36
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Viscosity solutions for geodesic active contour under geometrical conditions

Pages 1375-1395 | Received 05 Nov 2005, Accepted 24 Apr 2007, Published online: 20 Aug 2008
 

Abstract

This paper addresses the issue of introducing geometrical constraints into segmentation processes in image analysis. This question has emerged from the analysis of classical tools: indeed, usual methods such as deformable models, fast marching prove to be fruitless when image data are missing or of poor quality or when the image owns homogeneous-textured regions. To cope with these hindrances, the idea developed hereafter consists of integrating geometrical constraints in the modelling to make the segmentation process easier to handle.

We have devised a geodesic active contour-based model, in which we are trying to determine a curve that best approaches the given points (geometrical data) while detecting the object under consideration (see also Apparato et al., Segmentation of medical image sequence under constraints: application to non-invasive assessment of pulmonary arterial hypertension, Int. J. Comput. Math. 5(2004), pp. 527–536 and Gout and Vieira-Testé C. Gout and S. Vieira-Testé, An algorithm for segmentation under interpolation conditions using deformable models, Int. J. Comput. Math. 80(1) (2003), pp. 47–54 where other approaches are given for this kind of problems). In this paper the main results concern the study of the existence and uniqueness of the viscosity solution of this problem (following three different approaches). We also give numerical examples on real data sets.

2000 AMS Subject Classification :

CCS Category :

Acknowledgements

The author is very grateful to Carole Le Guyader (INSA Rennes) for valuable comments. A large part of this work has been done at the ‘Laboratoire de Mathématiques Appliquées)’ at INSA de Rouen during the Ph. D. thesis of C. Le Guyader. The author also thanks Tom Craven for the invitation at the Math Department of the University of Hawai'i during the summer 2006 where this work has been developed.

Additional information

Notes on contributors

Christian Gout

Emails: [email protected] christian.gout@univpaufr

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.