In: Paparoditis N., Pierrot-Deseilligny M.. Mallet C.. Tournaire O. (Eds), IAPRS. Vol. XXXVIII. Part ЗА - Saint-Mandé, France. September 1-3. 2010
220
Figure 3: The final configuration of 4> (thresholded) and v corre
sponding to the images in the third and fourth rows in figure 2.
The vector field is indeed zero outside the network and of con
stant (unit) magnitude inside, smooth, parallel to branch bound
aries, and conserved along network branches and at junctions.
El Ghoul, A., Jermyn, I. H. and Zerubia, J„ 2009b. A phase field
higher-order active contour model of directed networks. In: 2nd
IEEE Workshop on Non-Rigid Shape Analysis and Deformable
Image Alignment, at ICCV, Kyoto, Japan.
Foulonneau, A., Charbonnier, P. and Heitz, F., 2003. Geomet
ric shape priors for region-based active contours. In: Proceed
ings of the IEEE International Conference on Image Processing,
Barcelona, Spain.
Kass, M., Witkin, A. and Terzopoulos, D., 1988. Snakes: Active
contour models. Int. J. Comput. Vis. 1(4), pp. 321-331.
Lacoste, C., Descombes, X., Zerubia, J. and Baghdadi, N., 2004.
Unsupervised line network extraction from remotely sensed im
ages by polyline process. In: Proc. European Signal Processing
Conference, University of Technology, Vienna, Austria.
Lacoste, C., Descombes, X., Zerubia, J. and Baghdadi, N., 2005.
Extraction of hydrographic networks from satellite images using
a hierarchical model within a stochastic geometry framework. In:
Proc. European Signal Processing Conference, Antalya, Turkey.
McFeeters, S., 1996. The use of the normalized difference water
index (NDWI) in the delineation of open water features. Interna
tional Journal of Remote Sensing 17(7), pp. 1425-1432.
Figure 4: River network segmentation from a colour image using
the new algorithm. Row conservation is satisfied at junctions, il
lustrated by a significant change of width, and along branches, as
illustrated by a slow change of width. (©2010 Google - Imagery
©2010 TerraMetrics, Map data ©2010 Tele Atlas.)
Mena, J. B., 2003. State of the art on automatic road extraction for
GIS update: a novel classification. Pattern Recogn. Lett. 24(16),
pp.3037-3058.
Peng, T., Jermyn, I. H., Prinet, V. and Zerubia, J., 2010. Extended
phase field higher-order active contour models for networks. Int.
J. Comput. Vis. 88(1), pp. 111-128.
Rochery, M., Jermyn, I. and Zerubia, J., 2006. Higher order active
contours. Int. J. Comput. Vis. 69(1), pp. 21-42.
Rochery, M., Jermyn, I. H. and Zerubia, J., 2005. Phase field
models and higher-order active contours. In: Proceedings of
the IEEE International Conference on Computer Vision, Beijing,
China.
Rouse, J., Haas, R., Schell, J. and Deering. D., 1973. Monitor
ing vegetation systems in the great plains with ERTS. In: ERTS
Symposium, NASA SP-351, pp. 309-317.
Rousson, M. and Paragios, N., 2002. Shape priors for level set
representations. In: Proceedings of the European Conference on
Computer Vision, Copenhagen, Denmark.
Srivastava, A., Joshi, S., Mio, W. and Liu, X., 2003. Statistical
shape analysis: Clustering, learning, and testing. IEEE Trans.
Pattern Anal. Mach. Intell. 27(4), pp. 590-602.
Tucker, C., 1979. Red and photographic infrared linear combina
tions for monitoring vegetation. Remote Sensing of Environment
8(2), pp. 127-150.