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A phase field higher-order active contour model of directed networks.

El Ghoul, A. and Jermyn, I.H. and Zerubia, J. (2009) 'A phase field higher-order active contour model of directed networks.', in 2009 IEEE 12th International Conference on Computer Vision Workshops ; proceedings. Piscataway, NJ: IEEE, pp. 398-404.


The segmentation of directed networks is an important problem in many domains, e.g. medical imaging (vascular networks) and remote sensing (river networks). Directed networks carry a unidirectional flow in each branch, which leads to characteristic geometric properties. In this paper, we present a nonlocal phase field model of directed networks. In addition to a scalar field representing a region by its smoothed characteristic function and interacting non-locally so as to favour network configurations, the model contains a vector field representing the `flow' through the network branches. The vector field is strongly encouraged to be zero outside, and of unit magnitude inside the region; and to have zero divergence. This prolongs network branches; controls width variation along a branch; and produces asymmetric junctions for which total incoming branch width approximately equals total outgoing branch width. In conjunction with a new interaction function, it also allows a broad range of stable branch widths. We analyse the energy to constrain the parameters, and show geometric experiments confirming the above behaviour. We also show a segmentation result on a synthetic river image.

Item Type:Book chapter
Full text:(AM) Accepted Manuscript
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Publisher statement:© 2009 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Date accepted:No date available
Date deposited:15 April 2016
Date of first online publication:September 2009
Date first made open access:No date available

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