A New Operator Splitting Method for minimization of Euler's Elastica energy
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题 目：A New Operator Splitting Method for minimization of Euler's Elastica energy
报告人：台雪成 教授 （香港浸会大学数学系）
摘 要：Euler's elastica energy 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 energy. 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 and segmentation test problems demonstrate the efficiency and robustness of the proposed methodology.
This talk is based on: LJ Deng, R Glowinski, XC Tai, A New Operator Splitting
Method for Euler's Elastica Model, 2018, SIAM Journal on Imaging Sciences,
Volume 12, Issue 2, Pages 1190-1230.