Algorithms for optimal partial matching of free-form objects with scaling effects

A free-form object matching problem is addressed in this paper. Two methods are proposed to solve a partial matching problem with scaling effects and no prior information on correspondence or the rigid body transformation involved. The first method uses umbilical points, which behave as fingerprints of a surface and their qualitative properties can be used for matching purposes. The second method uses an optimization scheme based on the extension of the KH curvature matching method [Comput. Aided Design 35 (2003) 913], first introduced in the context of a matching problem without scaling effects. Two types of curvatures, the Gaussian and the mean curvatures, are used to establish correspondences between two objects. The curvature matching method is formulated in terms of minimization of an objective function depending on the unknown scaling factor, and the rigid body transformation parameters. The accuracy and complexity of the proposed methods as well as the convergence for the optimization approach are analyzed. Examples illustrate the two methods.

[1]  Nicholas M. Patrikalakis,et al.  An algorithm for optimal free-form object matching , 2003, Comput. Aided Des..

[2]  Richard A. Volz,et al.  Estimating 3-D location parameters using dual number quaternions , 1991, CVGIP Image Underst..

[3]  H. Piaggio Differential Geometry of Curves and Surfaces , 1952, Nature.

[4]  Ernest L. Hall,et al.  Three-Dimensional Moment Invariants , 1980, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  D. Struik Lectures on classical differential geometry , 1951 .

[6]  A. M. Peterson Applications of digital signal processing , 1979 .

[7]  William H. Press,et al.  The Art of Scientific Computing Second Edition , 1998 .

[8]  Ming-Kuei Hu,et al.  Visual pattern recognition by moment invariants , 1962, IRE Trans. Inf. Theory.

[9]  Nicholas M. Patrikalakis,et al.  Shape Intrinsic Properties for Free-Form Object Matching , 2003, Journal of Computing and Information Science in Engineering.

[10]  Baba C. Vemuri,et al.  Geometric Methods in Computer Vision , 1991 .

[11]  Sang Wook Lee,et al.  ICP Registration Using Invariant Features , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[12]  Reinhard Klein,et al.  A geometric approach to 3D object comparison , 2001, Proceedings International Conference on Shape Modeling and Applications.

[13]  Steven W. Zucker,et al.  Inferring Surface Trace and Differential Structure from 3-D Images , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  Andrew E. Johnson,et al.  Using Spin Images for Efficient Object Recognition in Cluttered 3D Scenes , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  Chitra Dorai,et al.  COSMOS - A Representation Scheme for 3D Free-Form Objects , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  Bernard Chazelle,et al.  Shape distributions , 2002, TOGS.

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

[18]  Chin Seng Chua,et al.  Point Signatures: A New Representation for 3D Object Recognition , 1997, International Journal of Computer Vision.

[19]  Nicholas M. Patrikalakis,et al.  Computation of stationary points of distance functions , 1993, Engineering with Computers.

[20]  Richard J. Prokop,et al.  A survey of moment-based techniques for unoccluded object representation and recognition , 1992, CVGIP Graph. Model. Image Process..

[21]  Zhengyou Zhang,et al.  Iterative point matching for registration of free-form curves and surfaces , 1994, International Journal of Computer Vision.

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

[23]  Josef Hoschek,et al.  Fundamentals of computer aided geometric design , 1996 .

[24]  Ray Jarvis,et al.  3D free-form surface registration and object recognition , 2004, International Journal of Computer Vision.

[25]  Glen Mullineux Proceedings of the 6th IMA Conference on the Mathematics of Surfaces, Brunel University, UK, September 1994 , 1996, IMA Conference on the Mathematics of Surfaces.

[26]  Nicholas M. Patrikalakis,et al.  Umbilics and lines of curvature for shape interrogation , 1996, Comput. Aided Geom. Des..

[27]  N. M. Patrikalakis,et al.  Localization of rational B-spline surfaces , 1991, Engineering with Computers.

[28]  Paul J. Besl,et al.  Principal patches-a viewpoint-invariant surface description , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[29]  Paul J. Besl,et al.  The Free-Form Surface Matching Problem , 1990 .

[30]  Andrew E. Johnson,et al.  Recognizing objects by matching oriented points , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[31]  Bernard Chazelle,et al.  Matching 3D models with shape distributions , 2001, Proceedings International Conference on Shape Modeling and Applications.

[32]  Nicholas M. Patrikalakis,et al.  Computation of the solutions of nonlinear polynomial systems , 1993, Comput. Aided Geom. Des..

[33]  Steven W. Zucker,et al.  Singularities of Principal Direction Fields from 3-D Images , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[34]  Patrick J. Flynn,et al.  A Survey Of Free-Form Object Representation and Recognition Techniques , 2001, Comput. Vis. Image Underst..

[35]  K. Snyder Ridges , 1988 .

[36]  Gérard G. Medioni,et al.  Structural Indexing: Efficient 3-D Object Recognition , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[37]  Robert Bergevin,et al.  Estimating the 3D rigid transformation between two range views of a complex object , 1992, [1992] Proceedings. 11th IAPR International Conference on Pattern Recognition.

[38]  Richard Morris,et al.  The Sub-Parabolic Lines of a Surface , 1994, IMA Conference on the Mathematics of Surfaces.

[39]  Ian R. Porteous,et al.  Geometric differentiation for the intelligence of curves and surfaces , 1994 .

[40]  Peter J. Giblin,et al.  Ridges, crests and sub-parabolic lines of evolving surfaces , 1996, International Journal of Computer Vision.

[41]  L. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communications.

[42]  K. S. Arun,et al.  Least-Squares Fitting of Two 3-D Point Sets , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[43]  Subodh Kumar,et al.  Repairing CAD models , 1997, Proceedings. Visualization '97 (Cat. No. 97CB36155).

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

[45]  Nicholas M. Patrikalakis,et al.  Efficient and reliable methods for rounded-interval arithmetic , 1998, Comput. Aided Des..

[46]  Berthold K. P. Horn,et al.  Closed-form solution of absolute orientation using orthonormal matrices , 1988 .

[47]  Michael Jastram Inspection and feature extraction of marine propellers , 1996 .

[48]  Michael I. Jordan Graphical Models , 2003 .

[49]  William H. Press,et al.  Numerical recipes in C , 2002 .

[50]  J. Navarro-Pedreño Numerical Methods for Least Squares Problems , 1996 .

[51]  Saravajit Sahay Sinha,et al.  Differential properties from adaptive thin-plate splines , 1991, Optics & Photonics.

[52]  M. Berry,et al.  Umbilic points on Gaussian random surfaces , 1977 .

[53]  Åke Björck,et al.  Numerical Methods , 1995, Handbook of Marine Craft Hydrodynamics and Motion Control.

[54]  Herbert Freeman,et al.  Machine Vision for Three-Dimensional Scenes , 1990 .

[55]  Nicholas M. Patrikalakis,et al.  Shape Interrogation for Computer Aided Design and Manufacturing , 2002, Springer Berlin Heidelberg.

[56]  Gene H. Golub,et al.  Singular value decomposition and least squares solutions , 1970, Milestones in Matrix Computation.

[57]  Farzin Mokhtarian,et al.  Silhouette-Based Isolated Object Recognition through Curvature Scale Space , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[58]  Micha Sharir,et al.  Partial surface matching by using directed footprints , 1996, SCG '96.

[59]  Weiyin Ma,et al.  Parameterization of randomly measured points for least squares fitting of B-spline curves and surfaces , 1995, Comput. Aided Des..