Abstract
We present a novel approach for representing and evolving deformable active contours by restricting the movement of the contour vertices to the grid lines of a uniform lattice. This restriction implicitly controls the (re)parameterization of the contour and hence makes it possible to employ parameterization-independent evolution rules. Moreover, the underlying uniform grid makes self-collision detection very efficient. Our contour model is also able to perform topology changes, but – more importantly – it can detect and handle self-collisions at subpixel precision. In applications where topology changes are not appropriate, we generate contours that touch themselves without any gaps or self-intersections.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Berger MO (1990) Snake growing. In: Proceedings of the 1st European conference on computer vision. Lecture notes in computer science. Springer, Berlin Heidelberg New York, pp 570–572
Cohen I, Cohen L, Ayache N (1992) Using deformable surfaces to segment 3-d images and infer differential structures. Comput Vision Graph Image Process Image Understand 56(2):242–263
Cohen L (1991) On active contour models and balloons. Vision Graph Image Process Image Understand 53(2):211–218
Cohen LD, Cohen I (1993) Finite element methods for active contour models and balloons for 2d and 3d images. IEEE Trans Patt Anal Mach Intell 15(11):1131–1147
Chopp DL (1993) Computing minimal surfaces via level set curvature flow. J Comput Phys 106:77–91
Davatzikos CA, Prince JL (1995) An active contour model for mapping the cortex. IEEE Trans Med Imag 14(1):112–115
DeCarlo D, Metaxas D (1994) Blended deformable models. In: Proceedings of CVPR ’94, pp 566–572
Delingette H, Montagnat J (2001) Shape and topology constraints on parametric active contours. Comput Vision Image Understand 83:140–171
Gage M (1986) On an area-preserving evolution equation for plane curves. Contemp Math 51:51–62
Gupta A, O’Donnell T, Singh A (1994) Segmentation and tracking of cine cardiac mr and ct images using a 3d deformable model. In: Proceedings of the IEEE conference on computers and cardiology, pp 661–664
Han X, Xu C, Prince JL (2001) A topology preserving deformable model using level sets. In: Proceedings of the conference on computer vision and pattern recognition, pp 765–770
Hug J, Brechbühler C, Szekely G (1999) Tamed snake: a particle system for robust semi-automatic segmentation. In: Proceedings of the conference on medical image computing and computer-assisted intervention. Lecture notes in computer science, vol 1679. Springer, Berlin Heidelberg New York, pp 106–115
Kass M, Witkin A, Terzopoulos D (1988) Snakes: active contour models. Int J Comput Vision 1:321–331
Kimia B, Tannenbaum A, Zucker S (1992) On the evolution of curves via a function of curvature i: the classical case. J Math Anal Appl 163:438–458
Lachaud J-O, Montanvert A (1999) Deformable meshes with automatic topology changes for coarse-to-fine three-dimensional surface extraction. Med Image Anal 3(2):187–207
Lobregt S, Viergever M (1995) A discrete dynamic contour model. IEEE Trans Med Imag 14(1):12–23
Lorensen WE, Cline HE (1987) Marching cubes: a high resolution 3d surface reconstruction algorithm. In: Proceedings of SIGGRAPH ’87, pp 163–169
McInerney T, Terzopoulos D (1995) Topologically adaptable snakes. In: Proceedings of the international conference on computer vision, pp 840–845
McInerney T, Terzopoulos D (1996) Deformable models in medical image analysis: a survey. Med Image Anal 1(2):91–108
McInerney T, Terzopoulos D (1999) Topology adaptive deformable surfaces for medical image volume segmentation. IEEE Trans Med Imag 18(10):840–850
McInerney T, Terzopoulos D (2000) T-snakes: topology adaptive snakes. Med Image Anal 4(2):73–91
Miller JV, Breen DE, Lorensen WE, O’Bara RM, Wozny MJ (1991) Geometrically deformed models: a method for extracting closed geometric models from volume data. In: Proceedings of SIGGRAPH ’91, pp 217–226
Osher SJ, Fedkiw RP (2002) Level set methods and dynamic implicit surfaces. Springer, Berlin Heidelberg New York
Osher S, Sethian JA (1988) Fronts propagating with curvature-dependent speed: algorithms based on hamilton-jacobi formulations. J Comput Phys 79(1):12–49
Prêteux F, Rougon N (1998) Directional adaptive deformable models for segmentation. J Electron Imag 7(1):231–256
Sethian JA (1996) A fast marching level set method for monotonically advancing fronts. Proc Natl Acad Sci 93(4):1591–1595
Sethian JA (1999) Level set methods and fast marching methods. Cambridge University Press, Cambridge, UK
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bischoff, S., Kobbelt, L. Parameterization-free active contour models with topology control . Visual Comp 20, 217–228 (2004). https://doi.org/10.1007/s00371-003-0228-9
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00371-003-0228-9