A New Operator Splitting Method for the Euler Elastica Model for Image Smoothing

Liang Jian Deng, Roland Glowinski, Xue Cheng Tai

Research output: Contribution to journalJournal articlepeer-review

32 Citations (Scopus)
54 Downloads (Pure)


Euler's elastica model has a wide range of applications in image processing and computer vision. However, the nonconvexity, the nonsmoothness, and the nonlinearity of the associated energy functional make its minimization a challenging task, further complicated by the presence of high order derivatives in the model. In this article we propose a new operator-splitting algorithm to minimize the Euler elastica functional. This algorithm is obtained by applying an operator-splitting based time discretization scheme to an initial value problem (dynamical flow) associated with the optimality system (a system of multivalued equations). The subproblems associated with the three fractional steps of the splitting scheme have either closed form solutions or can be handled by fast dedicated solvers. Compared with earlier approaches relying on ADMM (Alternating Direction Method of Multipliers), the new method has, essentially, only the time discretization step as free parameter to choose, resulting in a very robust and stable algorithm. The simplicity of the subproblems and its modularity make this algorithm quite efficient. Applications to the numerical solution of smoothing test problems demonstrate the efficiency and robustness of the proposed methodology.

Original languageEnglish
Pages (from-to)1190-1230
Number of pages41
JournalSIAM Journal on Imaging Sciences
Issue number2
Publication statusPublished - 25 Jun 2019

Scopus Subject Areas

  • Mathematics(all)
  • Applied Mathematics

User-Defined Keywords

  • Euler's elastica energy
  • Image smoothing
  • Operator splitting
  • Space projection


Dive into the research topics of 'A New Operator Splitting Method for the Euler Elastica Model for Image Smoothing'. Together they form a unique fingerprint.

Cite this