Search:
Computing and Library Services - delivering an inspiring information environment

Detecting and approximating fault lines from randomly scattered data

Crampton, Andrew and Mason, John C. (2005) Detecting and approximating fault lines from randomly scattered data. Journal of Numerical Algorithms, 39 (1-3). pp. 115-130. ISSN 1017-1398

[img] PDF
Restricted to Registered users only

Download (453kB)

    Abstract

    Discretely defined surfaces that exhibit vertical displacements across unknown fault lines can be difficult to approximate accurately unless a representation of the faults is known. Accurate representations of these faults enable the construction of constrained approximation models that can successfully overcome common problems such as over-smoothing.
    In this paper we review an existing method for detecting fault lines and present a new detection approach based on data triangulations and discrete Gaussian curvature (DGC). Furthermore, we show that if the fault line can be described non-parametrically, then accurate support vector machine (SVM) models can be constructed that are independent of the type of triangulation used in the detection algorithms. We shall also see that SVM models are particularly effective when the data produced by the detection algorithms are noisy. We compare the performances of the various new and established models.

    Item Type: Article
    Additional Information: UoA 23 (Computer Science and Informatics) © Springer 2005
    Subjects: Q Science > Q Science (General)
    Q Science > QE Geology
    Q Science > QA Mathematics
    Schools: School of Computing and Engineering
    School of Computing and Engineering > Automotive Engineering Research Group
    School of Computing and Engineering > Informatics Research Group
    School of Computing and Engineering > Informatics Research Group > Knowledge Engineering and Intelligent Interfaces
    School of Computing and Engineering > Informatics Research Group > Software Engineering Research Group
    School of Computing and Engineering > Informatics Research Group > XML, Database and Information Retrieval Research Group
    Related URLs:
    References:

    [1] G. Allasia, R. Besenghi and A. De Rossi, A scattered data approximation scheme for the detection
    of fault lines, in: Mathematical Methods for Curves and Surfaces: Oslo 2000, eds. T. Lyche and
    L.L. Schumaker (Vanderbilt Univ. Press, Nashville, TN, 2000) pp. 25–34.
    [2] D. Apprato and C. Gout, A result about scale transformation families in approximation: Application
    to surface fitting from rapidly varying data, Numer. Algorithms 23 (2000) 263–279.
    [3] E. Arge and M. Floater, Approximating scattered data with discontinuities, Numer. Algorithms 8
    (1994) 149–166.
    [4] I. Barrodale and F.D.K. Roberts, Solution of an overdetermined system of linear equations in the 1
    norm (Algorithm 478), Comm. of the ACM 17(6) (1974) 319–320.
    [5] R. Besenghi and G. Allasia, Scattered data near-interpolation with applications to discontinuous surfaces,
    in: Curve and Surface Fitting, eds. A. Cohen, C. Rabut and L.L. Schumaker (Vanderbilt Univ.
    Press, Nashville, TN, 2000) pp. 75–84.
    [6] J. Duchon, Splines minimising rotation-invariant seminorms in Sobolev spaces, in: Lecture Notes in
    Mathematics, Vol. 571, eds. W. Schempp and K. Zeller (Springer, Berlin, 1977) pp. 85–100.
    [7] N. Dyn, K. Hormann, S.-J. Kim and D. Levin, Optimizing 3D triangulations using discrete curvature
    analysis, in: Mathematical Methods for Curves and Surfaces: Oslo 2000, eds. T. Lyche and
    L.L. Schumaker (Vanderbilt Univ. Press, Nashville, TN, 2000) pp. 135–146.
    [8] T. Gutzmer and A. Iske, Detection of discontinuities in scattered data approximation, Numer. Algorithms
    16 (1997) 155–170.
    [9] D. Lei, Robust and efficient algorithms for 1 and ∞ approximations, Ph.D. thesis, School of Computing
    and Engineering, University of Huddersfield, Huddersfield, UK (2002).
    [10] R. Morandi and A. Sestini, Geometric knot selection for radial scattered data approximation,
    in: Algorithms for Approximation IV, eds. J. Levesley, J.C. Mason and I.J. Anderson (Univ. of
    Huddersfield, Huddersfield, UK, 2002) pp. 244–251.
    [11] M.C. Parra, M.C. López de Silanes and J.J. Torrens, Verticle fault detection from scattered data,
    J. Comput. Appl. Math. 73 (1996) 225–239.
    [12] J.C. Platt, Fast training of support vector machines using sequential minimal optimization, in:
    Advances in Kernel Methods — Support Vector Learning, eds. B. Schölkopf, C.J.C. Burges and
    A.J. Smola (MIT Press, Cambridge, MA, 1999) pp. 185–208.
    [13] A.J. Smola, B. Schölkopf and G. Rätsch, Linear programs for automatic accuracy control in regression,
    in: Ninth International Conference on Artificial Neural Networks, Conference Publications
    No. 470 (IEE, London, UK, 1999) pp. 575–580.
    [14] R.J. Vanderbei, LOQO: An interior point code for quadratic programming, Technical Report
    SOR-94-15, Statistics and Operations Research, Princeton University, Princeton, NJ (1994); revised
    (1998).
    [15] R.J. Vanderbei and D.F. Shanno, An interior-point algorithm for non-convex nonlinear programming,
    Technical Report SOR-97-21, Statistics and Operations Research, Princeton University, Princeton, NJ
    (1997).
    [16] V.N. Vapnik, Statistical Learning Theory (Wiley, New York, 1998).
    [17] G.R. Walsh, An Introduction to Linear Programming, 2nd ed. (Wiley, New York, 1985).

    Depositing User: Sara Taylor
    Date Deposited: 18 Jun 2007
    Last Modified: 10 Dec 2010 13:26
    URI: http://eprints.hud.ac.uk/id/eprint/233

    Document Downloads

    Downloader Countries

    More statistics for this item...

    Item control for Repository Staff only:

    View Item

    University of Huddersfield, Queensgate, Huddersfield, HD1 3DH Copyright and Disclaimer All rights reserved ©