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AI-GEOSTATS: summary of spatial point pattern

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  • Veerle Huvenne
    Dear Ai-Geostats members, Some 2 weeks ago I sent a question to all of you concerning spatial point patterns and the application of Ripley s K-function. The
    Message 1 of 1 , Apr 15, 2003
      Dear Ai-Geostats members,

      Some 2 weeks ago I sent a question to all of you concerning spatial
      point patterns and the application of Ripley's K-function. The questions
      basically were the following :

      * Therefore my question : is the K-function a good technique to study
      the spatial point pattern? (as I understood from Cressie (1993) it is
      one of the best ones?)? How sensitive is it to the estimation of lambda?

      And to non-stationarity? Any suggestions?
      * Hence my second question : should I consider these marked points as
      irregular lattice data? And then calculate a semivariogram, maybe
      interpolate a surface? I have the feeling there is quite a lot of
      variability in mound height over small areas. How do I express this

      I received following answers, for which I would like to thank all
      contributors once again!

      Re: [AI-GEOSTATS: spatial point patterns]
      Wed, 02 Apr 2003 12:14:31 +0200
      Gregoire Dubois <gregoire.dubois@...>
      Veerle Huvenne <veerle.huvenne@...>

      hello Veerle,

      a quick and lazy reply: the Crimestat software (Free) has a lot of
      functions for point pattern analysis. The manual is also well written
      describes all these functions.

      Info on Crimestat can be found at www.ai-geostats.org



      Re: AI-GEOSTATS: spatial point patterns
      Wed, 2 Apr 2003 14:28:27 -0800
      "Qinghua GUo" <gqh@...>
      "Veerle Huvenne" <veerle.huvenne@...>

      hi, Veerle

      Yes, Ripley's K is one of the best approach to study point pattern, but
      requires stationarity, for the non-stationarity, the result from
      will be misleading. I have tested it in trend data, and demonstrated
      riply's K is unable to study the non-stationarity data. You may correct
      trend first or apply some other methods.

      Traditional semivariogram is not suitable for uncontiunous data, which I

      think is your case.
      Depending on the purpose of this study, some cross (e.g. cross-Riply's
      analysis will be more useful.


      Qinghua Guo

      Upon further questions, Qinghua Guo gave me some more useful information

      Dear Huvenne:

      > Can you please suggest some references about alternative methods?

      there is a Ripley'k variant:
      r*K(h)=E(number of event within distance h)
      r is the intensity or mean number of events per unit area.
      Traditionally, r is assumed to be constant, but you can change it
      to trends (e.g. fitting a surface)

      > But when the data is not stationary, can I use a cross-Ripley then?
      > can you please suggest some references?

      Trend correction should be applied in order to use cross analysis.

      We are ongoing studying these areas, there are few references addressing

      point pattern analysis on data with trends.


      Qinghua Guo


      Fwd: AI-GEOSTATS: spatial point patterns
      Thu, 03 Apr 2003 12:55:28 +0200
      Eric Pirard <eric.pirard@...>

      Hello Veerle,

      I have no special experience with the practical use of Ripley's K
      But, the kind of problem you are adressing seems to me to be more
      related with stochastic geometry and in particular
      random processes of discs with variable diameters (I assume diameters
      and heights of your mouns are somehow related).
      In other words I think it would be more adequate to consider the
      random/non-random dispersion of your mounts
      including their exact shapes and not only their centres.

      A useful (but strong in mathematics) reference book on the topic is
      STOYAN, KENDALL MECKE Stochastic Geometry and its Applications, Wiley,

      Several papers on similar subjects although more related to material
      sciences have also been published by the Ecole des
      Mines de Paris and in particular Dominique JEULIN. He has organised a
      regular short course in Paris named
      "Modélisation des structures aléatoires" that might be of interest to

      Finally, I did use for an Image Analysis problem (yours is one!) a
      test developed by Bosco and consisting in measuring
      the evolution of the total perimeter of particles (in this case
      mounds) after successive dilations. (Perimeter-area laws for a
      random agglomeration of particles; Bosco Emmanuel in Phys. Rev. E 52,
      4681–4684 (1995))


      RE: AI-GEOSTATS: spatial point patterns
      Fri, 4 Apr 2003 12:10:13 +0100

      Dear Veerle,
      there is a paper by Baddeley, Moeller, and Waagepetersen, which
      an inhomgeneous version of the K-function:

      Baddeley, A., Møller, J., & Waagepetersen, R. (1998). Non- and
      semi-parametric estimation of interaction in inhomogeneous point
      Statistica Neerlandia, 54, 329-350.

      You might find this useful!



      Veerle Huvenne
      Renard Centre of Marine Geology
      University of Ghent

      Krijgslaan 281, S8
      9000 Gent, Belgium

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