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Mathematics of Surfaces pp 196–212Cite as

Filling Holes in Point Clouds

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2768))

Abstract

Laser scans of real objects produce data sets (point clouds) which may have holes, due to problems with visibility or with the optical properties of the surface. We describe a method for detecting and filling these holes. After detecting the boundary of the hole, we fit an algebraic surface patch to the neighbourhood and sample auxiliary points. The method is able to reproduce technically important surfaces, such as planes, cylinders, and spheres. Moreover, since it avoids the parameterization problem for scattered data fitting by parametric surfaces, it can be applied to holes with complicated topology.

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References

  1. Akkouche, S., Galin, E.: Adaptive implicit surface polygonization using marching triangles. Computer Graphics Forum 20(2), 67–80 (2001)

    Article  MATH  Google Scholar 

  2. Bajaj, C.L.: Implicit surface patches. In: Bloomenthal, J. (ed.) Introduction to implicit surfaces. Morgan Kaufmann, San Francisco (1997)

    Google Scholar 

  3. Clarenz, U., Rumpf, M., Telea, A.: Robust feature detection and local classification for surfaces based on moment analysis. IEEE Transactions on Visualization and Computer Graphics (2003) (submitted), available online at http://numerik.math.uni-duisburg.de/research/publications.htm

  4. DeRose, T., Goldman, R.N., Hagen, H., Mann, S.: Functional composition algorithms via blossoming. ACM Trans. Graph. 12(2), 113–135 (1993)

    Article  MATH  Google Scholar 

  5. Curless, B., et al.: The Digital Michelangelo Project (2000), http://graphics.stanford.edu/projects/mich/

  6. Farin, G., Hoschek, J., Kim, M.-S. (eds.): Handbook of computer aided geometric design. North-Holland, Amsterdam (2002)

    MATH  Google Scholar 

  7. Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., Stuetzle, W.: Surface reconstruction from unorganized points. Computer Graphics 26(2), 71–78 (1992)

    Article  Google Scholar 

  8. Hoschek, J., Lasser, D.: Fundamentals of Computer Aided Geometric Design. AK Peters, Wellesley (1993)

    MATH  Google Scholar 

  9. Jüttler, B., Felis, A.: Least-squares fitting of algebraic spline surfaces. Adv. Comput. Math. 17(1-2), 135–152 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  10. Kass, M., Witkin, A., Terzopoulos, D.: Snakes: Active contour models. International Journal of Computer Vision 1(4), 321–331 (1987)

    Article  Google Scholar 

  11. Ramshaw, L.: Blossoms are polar forms. Comput. Aided Geom. Des. 6(4), 323–358 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  12. Ramshaw, L.: On multiplying points: The paired algebras of forms and sites. SRC Research Report #169, COMPAQ Corp. (2001)

    Google Scholar 

  13. Rausch, T., Wolter, F.-E., Sniehotta, O.: Computation of medial curves on surfaces. In: Goodman, T., Martin, R. (eds.) The mathematics of surfaces VII, pp. 43–68. Information Geometers, Ltd. (1997)

    Google Scholar 

  14. Sack, J.-R., Urrutia, J. (eds.): Handbook of computational geometry. North-Holland, Amsterdam (2000)

    MATH  Google Scholar 

  15. Schaback, R.: Remarks on meshless local construction of surfaces. In: Cipolla, R., Martin, R. (eds.) The mathematics of surfaces IX. Proceedings of the 9th IMA conference Cambridge, pp. 34–58. Springer, London (2000)

    Google Scholar 

  16. Taubin, R.: Estimation of planar curves, surfaces, and non-planar space curves defined by implicit equations with applications to edge and range image segmentation. IEEE Trans. Pattern Anal. Mach. Intelligence 13, 1115–1139 (1991)

    Article  Google Scholar 

  17. Tucholsky, K.: Zur soziologischen Psychologie der Löcher. In: Zwischen Gestern und Morgen. Rohwolt, Hamburg (1952)

    Google Scholar 

  18. Varady, T., Martin, R.R., Cox, J.: Reverse engineering of geometric models - an introduction. Comput.–Aided Des. 29(4), 255–268 (1997)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Spezialforschungsbereich SFB 013, Johannes Kepler University, Freistädter Str. 313, 4040, Linz

    Pavel Chalmovianský

  2. Dept. of Applied Geometry, Johannes Kepler University, Altenberger Str. 69, 4040, Linz

    Bert Jüttler

Authors
  1. Pavel Chalmovianský
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  2. Bert Jüttler
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Editor information

Editors and Affiliations

  1. School of Mathematics, University of Leeds, P.O. Box, LS2 9JT, Leeds, UK

    Michael J. Wilson

  2. School of Computer Science, Cardiff University, Wales, UK

    Ralph R. Martin

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© 2003 Springer-Verlag Berlin Heidelberg

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Chalmovianský, P., Jüttler, B. (2003). Filling Holes in Point Clouds. In: Wilson, M.J., Martin, R.R. (eds) Mathematics of Surfaces. Lecture Notes in Computer Science, vol 2768. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39422-8_14

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  • DOI: https://doi.org/10.1007/978-3-540-39422-8_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20053-6

  • Online ISBN: 978-3-540-39422-8

  • eBook Packages: Springer Book Archive

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