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Euler's elastica model has a wide range of applications in Image Processingand Computer Vision. However, the non-convexity, the non-smoothness and thenonlinearity of the associated energy functional make its minimization achallenging task, further complicated by the presence of high order derivativesin the model. In this article we propose a new operator-splitting algorithm tominimize the Euler elastica functional. This algorithm is obtained by applyingan operator-splitting based time discretization scheme to an initial valueproblem (dynamical flow) associated with the optimality system (a system ofmultivalued equations). The sub-problems associated with the three fractionalsteps of the splitting scheme have either closed form solutions or can behandled by fast dedicated solvers. Compared with earlier approaches relying onADMM (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 thesub-problems and its modularity make this algorithm quite efficient.Applications to the numerical solution of smoothing test problems demonstratethe efficiency and robustness of the proposed methodology.

A New Operator Splitting Method for Euler's Elastica Model