  Euler's elastica model has a wide range of applications in Image Processing
and Computer Vision. However, the non-convexity, the non-smoothness 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 sub-problems 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
sub-problems 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.
