Journal
SIAM JOURNAL ON IMAGING SCIENCES
Volume 4, Issue 1, Pages 313-344Publisher
SIAM PUBLICATIONS
DOI: 10.1137/100803730
Keywords
Euler's elastica; image inpainting; image denoising; image zooming; constrained minimization; augmented Lagrangian method
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Funding
- MOE (Ministry of Education) [T207N2202]
- IDM [NRF2007IDMIDM002-010]
- Austrian Science Fund (FWF) under the START-Program [Y305]
- SFB Mathematical Optimization and Its Applications in Biomedical Sciences
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Minimization of functionals related to Euler's elastica energy has a wide range of applications in computer vision and image processing. A high order nonlinear partial differential equation (PDE) needs to be solved, and the gradient descent method usually takes high computational cost. In this paper, we propose a fast and efficient numerical algorithm to solve minimization problems related to Euler's elastica energy and show applications to variational image denoising, image inpainting, and image zooming. We reformulate the minimization problem as a constrained minimization problem, followed by an operator splitting method and relaxation. The proposed constrained minimization problem is solved by using an augmented Lagrangian approach. Numerical tests on real and synthetic cases are supplied to demonstrate the efficiency of our method.
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