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Pairwise Matching of 3D Fragments Using Cluster Trees

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Abstract

We propose a novel and efficient surface matching approach for reassembling broken solids as well as for matching assembly components using cluster trees of oriented points. The method rapidly scans through the space of all possible contact poses of the fragments to be (re)assembled using a tree search strategy, which neither relies on any surface features nor requires an initial solution. The new method first decomposes each point set into a binary tree structure using a hierarchical clustering algorithm. Subsequently the fragments are matched pairwise by descending the cluster trees simultaneously in a depth-first fashion. In contrast to the reassemblage of pottery and thin walled artifacts, this paper addresses the problem of matching broken 3D solids on the basis of their 2.5D fracture surfaces, which are assumed to be reasonable large. Our proposed contact area maximization is a powerful common basis for most surface matching tasks, which can be adapted to numerous special applications. The suggested approach is very robust and offers an outstanding efficiency.

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References

  • Barequet, G., & Sharir, M. (1996). Partial surface matching by using directed footprints. In Proc. of the 12th annual symposium on computational geometry (pp. 409–410). New York: ACM Press.

    Google Scholar 

  • Besl, P. J., & McKay, N. D. (1992). A method for registration of 3-D shapes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(2), 239–258.

    Article  Google Scholar 

  • Chua, C. S., & Jarvis, R. (1997). Point signatures: A new representation for 3D object recognition. International Journal of Computer Vision, 25(1), 63–85.

    Article  Google Scholar 

  • Cooper, D., Willis, A., Andrews, S., Baker, J., Cao, Y., Han, D., Kang, K., Kong, W., Leymarie, F. F., Orriols, X., et al. (2002). Bayesian pot-assembly from fragments as problems in perceptual-grouping and geometric-learning. International Conference on Pattern Recognition, 16(3), 297–302.

    Google Scholar 

  • da Gama Leitão, H. C., & Stolfi, J. (2002). A multiscale method for the reassembly of two-dimensional fragmented objects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24(9), 1239–1251.

    Article  Google Scholar 

  • Dalley, G., & Flynn, P. (2002). Pair-wise range image registration: a study in outlier classification. Computer Vision and Image Understanding, 87(1-3), 104–115.

    Article  MATH  Google Scholar 

  • Ericson, C. (2005). Real-time collision detection. Kaufmann series in interactive 3D technology. Amsterdam: Elsevier.

    Google Scholar 

  • Fischler, M. A., & Bolles, R. C. (1981). Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Communications of the ACM, 24(6), 381–395.

    Article  MathSciNet  Google Scholar 

  • Goldberg, D., Malon, C., & Bern, M. (2004). A global approach to automatic solution of jigsaw puzzles. Computational Geometry, 28(2–3), 165–174.

    Article  MathSciNet  Google Scholar 

  • Hartigan, J. A., & Wong, M. A. (1978). A k-means clustering algorithm. Applied Statistics, 28, 100–108.

    Article  Google Scholar 

  • Huang, Q.-X., Flöry, S., Gelfand, N., Hofer, M., & Pottmann, H. (2006). Reassembling fractured objects by geometric matching. In SIGGRAPH ’06 (pp. 569–578). New York: ACM Press.

    Chapter  Google Scholar 

  • Johnson, A., & Hebert, M. (1997). Recognizing objects by matching oriented points. In Proc. IEEE conf. computer vision and pattern recognition (CVPR’97) (pp. 684–689).

  • Kampel, M., & Sablatnig, R. (2003a). Profile-based pottery reconstruction. Conference on Computer Vision and Pattern Recognition Workshop, 1, 4.

    Article  Google Scholar 

  • Kampel, M., & Sablatnig, R. (2003b). Virtual reconstruction of broken and unbroken pottery. In International conference on 3-D digital imaging and modeling (3DIM) (pp. 318–325).

  • Krsek, P., Pajdla, T., & Hlaváč, V. (2002). Differential invariants as the base of triangulated surface registration. Computer Vision and Image Understanding, 87, 27–38.

    Article  MATH  Google Scholar 

  • Linnainmaa, S., Harwood, D., & Davis, L. S. (1988). Pose determination of a three-dimensional object using triangle pairs. IEEE Transactions on Pattern Analysis and Machine Intelligence, 10(5), 634–647.

    Article  Google Scholar 

  • Mitra, N. J., & Nguyen, A. (2003). Estimating surface normals in noisy point cloud data. In SCG ’03: Proceedings of the nineteenth annual symposium on computational geometry (pp. 322–328).

  • Papaioannou, G., & Theoharis, T. (1999). Fast fragment assemblage using boundary line and surface matching. In IEEE/CVPR workshop on applicat. of computer vision in archaeology.

  • Papaioannou, G., Karabassi, A., & Theoharis, T. (2000). Automatic reconstruction of archaeological finds—a graphics approach. In Proc. 4th int. conf. computer graphics and artificial intell. (pp. 117–125).

  • Papaioannou, G., Karabassi, E., & Theoharis, T. (2002). Reconstruction of three-dimensional objects through matching of their parts. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24(1), 114–124.

    Article  Google Scholar 

  • Pottmann, H., Huang, Q.-X., Yang, Y.-L., & Hu, S.-M. (2006). Geometry and convergence analysis of algorithms for registration of 3D shapes. International Journal of Computer Vision, 67(3), 277–296.

    Article  Google Scholar 

  • Rusinkiewicz, S., & Levoy, M. (2001). Efficient variants of the icp algorithm. In International conference on 3D digital imaging and modeling (3DIM 2001) (pp. 145–152).

  • Sappa, A., Restrepo-Specht, A., & Devy, M. (2001). Range image registration by using an edge-based representation. In International symposium on intelligent robotic systems (SIRS’01) (pp. 167–176).

  • Schön, N., & Häusler, G. (2005). Automatic coarse registration of 3D surfaces. In Vision, modeling, and visualization 2005 (pp. 71–178).

  • Seeger, S., & Labourex, X. (2000). Feature extraction and registration: An overview. In Principles of 3D image analysis and synthesis (pp. 153–166).

  • Stockman, G. (1987). Object recognition and localization via pose clustering. Computer Vision, Graphics, and Image Processing, 40(3), 361–387.

    Article  Google Scholar 

  • Vanden Wyngaerd, J., & Van Gool, L. (2002). Automatic crude patch registration: Toward automatic 3D model building. Computer Vision and Image Understanding, 87, 8–26.

    Article  MATH  Google Scholar 

  • Vienna University of Technology. 3D Puzzles—reassembling fractured objects by geometric matching. www.geometrie.tuwien.ac.at/geom/ig/3dpuzzles.html, undated.

  • Wahl, E., Hillenbrand, U., & Hirzinger, G. (2003). Surflet-pair-relation histograms: A statistical 3D-shape representation for rapid classification. In Proc. 4th international conf. on 3-D digital imaging and modeling (3DIM’03) (pp. 474–481). IEEE Computer Society Press.

  • Willis, A., & Cooper, D. (2004). Bayesian assembly of 3D axially symmetric shapes from fragments. IEEE Conference on Computer Vision and Pattern Recognition, 1, 82–89.

    Google Scholar 

  • Winkelbach, S., Westphal, R., & Gösling, T. (2003). Pose estimation of cylindrical fragments for semi-automatic bone fracture reduction. In B. Michaelis & G. Krell (Eds.), Lecture Notes in Computer Science : Vol. 2781. Pattern recognition, 25th DAGM symposium (pp. 566–573). Berlin: Springer.

    Google Scholar 

  • Winkelbach, S., Rilk, M., Schönfelder, C., & Wahl, F. M. (2004). Fast random sample matching of 3D fragments. In C. E. Rasmussen, H. H. Bülthoff, H. H. Giese, & B. Schölkopf (Eds.), Lecture Notes in Computer Science : Vol. 3175. Pattern recognition, 26th DAGM symposium (pp. 129–136). Berlin: Springer.

    Google Scholar 

  • Winkelbach, S., Molkenstruck, S., & Wahl, F. (2006). Low-cost laser range scanner and fast surface registration approach. In K. Franke, K.-R. Müller, B. Nickolay, & R. Schäfer (Eds.), Lecture Notes in Computer Science : Vol. 4174. Pattern recognition, 28th DAGM symposium (pp. 718–728). Berlin: Springer.

    Chapter  Google Scholar 

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Authors and Affiliations

  1. Institute for Robotics and Process Control, Technical University of Braunschweig, Braunschweig, Germany

    Simon Winkelbach & Friedrich M. Wahl

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  1. Simon Winkelbach
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  2. Friedrich M. Wahl
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Correspondence to Simon Winkelbach.

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Winkelbach, S., Wahl, F.M. Pairwise Matching of 3D Fragments Using Cluster Trees. Int J Comput Vis 78, 1–13 (2008). https://doi.org/10.1007/s11263-007-0121-5

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  • DOI: https://doi.org/10.1007/s11263-007-0121-5

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