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GEOSTATS: topography & modelling

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  • Umberto Fracassi
    Hi all, and sincere apologies for cross postings! I am in the process of starting a phd project on analytical restoration of paleosurfaces displaced in
    Message 1 of 5 , Nov 6, 1998
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      Hi all,

      and sincere apologies for cross postings!

      I am in the process of starting a phd project on analytical restoration of
      paleosurfaces displaced in neotectonics basins in south-central Apennines,
      Italy.

      One of the key issues at the base of the project is to try and
      model in 3- (or 3.5-) D the landforms detected from digital topography,
      i.e. to write a system that can discriminate landforms on the DEM,
      clusterize them (on the ground of given slope/gradient parameters) and
      analytically 'shape-fit' the landform (such as a badland, for instance).
      The idea would be to render classes of landforms under an analytical form
      which can then be digested by an algorithm to process a DEM, and to cluster
      classes of landforms detected on the ground of their shape _and_ of their
      analytical description.

      I don't exactly know whether/how this would be possibly done, or how has
      this been (successfully?) attempted before. Curve fitting may work +/- well
      for voice waveforms, and shape fitting may work well for close-range
      photogrammetry (a building's deformed wall), but what about naturally
      complex, chaotic, fuzzy (?) landforms, that bear a deformational and
      erosional history..?
      I am thinking about neural networks (for pattern discrimination) and
      perhaps finite elements.. to discriminate gradients on the DEM. But I am
      very unsure on how to analytically reproduce a landform (provided this is
      feasible..) - perhaps with mathematical morphology..? A simple form like an
      eroded crater may perhaps be approximated with a spherical integral using a
      gauss-like function.. but what about a faulted terrane of which you only
      have a few remnants?

      Any views, criticisms, suggestions of papers are all most welcome..

      Many thanks in advance,


      Umberto Fracassi, PhD student

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    • Eric Pirard
      Message 2 of 5 , Nov 10, 1998
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      • Marcel Nzeukou
        Hi everyone, I am interested in investigating the possible relationship between a VARIOGRAM and a WEIGHT MATRIX as both concepts are used to correct for a
        Message 3 of 5 , Nov 10, 1998
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          Hi everyone,

          I am interested in investigating the possible relationship between a
          VARIOGRAM and a WEIGHT MATRIX as both concepts are used to correct for a
          possible spatial pattern in the regression of a geographically referenced
          data set.
          I will be very grateful for help on any reference about any previous work
          done on this subject or any suggestion.

          Marcel Nzeukou
          U. of Arizona
          Dpt. of Mathematics


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        • John Kern
          Marcel and others, For situations where one is interested in a linear model Z=XB+resids, if the residuals are assumed to be from a stationary random function,
          Message 4 of 5 , Nov 10, 1998
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            Marcel and others,

            For situations where one is interested in a linear model Z=XB+resids, if the
            residuals are assumed to be from a stationary random function, then the
            weight matrix is simply the spatial covariance matrix for the residuals.
            Further, under stationarity, we have a one to one relationship between the
            variogram and covariance function so it is a fairly straight forward step.
            We can estimate the covariance function parameters by restricted maximum
            likelihood followed by refinement of the regression parameters as
            Generalized least squares estimates. These are the BLUE estimators under the
            second order stationarity assumption.

            Interesting research questions probably arrise in handling non-stationarity
            in the covariance function. As question I am wonderingif this is taken care
            of using intrinsic random function models. Anyone?

            See Cressie 1990 for this development under universal kriging and
            generalized linear models.


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          • Wulder, Mike
            Greetings, Concerning landform classifications from DEM data. Dr. Phil Giles undertook a number of studies to generate geomorphological signatures from slope
            Message 5 of 5 , Nov 10, 1998
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              Greetings,

              Concerning landform classifications from DEM data.

              Dr. Phil Giles undertook a number of studies to generate geomorphological
              signatures from slope units computed from DEMs. An example of this work
              is:

              Giles, P. T., 1998; Geomorphological Signatures: Classification of
              Aggregated Slope Unit Objects from Digital Elevation and Remote Sensing
              Data, Earth surface processes and landforms, v 23 n 7, pp. 581-

              Best regards...Mike

              > ----------
              > From: Eric Pirard[SMTP:eric.pirard@...]
              > Sent: November 10, 1998 6:38 AM
              > To: ai-geostats@...
              > Subject: Re: GEOSTATS: topography & modelling
              >
              > Hello Umberto,
              >
              > I have no knowledge of previous attempts of this kind to analyze DEMs and
              > classify landforms. My experience with topography is more at microscopical
              > level (surfometry).
              > I would like to draw your attention on the potential of mathematical
              > morphology to tackle the problem of analysis of landforms. Basic tools
              > such as Opening / Closing and other subsequent classification tools such
              > as Watersheds and Tophats are designed to tackle the problems you want to
              > solve.
              > I had experience of using fractal dimensions, Fourier transforms and
              > Mathematical Morphology in the analysis of roughness and found that Morpho
              > Math is the most sensitive and most robust tool for such work.
              > In any case, you should not neglect the literature on surface topography
              > in tribology (mechanics) and in grey level image analysis. These
              > disciplines are much closer to your work than you might expect.
              > Basically, this cross disciplinary need is the reason why we are
              > organising GEOVISION 99 in Liege. I hope to welcome you there.
              >
              > The second circular is no available from :
              >
              > http://www.lgih.ulg.ac.be/geovision/circular2/circular2.htm
              >
              >
              > Best regards and greetings from Enrico BONINO
              >
              >
              >
              > Prof. Eric PIRARD /.
              > Universite de Liege
              > ---- MICA ----
              > Caracterisation des Matieres Minerales Naturelles
              > Avenue des Tilleuls, 45
              > 4000 LIEGE
              > BELGIUM
              >
              > Tel.: +32-4-366.95.28. FAX: +32-4-366.95.20. e-mail :
              > Eric.Pirard@...
              > http://www.ulg.ac.be/mica
              > Join us at GEOVISION '99 ... http://www.lgih.ulg.ac.be/geovision -- *To
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