso Díaz. On the free boundary for quenching type parabolic problems via local energy methods. Communications on Pure and Applied Analysis, 2014, 13 (5) : 1799-1814. doi: 10.3934/cpaa.2014.13.1799
[18]

Mingxin Wang. Erratum: Existence and uniqueness of solutions of free boundary problems in heterogeneous environments. Discrete and Continuous Dynamical Systems - B, 2022, 27 (9) : 5179-5180. doi: 10.3934/dcdsb.2021269
[19]

Zbigniew Gomolka, Boguslaw Twarog, Jacek Bartman. Improvement of image processing by using homogeneous neural networks with fractional derivatives theorem. Conference Publications, 2011, 2011 (Special) : 505-514. doi: 10.3934/proc.2011.2011.505
[20]

Juan C. Moreno, V. B. Surya Prasath, João C. Neves. Color image processing by vectorial total variation with gradient channels coupling. Inverse Problems and Imaging, 2016, 10 (2) : 461-497. doi: 10.3934/ipi.2016008

 Impact Factor: 

Tools

Metrics

  • PDF downloads (117)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy