Elastic Morphing of 2D and 3D Objects on a Shape Manifold
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.
KeywordsRiemannian Manifold Control Point Euclidean Plane Closed Curf Lagrange Interpolation
Unable to display preview. Download preview PDF.
- 1.Altafini, C.: The de casteljau algorithm on se(3). In: Nonlinear control in the Year 2000, pp. 23–34 (2000)Google Scholar
- 4.Hughes, J.F.: Scheduled fourier volume morphing. In: Computer Graphics (SIGGRAPH 1992), pp. 43–46 (1992)Google Scholar
- 5.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)Google Scholar
- 6.Joshi, S.H., Klassen, E., Srivastava, A., Jermyn, I.: A novel representation for riemannian analysis of elastic curves in Rn, CVPR (2007)Google Scholar
- 9.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)Google Scholar
- 11.Lazarus, F., Verroust, A.: Three-dimensional metamorphosis: a survey. The Visual Computer, 373–389 (1998)Google Scholar
- 12.Lin, A., Walker, M.: Cagd techniques for differentiable manifolds, Tech. report, York University (July 2001)Google Scholar
- 13.Popeil, T., Noakes, L.: Bézier curves and c 2 interpolation in Riemannian manifolds. Journal of Approximation Theory, 111–127 (2007)Google Scholar
- 17.Whitaker, R., Breen, D.: Level-set models for the deformation of solid object. In: Third International Workshop on Implicit Surfaces, pp. 19–35 (1998)Google Scholar