Deconfliction and Surface Generation from Bathymetry Data Using LR B-splines

  • Conference paper
  • First Online:
Mathematical Methods for Curves and Surfaces (MMCS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10521))

Abstract

A set of bathymetry point clouds acquired by different measurement techniques at different times, having different accuracy and varying patterns of points, are approximated by an LR B-spline surface. The aim is to represent the sea bottom with good accuracy and at the same time reduce the data size considerably. In this process the point clouds must be cleaned by selecting the “best” points for surface generation. This cleaning process is called deconfliction, and we use a rough approximation of the combined point clouds as a reference surface to select a consistent set of points. The reference surface is updated using only the selected points to create an accurate approximation. LR B-splines is the selected surface format due to its suitability for adaptive refinement and approximation, and its ability to represent local detail without a global increase in the data size of the surface.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
EUR 29.95
Price includes VAT (Germany)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
EUR 42.79
Price includes VAT (Germany)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
EUR 53.49
Price includes VAT (Germany)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Bhattacharyya, G.K., Johnson, R.A.: Statistical Concepts and Methods. Wiley, New York (1977)

    Google Scholar 

  2. Büchenschütz-Nothdurft, O., Pronk, M.J., van Opstal, L.H.: Latest Developments in Bathymetry Data Processing and its Application to Sandwave Detection. Marine Sandwave and River Dune Dynamics, 1–2 April 2004

    Google Scholar 

  3. Davydov, O., Zeilfelder, F.: Scattered data fitting by direct extension of local polynomials to bivariate splines. Adv. Comp. Math. 21, 223–271 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  4. Davydov, O., Morandi, R., Sestini, A.: Local hybrid approximations for scattered data fitting with bivariate splines. CAGD 23, 703–721 (2006)

    MathSciNet  MATH  Google Scholar 

  5. Debese, N.: Multibeam Echosounder Data Cleaning Through an Adaptive Surface-based Approach. US Hydro 07 Norfolk, May 2007

    Google Scholar 

  6. Dokken, T., Pettersen, K.F., Lyche, T.: Polynomial splines over locally refined box-partitions. Comput. Aided Geom. Des. 30(3), 331–356 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  7. Floater, M.S., Iske, A.: Multistep scattered data interpolation using compactly supported radial basis functions. J. Comput. Appl. Math. 73, 65–78 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  8. Forsey, D.R., Bartels, R.H.: Surface fitting with hierarchical splines. ACM Trans. Graph. 14(2), 134–161 (1995)

    Article  Google Scholar 

  9. Greiner, G., Hormann, K.: Interpolating and approximating scattered 3D-data with hierarchical tensor product B-splines. In: Le Méhauté, A., Rabut, C., Shumaker, L.L. (eds.) Surface Fitting and Multiresolution Methods, pp. 163–172. Vanderbildt University Press, Nashville (1997)

    Google Scholar 

  10. Hennis, N.: Automatic outlier detection in multibeam data. Master thesis, Delft University of Technology, September 2003

    Google Scholar 

  11. Hodge, V.J., Austin, J.: A survey of outlier detection methodologies. Artif. Intell. Rev. 22(2), 85–126 (2004)

    Article  MATH  Google Scholar 

  12. Johannessen, K.A., Kvamsdal, T., Dokken, T.: Isogeometric analysis using LR B-splines. Comput. Meth. Appl. Mech. Eng. 269, 471–514 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  13. Lee, S., Wolberg, G., Shin, S.Y.: Scattered data interpolation with multilevel B-splines. IEEE Trans. Visual. Comput. Graph. 3(3), 229–244 (1997)

    Article  Google Scholar 

  14. Lu, D., Li, H., Wei, Y., Zhou, T.: Automatic outlier detection in multibeam bathymetry data using robust LTS estimation. In: 2010 3rd International Congress on Image and Signal Processing (CISP) (2010)

    Google Scholar 

  15. Mehlum, E., Skytt, V.: Surface editing. In: Dœhlen, M., Tveito, A. (eds.) Numerical Methods and Software Tools in Industrial Mathematics. Birkhäusser, Boston (1997)

    Google Scholar 

  16. Mitas, L., Mitasova, H.: Spatial interpolation. In: Longley, P., Goodchild, M.F., Maguire, D.J., Rhind, D.W. (eds.) Geographic Information Systems - Principles, Techniques, Management, and Applications, pp. 481–498 (2005)

    Google Scholar 

  17. NIST/SEMATECH e-Handbook of Statistical Methods (2012). http://www.itl.nist.gov/div898/handbook/eda/section3//eda3672.htm

  18. NIST/SEMATECH e-Handbook of Statistical Methods (2012). http://www.itl.nist.gov/div898/handbook/eda/section3//eda353.htm

  19. Nowacki, H., Westgaard, G., Heimann, J.: Creation of fair surfaces based on higher order fairness measures with interpolation constraints. In: Nowacki, H., Kaklis, P.D. (eds.) Creating Fair and Shape-Preserving Curves and Surfaces. B.G. Teubner, Stuttgart (1998)

    Google Scholar 

  20. Oliver, M.A., Webster, R.: Kriging: a method of interpolation for geographical information system. Int. J. Geogr. Inf. Syst. 4(3), 323–332 (1990)

    Google Scholar 

  21. Sederberg, T.W., Zheng, J., Bakenov, A., Nasri, A.: T-splines and T-NURCCs. ACM Trans. Graph. 22(3), 477–484 (2003)

    Article  Google Scholar 

  22. Shepard, D.: A two-dimensional interpolation function for irregularly spaced data. In: Proceedings of 23rd National Conference, pp. 517–523. ACM (1968)

    Google Scholar 

  23. Skytt, V., Barrowclough, O., Dokken, T.: Locally refined spline surfaces for representation of terrain data. Comput. Graph. 49, 48–58 (2015)

    Article  Google Scholar 

  24. Skytt, V., Patané, G., Barrowclough, O., Dokken, T., Spagnuolo, M.: Spatial and environmental data approximation. In: Patané, G., Spagnuolo, M. (eds.) Heterogeneous Spatial Data: Fusion, Modeling and Analysis for GIS Applications. Synthesis Lectures on Visual Computing. Morgan & Claypool Publishers, April 2016

    Google Scholar 

  25. Sulebak, J.R., Hjelle, Ø.: Multiresolution spline models and their applications in geomorphology. In: Evans, I.S., Dikau, R., Tokunaga, R., Ohmori, H., Hirano, M. (eds.) Concepts and Modeling in Geomorphology: International Perspectives, pp. 221–237. Terra Publications, Tokyo (2003)

    Google Scholar 

  26. Zhang, W., Tang, Z., Li, J.: Adaptive hierachical B-spline surface approximation of large-scale scattered data. In: Sixth Pacific Conference on Computer Graphics and Applications, Pacific Graphics 1998 (1998)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vibeke Skytt .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Skytt, V., Harpham, Q., Dokken, T., Dahl, H.E.I. (2017). Deconfliction and Surface Generation from Bathymetry Data Using LR B-splines. In: Floater, M., Lyche, T., Mazure, ML., Mørken, K., Schumaker, L. (eds) Mathematical Methods for Curves and Surfaces. MMCS 2016. Lecture Notes in Computer Science(), vol 10521. Springer, Cham. https://doi.org/10.1007/978-3-319-67885-6_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-67885-6_15

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67884-9

  • Online ISBN: 978-3-319-67885-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Navigation