Non-rigid range-scan alignment using thin-plate splines

We present a nonrigid alignment algorithm for aligning high-resolution range data in the presence of low-frequency deformations, such as those caused by scanner calibration error. Traditional iterative closest points (ICP) algorithms, which rely on rigid-body alignment, fail in these cases because the error appears as a nonrigid warp in the data. Our algorithm combines the robustness and efficiency of ICP with the expressiveness of thin-plate splines to align high-resolution scanned data accurately, such as scans from the Digital Michelangelo Project [M. Levoy et al. (2000)]. This application is distinguished from previous uses of the thin-plate spline by the fact that the resolution and size of warping are several orders of magnitude smaller than the extent of the mesh, thus requiring especially precise feature correspondence.

[1]  Anand Rangarajan,et al.  A new point matching algorithm for non-rigid registration , 2003, Comput. Vis. Image Underst..

[2]  Marc Levoy,et al.  A volumetric method for building complex models from range images , 1996, SIGGRAPH.

[3]  Fred L. Bookstein,et al.  Principal Warps: Thin-Plate Splines and the Decomposition of Deformations , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[4]  Jean Duchon,et al.  Splines minimizing rotation-invariant semi-norms in Sobolev spaces , 1976, Constructive Theory of Functions of Several Variables.

[5]  Zoran Popovic,et al.  The space of human body shapes: reconstruction and parameterization from range scans , 2003, ACM Trans. Graph..

[6]  Andrew E. Johnson,et al.  Surface registration by matching oriented points , 1997, Proceedings. International Conference on Recent Advances in 3-D Digital Imaging and Modeling (Cat. No.97TB100134).

[7]  Gérard G. Medioni,et al.  Object modeling by registration of multiple range images , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[8]  Gabriel Taubin,et al.  The ball-pivoting algorithm for surface reconstruction , 1999, IEEE Transactions on Visualization and Computer Graphics.

[9]  Gabriel Taubin,et al.  Building a Digital Model of Michelangelo's Florentine Pietà , 2002, IEEE Computer Graphics and Applications.

[10]  G. Wahba Spline models for observational data , 1990 .

[11]  J. Duchon Spline minimizing rotation-invariant seminorms in Sobolev spaces , 1977 .

[12]  Marc Levoy,et al.  Geometrically stable sampling for the ICP algorithm , 2003, Fourth International Conference on 3-D Digital Imaging and Modeling, 2003. 3DIM 2003. Proceedings..

[13]  Paul J. Besl,et al.  A Method for Registration of 3-D Shapes , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  Karl Rohr,et al.  Spline-based elastic image registration: integration of landmark errors and orientation attributes , 2003, Comput. Vis. Image Underst..

[15]  Jürgen Weese,et al.  Point-Based Elastic Registration of Medical Image Data Using Approximating Thin-Plate Splines , 1996, VBC.

[16]  Marc Levoy,et al.  The digital Michelangelo project: 3D scanning of large statues , 2000, SIGGRAPH.

[17]  Evangelos E. Milios,et al.  Globally Consistent Range Scan Alignment for Environment Mapping , 1997, Auton. Robots.

[18]  Marc Levoy,et al.  A hierarchical method for aligning warped meshes , 2003, Fourth International Conference on 3-D Digital Imaging and Modeling, 2003. 3DIM 2003. Proceedings..

[19]  Gérard G. Medioni,et al.  Object modelling by registration of multiple range images , 1992, Image Vis. Comput..