AI-GEOSTATS: summary of spatial point pattern
- 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@...>
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@...>
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.
Upon further questions, Qinghua Guo gave me some more useful information
>there is a Ripley'k variant:
> Can you please suggest some references about alternative methods?
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?And
> 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.
Fwd: AI-GEOSTATS: spatial point patterns
Thu, 03 Apr 2003 12:55:28 +0200
Eric Pirard <eric.pirard@...>
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,
RE: AI-GEOSTATS: spatial point patterns
Fri, 4 Apr 2003 12:10:13 +0100
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!
Renard Centre of Marine Geology
University of Ghent
Krijgslaan 281, S8
9000 Gent, Belgium
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