Abstract
This paper deals with the matching of geometric shapes. Our primary contribution is the use of a simple, robust, rich and efficient way to represent shapes, the level set representations according to singed distance transforms. Based on these representations we propose a variational framework for global as well as local shape registration that can be extended to deal with structures of higher dimension. The optimization criterion is invariant to rotation, translation and scale and combines efficiently a global motion model with local pixel-wise deformations. Promising results are obtained on examples showing small and large global deformations as well as arbitrary topological changes.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
S. Belongie, J. Malik, and J. Puzicha. Matching Shapes. In IEEEICCV, pages 456–461, Vancouver, Canada, 2001.
A. Blake and M. Isard. Active Contours. Springer-Verlag Press, 1997.
V. Caselles, R. Kimmel, and G. Sapiro. Geodesic active contours. In IEEEICCV, pages 694–699, Boston, USA, 1995.
C. Chefd’Hotel, G. Hermosillo, and O. Faugeras. A Variational Aproach to Multi-Modal Image Matching. In IEEEWorkshop on Variational and Level Set Methods, pages 21–28, 2001.
H. Chui and A. Rangarajan. A New Algorithm for Non-Rigid Point Matching. In IEEECVPR, pages II: 44–51, Hilton Island, USA, 2000.
I. Cohen and I. Herlin. Curve Matching Using Geodesic Paths. In IEEECVPR, pages 741–746, Santa Barbara, USA, 1998.
T. Cootes, C. Taylor, D. Cooper, and J. Graham. Active Shape Models-their traing and applications. CVGIP: Image Understanding, 61, 1995.
A. Fitzgibbon. Robust Registration of 2D and 3D Point Sets. volume 2, pages 411–420, 2001.
S. Joshi and M. Miller. Ladmark Matching via Large Deformation Diffeomorphism. IEEE TIP, 9:1357–1370, 2000.
M. Kass, A. Witkin, and D. Terzopoulos. Snakes: Active contour models. In IEEE ICCV, pages 261–268, 1987.
B. Kimia, A. Tannenbaum, and S. Zucker. Shocks and Deformations i: The Components of two-dimensional Shape and the reaction-diffusion space. IJCV, 15:189–224, 1995.
D. Kozinska, O. Tretiak, J. Nissanov, and C. Ozturk. Multidimensional Alignment Using the Euclidean Distance Transform. Graphical Models and Image Processing, 6:373–385, 1997.
S. Lavalle and R. Szilinski. Recovery of the Position and Orientation of free-form Objects from Image Contours using 3D Distance Maps. IEEE PAMI, 17:378–390, 1995.
J. Maintz and M. Viergever. A Survey for Medical Image Registration. Medical Image Analysis, 2:1–36, 1998.
R. Malladi and J. Sethian. A unified framework for shape segmentation representation, and recognition. Technical Report LBL-36069 UC-405, Lawrence Berkeley Laboratory, Berkeley, 1994.
S. Osher and J. Sethian. Fronts propagating with curvature-dependent speed: algorithms based on the hamilton-jacobi formulation. Journal of Computational Physics, 79:12–49, 1988.
N. Paragios and M. Rousson. Shape Priors for Level Set Representations. Copenhangen, Denmark, 2002.
A. Rosenfeld and J. Pfaltz. Distance Functions on Digital Pictures. Pattern Recognition, 1:33–61, 1968.
T. Sebastian, P. Klein, and B. Kimia. Recognition of Shapes by Editting Shock Graphs. In IEEE ICCV, pages 755–762, Vancouver, Canada, 2001.
J. Sethian. Level Set Methods. Cambridge University Press, 1996.
K.Siddiqi, A. Shokoufandeh, S. Dickinson, and S. Zucker. Shocks Graphs and Shape Matching. IJCV, 35:13–32, 1999.
K. Siddiqi, A. Shokoufandeh, S. Dikinson, and S. Zucker. Shock Graphs and Shape Matching. In IEEEICCV, pages 222–229, Bombay, India, 1998.
R. Veltkamp and M. Hagedoorn. State-of-the-art in Shape Matching. Technical Report UU-CS-1999-27, Utrecht University, Sept. 1999.
P. Viola and W. Wells. Aligment by Maximization of Mutual Information. In IEEE ICCV, pages 16–23, Boston, USA, 1995.
J. Weickert, B. M. t. Haar Romeny, and M. Viergener. Efficient and Reliable Scheme for Non-Linear Diffusion and Filtering. IEEE TIP, 7:398–410, 1998.
S. Zhu and A. Yuille. FORMS: A flexible object recognition and modeling system. IJCV, 20:187–212, 1996.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Paragios, N., Rousson, M., Ramesh, V. (2002). Matching Distance Functions: A Shape-to-Area Variational Approach for Global-to-Local Registration. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds) Computer Vision — ECCV 2002. ECCV 2002. Lecture Notes in Computer Science, vol 2351. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47967-8_52
Download citation
DOI: https://doi.org/10.1007/3-540-47967-8_52
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43744-4
Online ISBN: 978-3-540-47967-3
eBook Packages: Springer Book Archive