Transformed polynomials for global registration of point clouds

In this paper, we introduce a novel approach for global registration of partially overlapping point clouds. The approach identifies feature points of matching objects based on surface-approximating polynomials and finds an initial transformation depending on these polynomials. We compute an extended set of rotationally-invariant features for polynomials. In contrast to purely feature-based approaches, we do not only compute transformations based on the invariant properties of polynomials, but actually transform the polynomials into a common coordinate system and compare the transformed coefficients. This results in an improved correspondence analysis of local surfaces. Hence, using transformed polynomials, we gain more discriminating information about different structures. Therefore, the approach can handle partial scans of different objects simultaneously. Each partial scan is assigned to one of the objects and registered accordingly. Moreover, the approach is robust against noise and can process real data.

[1]  Raif M. Rustamov,et al.  Augmented planar reflective symmetry transform , 2008, The Visual Computer.

[2]  Daniel Cohen-Or,et al.  Part Analogies in Sets of Objects , 2008, 3DOR@Eurographics.

[3]  Daniel Cohen-Or,et al.  4-points congruent sets for robust pairwise surface registration , 2008, ACM Trans. Graph..

[4]  Thomas A. Funkhouser,et al.  Möbius voting for surface correspondence , 2009, ACM Trans. Graph..

[5]  Alexander M. Bronstein,et al.  Topology-Invariant Similarity of Nonrigid Shapes , 2009, International Journal of Computer Vision.

[6]  Leonidas J. Guibas,et al.  Discovering structural regularity in 3D geometry , 2008, ACM Trans. Graph..

[7]  Marc Levoy,et al.  Efficient variants of the ICP algorithm , 2001, Proceedings Third International Conference on 3-D Digital Imaging and Modeling.

[8]  Helmut Pottmann,et al.  Registration of point cloud data from a geometric optimization perspective , 2004, SGP '04.

[9]  Ghassan Hamarneh,et al.  A Survey on Shape Correspondence , 2011, Comput. Graph. Forum.

[10]  Marc Pouget,et al.  Estimating differential quantities using polynomial fitting of osculating jets , 2003, Comput. Aided Geom. Des..

[11]  Yi Ping Hung,et al.  A fast automatic method for registration of partially-overlapping range images , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[12]  Tim Weyrich,et al.  Multi-feature matching of fresco fragments , 2010, ACM Trans. Graph..

[13]  N. Mitra,et al.  4-points congruent sets for robust pairwise surface registration , 2008, SIGGRAPH 2008.

[14]  Szymon Rusinkiewicz,et al.  Symmetry descriptors and 3D shape matching , 2004, SGP '04.

[15]  H. Seidel,et al.  Isometric registration of ambiguous and partial data , 2009, 2009 IEEE Conference on Computer Vision and Pattern Recognition.

[16]  Marc Alexa,et al.  Point set surfaces , 2001, Proceedings Visualization, 2001. VIS '01..

[17]  Hans-Peter Seidel,et al.  Isometric registration of ambiguous and partial data , 2009, CVPR.

[18]  Leonidas J. Guibas,et al.  Robust global registration , 2005, SGP '05.

[19]  Daniel Cohen-Or,et al.  Consensus Skeleton for Non‐rigid Space‐time Registration , 2010, Comput. Graph. Forum.

[20]  Leonidas J. Guibas,et al.  Partial and approximate symmetry detection for 3D geometry , 2006, ACM Trans. Graph..

[21]  Daniel Cohen-Or,et al.  A Part‐aware Surface Metric for Shape Analysis , 2009, Comput. Graph. Forum.

[22]  Shi-Min Hu,et al.  Principal curvatures from the integral invariant viewpoint , 2007, Comput. Aided Geom. Des..

[23]  Yi-Ping Hung,et al.  RANSAC-Based DARCES: A New Approach to Fast Automatic Registration of Partially Overlapping Range Images , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[24]  Ariel Shamir,et al.  Pose-Oblivious Shape Signature , 2007, IEEE Transactions on Visualization and Computer Graphics.

[25]  Alexander M. Bronstein,et al.  Full and Partial Symmetries of Non-rigid Shapes , 2010, International Journal of Computer Vision.

[26]  Daniel Cohen-Or,et al.  Electors Voting for Fast Automatic Shape Correspondence , 2010, Comput. Graph. Forum.

[27]  Leonidas J. Guibas,et al.  Non-Rigid Registration Under Isometric Deformations , 2008 .

[28]  Leonidas J. Guibas,et al.  Example-Based 3D Scan Completion , 2005 .

[29]  Andrew E. Johnson,et al.  Spin-Images: A Representation for 3-D Surface Matching , 1997 .

[30]  Helmut Pottmann,et al.  Reassembling fractured objects by geometric matching , 2006, ACM Trans. Graph..

[31]  Leonidas J. Guibas,et al.  Global Intrinsic Symmetries of Shapes , 2008, Comput. Graph. Forum.

[32]  Igor Guskov,et al.  Multi-scale features for approximate alignment of point-based surfaces , 2005, SGP '05.

[33]  Szymon Rusinkiewicz,et al.  Global non-rigid alignment of 3-D scans , 2007, ACM Trans. Graph..

[34]  Hao Zhang,et al.  Non-Rigid Spectral Correspondence of Triangle Meshes , 2007, Int. J. Shape Model..

[35]  Daniel Cohen-Or,et al.  Salient geometric features for partial shape matching and similarity , 2006, TOGS.

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

[37]  Leonidas J. Guibas,et al.  Discovering structural regularity in 3D geometry , 2008, SIGGRAPH 2008.

[38]  Tim Weyrich,et al.  A system for high-volume acquisition and matching of fresco fragments: reassembling Theran wall paintings , 2008, ACM Trans. Graph..

[39]  T. Funkhouser,et al.  A planar-reflective symmetry transform for 3D shapes , 2006, SIGGRAPH '06.

[40]  Berthold K. P. Horn,et al.  Closed-form solution of absolute orientation using unit quaternions , 1987 .

[41]  Robert C. Bolles,et al.  Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography , 1981, CACM.

[42]  Kari Pulli,et al.  Multiview registration for large data sets , 1999, Second International Conference on 3-D Digital Imaging and Modeling (Cat. No.PR00062).

[43]  Marc Levoy,et al.  Real-time 3D model acquisition , 2002, ACM Trans. Graph..

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

[45]  D. Levin,et al.  Mesh-Independent Surface Interpolation , 2004 .