Abstract
We present a new method for morphing 2D and 3D objects. In particular we focus on the problem of smooth interpolation on a shape manifold. The proposed method takes advantage of two recent works on 2D and 3D shape analysis to compute elastic geodesics between any two arbitrary shapes and interpolations on a Riemannian manifold. Given a finite set of frames of the same (2D or 3D) object from a video sequence, or different expressions of a 3D face, our goal is to interpolate between the given data in a manner that is smooth. Experimental results are presented to demonstrate the effectiveness of our method.
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.
References
Altafini, C.: The de casteljau algorithm on se(3). In: Nonlinear control in the Year 2000, pp. 23–34 (2000)
Crouch, P., Kun, G., Leite, F.S.: The de casteljau algorithm on the lie group and spheres. Journal of Dynamical and Control Systems 5, 397–429 (1999)
Glaunes, J., Qiu, A., Miller, M., Younes, L.: Large deformation diffeomorphic metric curve mapping. International Journal of Computer Vision 80, 317–336 (2008)
Hughes, J.F.: Scheduled fourier volume morphing. In: Computer Graphics (SIGGRAPH 1992), pp. 43–46 (1992)
Jakubiak, J., Leite, F.S., Rodrigues, R.C.: A two-step algorithm of smooth spline generation on Riemannian manifolds. Journal of Computational and Applied Mathematics, 177–191 (2006)
Joshi, S.H., Klassen, E., Srivastava, A., Jermyn, I.: A novel representation for riemannian analysis of elastic curves in Rn, CVPR (2007)
Klassen, E., Srivastava, A.: Geodesics between 3D closed curves using path-straightening. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3951, pp. 95–106. Springer, Heidelberg (2006)
Klassen, E., Srivastava, A., Mio, W., Joshi, S.: Analysis of planar shapes using geodesic paths on shape spaces. IEEE Patt. Analysis and Machine Intell. 26(3), 372–383 (2004)
Kume, A., Dryden, I.L., Le, H., Wood, A.T.A.: Fitting cubic splines to data in shape spaces of planar configurations. Proceedings in Statistics of Large Datasets, LASR, 119–122 (2002)
Lancaster, P., Salkauskas, K.: Curve and surface fitting. Academic Press, London (1986)
Lazarus, F., Verroust, A.: Three-dimensional metamorphosis: a survey. The Visual Computer, 373–389 (1998)
Lin, A., Walker, M.: Cagd techniques for differentiable manifolds, Tech. report, York University (July 2001)
Popeil, T., Noakes, L.: Bézier curves and c 2 interpolation in Riemannian manifolds. Journal of Approximation Theory, 111–127 (2007)
Samir, C., Srivastava, A., Daoudi, M., Klassen, E.: An intrinsic framework for analysis of facial surfaces. International Journal of Computer Vision 82, 80–95 (2009)
Schmidt, F.R., Clausen, M., Cremers, D.: Shape matching by variational computation of geodesics on a manifold. In: Franke, K., Müller, K.-R., Nickolay, B., Schäfer, R. (eds.) DAGM 2006. LNCS, vol. 4174, pp. 142–151. Springer, Heidelberg (2006)
Spivak, M.: A comprehensive introduction to differential geometry, vol. i & ii. Publish or Perish, Inc., Berkeley (1979)
Whitaker, R., Breen, D.: Level-set models for the deformation of solid object. In: Third International Workshop on Implicit Surfaces, pp. 19–35 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Samir, C., Van Dooren, P., Laurent, D., Gallivan, K.A., Absil, P.A. (2009). Elastic Morphing of 2D and 3D Objects on a Shape Manifold. In: Kamel, M., Campilho, A. (eds) Image Analysis and Recognition. ICIAR 2009. Lecture Notes in Computer Science, vol 5627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02611-9_56
Download citation
DOI: https://doi.org/10.1007/978-3-642-02611-9_56
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02610-2
Online ISBN: 978-3-642-02611-9
eBook Packages: Computer ScienceComputer Science (R0)