Abstract

We present a spline-based nonrigid motion and point correspondence recovery method for 3D surfaces. This method is based on differential geometry. Shape information is used to recover the point correspondences. In contrast to the majority of shape-based methods, which assume that shape (unit normal, curvature) changes are minimum after motion, our method focuses on the nonrigid relationship between before-motion and after-motion shapes. This nonrigid shape relationship is described by modeling the underlying nonrigid motion; we model it as a spline transformation, which has global control over the entire motion field along with the local deformation integrated within. This provides our method certain advantages over some pure differential geometric methods, which also utilize the nonrigid shape relationship but only work on local areas without a global control. For example, motion regularity is hard to implement in these pure differential geometric methods but is not a problem when the motion field is controlled by a spline transformation. The orthogonal parameterization requirement of the nonrigid shape relationship has to be approximated in these previous methods but is easy to meet in our method. Furthermore, the small deformation constraint introduced by the previous works is relaxed in our method.

Experiments on both synthetic and real motions have been conducted. The quantitative and qualitative evaluations of our method are presented. The application of our method to the human tongue motion analysis is also presented in this paper.

Keywords: Nonrigid motion; Correspondence; Spline; Shape-based methods

Article Outline

1. Introduction

1.1. The direct shape-based method

1.2. The nonrigid shape-based method

1.3. Our approach

2. Background

3. Nonrigid motion modeling: GRBF

4. Motion recovery

4.1. Approximation of A(r, P)

4.2. Approximation of n′(r+s(r, P))

4.3. Unit normal equation

4.4. Additional constraints

4.5. Recovery solution

5. Experiments

5.1. Synthetic motion

5.2. Real motion

5.2.1. Real motion mapping

5.2.2. Evaluation with real motion

5.3. Cyberware data

5.4. Human tongue motion analysis

6. Conclusion

Acknowledgements

References