Abstract
Since the work by Osher and Sethian on level-sets algorithms for numerical shape evolutions, this technique has been used for a large number of applications in numerous fields. In medical imaging, this nu- merical technique has been successfully used for example in segmentation and cortex unfolding algorithms. The migration from a Lagrangian im- plementation to an Eulerian one via implicit representations or level-sets brought some of the main advantages of the technique, mainly, topology independence and stability. This migration means also that the evolution is parametrization free, and therefore we do not know exactly how each part of the shape is deforming, and the point-wise correspondence is lost. In this note we present a technique to numerically track regions on sur- faces that are being deformed using the level-sets method. The basic idea is to represent the region of interest as the intersection of two implicit surfaces, and then track its deformation from the deformation of these surfaces. This technique then solves one of the main shortcomings of the very useful level-sets approach. Applications include lesion localization in medical images, region tracking in functional MRI visualization, and geometric surface mapping.
A journal version of this paper appears in the May 1999 issue of IEEE Trans. Medical Imaging.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
L. Ambrosio and M. Soner, “Level set approach to mean curvature flow in arbitrary codimension,” Journal of Differential Geometry 43, pp. 693–737, 1996.
M. Bertalmio, Morphing Active Contours, M.Sc. Thesis, I.I.E., Universidad de la Republica, Uruguay, June 1998.
M. Bertalmio, G. Sapiro, and G. Randall, “Morphing active contours,” Proc. IEEE-ICIP, Chicago, October 1998.
P. Burchard, L. T. Cheng, B. Merriman, and S. Osher, “Level set based motion of curves in IR3,” UCLA CAM Report, May 1999.
V. Caselles, R. Kimmel, and G. Sapiro, “Geodesic active contours,” International Journal of Computer Vision 22:1, pp. 61–79, 19
Y. G. Chen, Y. Giga, and S. Goto, “Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations,” Journal of Differential Geometry 33, 1991.
L. C. Evans and J. Spruck, “Motion of level sets by mean curvature, I,” Journal of Differential Geometry 33, 1991.
L. C. Evans and J. Spruck, “Motion of level sets by mean curvature, II,” Trans. Amer. Math. Soc. 330, pp. 321–332, 1992.
G. Hermosillo, O. Faugeras, and J. Gomes, “Cortex unfolding using level set methods,” INRIA Sophia Antipolis Technical Report 3663, April 1999.
L. M. Lorigo, O. Faugeras, W. E. L. Grimson, R. Keriven, and R. Kikinis, “Segmentation of bone in clinical knee MRI using texture-based geodesic active contours,” Proceedings Medical Image Computing and Computer-Assisted Intervention, MIC-CAI’ 98, pp. 1195–1204, Cambridge, MA, Springer, 1998.
L. Lorigo, O. Faugeras, W.E.L. Grimson, R. Keriven, R. Kikinis, and C-F. Westin, “Co-dimension 2 geodesic active contours for MRA segmentation,” International Conference on Information Processing in Medical Imaging, June 1999, forthcoming.
R. Malladi, J. A. Sethian and B. C. Vemuri, “Shape modeling with front propagation: A level set approach,” IEEE Trans. on PAMI 17, pp. 158–175, 1995.
B. Merriman, J. Bence, and S. Osher, “Motion of multiple junctions: A level-set approach,’ Journal of Computational Physics 112, pp. 334–363, 1994.
B. Merriman, R. Caflisch, and S. Osher, “Level set methods, with an application to modeling the growth of thin films, UCLA CAM Report 98-10, February 1998.
W. J. Niessen, B. M. Romeny, and M. A. Viergever, “Geodesic deformable models for medical image analysis,” IEEE Trans. Medical Imaging 17, pp. 634–641, 1998.
S. Osher, Personal communication, March 1999.
S. Osher and J. Sethian, “Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations,” Journal of Computational Physics 79, pp. 12–49, 1988.
J. Sethian, Level Set Methods: Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision and Material Sciences, Cambridge University Press, Cambridge, UK, 1996.
P. Teo, G. Sapiro, and B. Wandell, “Creating connected representations of cortical gray matter for functional MRI visualization,” IEEE Trans. Medical Imaging 16:06, pp. 852–863, 1997.
A. Yezzi, S. Kichenassamy, P. Olver, and A. Tannenbaum, “Geometric active contours for segmentation of medical imagery,” IEEE Trans. Medical Imaging 16, pp.199–210, 1997.
X. Zeng, L. H. Staib, R. T. Schultz, and J. S. Duncan, “Segmentation and measurement of the cortex from 3D MR Images,” Proceedings Medical Image Computing and Computer-Assisted Intervention, MICCAI’ 98, pp. 519–530, Cambridge, MA, Springer, 1998.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bertalmio, M., Sapiro, G., Randall, G. (1999). Region Tracking on Surfaces Deforming via Level-Sets Methods. In: Nielsen, M., Johansen, P., Olsen, O.F., Weickert, J. (eds) Scale-Space Theories in Computer Vision. Scale-Space 1999. Lecture Notes in Computer Science, vol 1682. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48236-9_29
Download citation
DOI: https://doi.org/10.1007/3-540-48236-9_29
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66498-7
Online ISBN: 978-3-540-48236-9
eBook Packages: Springer Book Archive