A fast augmented lagrangian method for euler's elastica model

Authors:
Yuping Duan;Yu Wang;Xue-Cheng Tai;Jooyoung Hahn
Affiliations:
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore;Computer Science Department, Technion, Haifa, Israel;Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore and Department of Mathematics, University of Bergen, Bergen, Norway;Institute for Mathematics and Scientific Computing, University of Graz, Austria
Venue:
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Year:
2011

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Abstract

In this paper, a fast algorithm for Euler's elastica functional is proposed, in which the Euler's elastica functional is reformulated as a constrained minimization problem. Combining the augmented Lagrangian method and operator splitting techniques, the resulting saddle-point problem is solved by a serial of sub-problems. To tackle the nonlinear constraints arising in the model, a novel fixed-point-based approach is proposed so that all the sub-problems either are linear problems or have closed form solutions. Numerical examples are provided to demonstrate the performance of the proposed method.