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

El Ghoul, A.; Jermyn, I.H.; Zerubia, J.

Abstract

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.

Citation

El Ghoul, A., Jermyn, I., & Zerubia, J. (2009, September). A phase field higher-order active contour model of directed networks. Presented at 2009 IEEE 12th International Conference on Computer Vision Workshops (Non-Rigid Shape Analysis and Deformable Image Alignment), at ICCV, Kyoto

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 2009 IEEE 12th International Conference on Computer Vision Workshops (Non-Rigid Shape Analysis and Deformable Image Alignment)
• Publication Date: Sep 1, 2009
• Deposit Date: Aug 12, 2011
• Publicly Available Date: Apr 15, 2016
• Publisher: Institute of Electrical and Electronics Engineers
• Pages: 398-404
• Book Title: 2009 IEEE 12th International Conference on Computer Vision Workshops ; proceedings.
• DOI: https://doi.org/10.1109/iccvw.2009.5457672
• Public URL: https://durham-repository.worktribe.com/output/1158813