Part-in-whole matching of rigid 3D shapes using geodesic disk spectrum

Part-in-whole matching of rigid 3D shapes has attracted great interest in shape analysis and has various applications in computational archaeology. Rigid part-in-whole matching algorithms are mainly based on methods minimizing geometric distances and methods using local shape descriptors, which are challenging when the partial shapes are relatively small and smooth. This paper proposes a part-in-whole matching algorithm of rigid 3D shapes using geodesic disk spectrum (GDS), which achieves accurate matching results for partial shapes with arbitrary boundaries or smooth appearances. The largest enclosing geodesic disk of the partial shape and geodesic disks on the complete shape are extracted in the matching process. GDS is used as the matching descriptor, which is the distribution of shape index for enclosing points of the disk. The problem of matching partial surfaces with arbitrarily irregular boundaries to the complete shape is transformed into the matching of geodesic disks with the same radius using the proposed algorithm. GDS is discriminative, which can handle the situation when partial surfaces have few distinctive features. The proposed algorithm has been tested on various partial surfaces and obtained accurate matching results. A higher precision is achieved by comparing with existing part-in-whole matching algorithms, which proves the efficiency of the proposed algorithm.

[1]  Szymon Rusinkiewicz,et al.  Global non-rigid alignment of 3-D scans , 2007, SIGGRAPH 2007.

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

[3]  Niloy J. Mitra,et al.  Super4PCS: Fast Global Pointcloud Registration via Smart Indexing , 2019 .

[4]  Szymon Rusinkiewicz,et al.  Rotation Invariant Spherical Harmonic Representation of 3D Shape Descriptors , 2003, Symposium on Geometry Processing.

[5]  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).

[6]  Michael G. Strintzis,et al.  This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE Snapshots: A Novel Local Surface , 2022 .

[7]  M. Teschner,et al.  Meshless deformations based on shape matching , 2005, SIGGRAPH 2005.

[8]  Sim Heng Ong,et al.  Efficient partial-surface registration for 3D objects , 2005, Comput. Vis. Image Underst..

[9]  Chitra Dorai,et al.  Shape Spectrum Based View Grouping and Matching of 3D Free-Form Objects , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  R. Kimmel,et al.  Matching shapes by eigendecomposition of the Laplace-Beltrami operator , 2010 .

[11]  Kun Zhou,et al.  A Survey on Partial Retrieval of 3D Shapes , 2013, Journal of Computer Science and Technology.

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

[13]  S. Rusinkiewicz.  Estimating curvatures and their derivatives on triangle meshes , 2004 .

[14]  Xulei Wang,et al.  Global and local isometry-invariant descriptor for 3D shape comparison and partial matching , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[15]  Andrea J. van Doorn,et al.  Surface shape and curvature scales , 1992, Image Vis. Comput..

[16]  Ayellet Tal,et al.  Surface partial matching and application to archaeology , 2011, Comput. Graph..

[17]  Kang Zhang,et al.  3D Fragment Reassembly Using Integrated Template Guidance and Fracture-Region Matching , 2015, 2015 IEEE International Conference on Computer Vision (ICCV).

[18]  Jing Hua,et al.  Salient spectral geometric features for shape matching and retrieval , 2009, The Visual Computer.

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

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

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

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

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

[24]  Marco Attene,et al.  Part-in-whole 3D shape matching and docking , 2011, The Visual Computer.

[25]  Günther Greiner,et al.  Interactive partial 3D shape matching with geometric distance optimization , 2014, The Visual Computer.

[26]  Federico Tombari,et al.  Unique Signatures of Histograms for Local Surface Description , 2010, ECCV.

[27]  Olivier D. Faugeras,et al.  A 3-D Recognition and Positioning Algorithm Using Geometrical Matching Between Primitive Surfaces , 1983, IJCAI.

[28]  Umberto Castellani,et al.  Statistical 3D Shape Analysis by Local Generative Descriptors , 2011, IEEE Transactions on Pattern Analysis and Machine Intelligence.

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

[30]  Xin Li,et al.  Skull Assembly and Completion Using Template-Based Surface Matching , 2011, 2011 International Conference on 3D Imaging, Modeling, Processing, Visualization and Transmission.

[31]  Joseph S. B. Mitchell,et al.  The Discrete Geodesic Problem , 1987, SIAM J. Comput..

[32]  Kang Zhang,et al.  Reassembling 3D thin shells using integrated template guidance and fracture region matching , 2015, SIGGRAPH Posters.

[33]  Yu Zhong,et al.  Intrinsic shape signatures: A shape descriptor for 3D object recognition , 2009, 2009 IEEE 12th International Conference on Computer Vision Workshops, ICCV Workshops.

[34]  Guillaume Lavoué,et al.  Bag of Words and Local Spectral Descriptor for 3D Partial Shape Retrieval , 2011, 3DOR@Eurographics.

[35]  Leonidas J. Guibas,et al.  A concise and provably informative multi-scale signature based on heat diffusion , 2009 .

[36]  Andrea Torsello,et al.  Fast and accurate surface alignment through an isometry-enforcing game , 2015, Pattern Recognit..

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

[38]  Wei Yu,et al.  Fragmented skull modeling using heat kernels , 2012, Graph. Model..

[39]  Szymon Rusinkiewicz,et al.  Estimating curvatures and their derivatives on triangle meshes , 2004, Proceedings. 2nd International Symposium on 3D Data Processing, Visualization and Transmission, 2004. 3DPVT 2004..