Skip to main content
SpringerLink
Account

Optimal Surface Fitting of Point Clouds Using Local Refinement

Application to GIS Data

  • Book
  • Open Access
  • © 2023

You have full access to this open access Book

Download book PDF
Download book EPUB

Overview

Authors:
  1. Gaël Kermarrec

    1. Institute for meteorology and climatology, Leibniz University Hanover, Hannover, Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Vibeke Skytt

    1. Mathematics and Cybernetics, SINTEF Digital, Oslo, Norway

    View author publications

    You can also search for this author in PubMed   Google Scholar

  3. Tor Dokken

    1. Mathematics and Cybernetics, SINTEF Digital, Oslo, Norway

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • This book is open access, which means that you have free and unlimited access
  • Provides a comprehensive description of an innovative surface approximation method for large data set
  • Shows a new procedure to optimize the surface fitting by means of statistical method
  • Contains a special chapter on a detailed case study using sea bed data

Part of the book series: SpringerBriefs in Earth System Sciences (BRIEFSEARTHSYST)

  • 7235 Accesses

Buy print copy

Softcover Book USD 16.99 USD 37.99
Discount applied Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Table of contents (7 chapters)

  1. Front Matter

    Pages i-xix
    Download chapter PDF

  2. Introduction

    • Gaël Kermarrec, Vibeke Skytt, Tor Dokken
    Pages 1-12Open Access
    Download chapter PDF

  3. Locally Refined B-Splines

    • Gaël Kermarrec, Vibeke Skytt, Tor Dokken
    Pages 13-21Open Access
    Download chapter PDF

  4. Adaptive Surface Fitting with Local Refinement: LR B-Spline Surfaces

    • Gaël Kermarrec, Vibeke Skytt, Tor Dokken
    Pages 23-39Open Access
    Download chapter PDF

  5. A Statistical Criterion to Judge the Goodness of Fit of LR B-Splines Surface Approximation

    • Gaël Kermarrec, Vibeke Skytt, Tor Dokken
    Pages 41-56Open Access
    Download chapter PDF

  6. LR B-Splines for Representation of Terrain and Seabed: Data Fusion, Outliers, and Voids

    • Gaël Kermarrec, Vibeke Skytt, Tor Dokken
    Pages 57-80Open Access
    Download chapter PDF

  7. LR B-Spline Surfaces and Volumes for Deformation Analysis of Terrain Data

    • Gaël Kermarrec, Vibeke Skytt, Tor Dokken
    Pages 81-107Open Access
    Download chapter PDF

  8. Conclusion

    • Gaël Kermarrec, Vibeke Skytt, Tor Dokken
    Pages 109-111Open Access
    Download chapter PDF
Back to top

Keywords

About this book

This open access book provides insights into the novel Locally Refined B-spline (LR B-spline) surface format, which is suited for representing terrain and seabed data in a compact way. It provides an alternative to the well know raster and triangulated surface representations. An LR B-spline surface has an overall smooth behavior and allows the modeling of local details with only a limited growth in data volume. In regions where many data points belong to the same smooth area, LR B-splines allow a very lean representation of the shape by locally adapting the resolution of the spline space to the size and local shape variations of the region. The iterative method can be modified to improve the accuracy in particular domains of a point cloud. The use of statistical information criterion can help determining the optimal threshold, the number of iterations to perform as well as some parameters of the underlying mathematical functions (degree of the splines, parameter representation). The resulting surfaces are well suited for analysis and computing secondary information such as contour curves and minimum and maximum points. Also deformation analysis are potential applications of fitting point clouds with LR B-splines.

Authors and Affiliations

  • Institute for meteorology and climatology, Leibniz University Hanover, Hannover, Germany

    Gaël Kermarrec

  • Mathematics and Cybernetics, SINTEF Digital, Oslo, Norway

    Vibeke Skytt, Tor Dokken

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation