Augmented Lagrangian method for an Euler's elastica based segmentation model that promotes convex contours

Author
Bae, Egil
Tai, Xue-Cheng
Wei, Zhu
Date Issued
2017
Keywords
Variasjonsregning
Bildebehandling
Permalink
http://hdl.handle.net/20.500.12242/626
https://ffi-publikasjoner.archive.knowledgearc.net/handle/20.500.12242/626
DOI
10.3934/ipi.2017001
Collection
Articles
Description
Bae, Egil; Tai, Xue-Cheng; Wei, Zhu. Augmented Lagrangian method for an Euler's elastica based segmentation model that promotes convex contours. Inverse Problems and Imaging 2017 ;Volum 11.(1) s. 1-23
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Abstract
In this paper, we propose an image segmentation model where an L1 variant of the Euler's elastica energy is used as boundary regularization. An interesting feature of this model lies in its preference for convex segmentation contours. However, due to the high order and non-differentiability of Euler's elastica energy, it is nontrivial to minimize the associated functional. As in recent work on the ordinary L2 Euler's elastica model in imaging, we propose using an augmented Lagrangian method to tackle the minimization problem. Specifically, we design a novel augmented Lagrangian functional that deals with the mean curvature term differently than in previous works. The new treatment reduces the number of Lagrange multipliers employed, and more importantly, it helps represent the curvature more effectively and faithfully. Numerical experiments validate the efficiency of the proposed augmented Lagrangian method and also demonstrate new features of this particular segmentation model, such as shape driven and data driven properties.
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