Spatial statistics in agriculture
This page contains an overview of research acticities in spatial statistics
and related areas within the Dina network.
Its purpose is to aid the coordination of these activities within Dina.
Contents
News and announcements
Here workshops and other activities within the network will be announced.
Previous events
Previous events with relation to spatial statistics and image analysis
are listed here.
Workshop 2003: Dispersal models with agricultural applications
October 21-22, 2003; Brorfelde Observatory Complex, Denmark
See the workshop webpage for details.
Nordic Dina Workshop on spatial statistics in agriculture and forestry
November 1, 2001 at KVL.
The workshop covered a broad range of topics within the area
of spatial statistics and a wide range of applications in agriculture
and forestry, including yield meaurement, precision field management and
forest modelling, as well as more theoretical or research oriented
contributions.
Details such as the programme and abstracts can be found at
http://www.dina.kvl.dk/~ml/dina/itcoord/Workshop2001/.
DINA Workshop on Statistics and Image Analysis in Precision Agriculture.
Thursday November 16, 2000, at Aalborg University.
Precision agriculture requires processing of a wide variety of data
concerning e.g. soil properties, yield variation and weed occurrence. The
aim of this workshop was to provide a perspective on danish research in
precision agriculture with a focus on practical and theoretical aspects
of the analysis and application of data used in precision agriculture.
The programme (with abstracts) for the workshop is available here. A list of participants is also available.
Workshop: Image analysis and spatial statistics in forestry
A one-day Dina workshop on
image
analysis and spatial statistics in forestry was held on November
2, 1999 at KVL, The Royal Veterinary and Agricultural University of
Denmark.
Spatial statistics and precision agriculture
At the IBS Nordic Regional Conference June 9-11 1999 in Copenhagen there
was a session on "Spatial statistics and precision agriculture" (organized
by Rasmus Waagepetersen) and also
a session on "Image analysis in forestry". Ole
Fredslund Christensen whose Ph.D. research is funded by DINA gave a
talk with the title "Modelling of weed counts using spatial generalized
linear mixed models and MCMC".
The programme and abstracts for the two sessions are available here.
Further information is available from IBS
Nordic Regional Conference web page
Geostatistics in the Agricultural Sciences
In September 1998 we held a successful workshop on Geostatistics
in the Agricultural Sciences.
Spatial statistics in agriculture as a Dina priority area
Spatial statistics has many important applications in agriculture and related
fields and it is therefore natural that Dina has designated spatial
statistics in agriculture as a priority research area. The present
activities within Dina in this area are concentrated in the five sub-areas
stochastic
geometry and stereology, point processes in space
and time, image analysis,
geostatistics
and Markov chain Monte Carlo.
Organisation
The following Dina nodes host research in spatial statistics and related
areas:
-
Dina Foulum
-
Stochastic geometry and stereology, Markov
chain Monte Carlo, point processes, geostatistics.
-
Dina Aalborg
-
Markov chain Monte Carlo, point processes,
image
analysis, geostatistics.
-
Dina Risø
-
Point processes, image analysis,
geostatistics.
-
Dina KVL
-
Point processes, image analysis,
Markov
chain Monte Carlo.
The Dina IT coordinator for this area is presently
Morten Larsen, Dina KVL,
(ml@dina.kvl.dk)
who is mostly at home in the sub-area image
analysis. Dina will probably appoint a co-coordinator for this
area to replace Rasmus Waagepetersen who served as co-coordinator
until spring 2002.
Research areas and projects
Stochastic geometry and stereology
Stochastic geometry deals with questions concerning random geometric objects.
Such questions are related to a branch of statistics called stereology.
Stereological methods can e.g. be used to estimate the number, volume,
and surface area of three-dimensional objects from data consisting of two-dimensional
intersections (slices) of the original objects.
In the agricultural sciences, stereology has e.g. been used to count
and measure cells in onions, to quantify spraing in potatoes, and to quantify
the open space structure in grass swards.
An important statistical model based on stochastic geometry is the socalled
Boolean model which can be used as a model for random subsets of the plane.
In binary black or white images, for example, the black (or white) part
of the image may be considered as a realization of a random set when statistical
methods are used to analyze the image.
Project links
Point processes in space and time
Data which can be represented as point patterns occur frequently in spatial
statistics. In forestry, for example, the positions of trees in a forest
forms a point pattern in the plane. There may be attached marks to points;
the height of a tree may e.g. have been recorded along with the position
of the tree.
A point process is a model for the spatial distribution of the points
in a point pattern. The positions of the points may be completely independent
of each other but there are also models for point patterns where the points
appear in clusters or where the points repels each other. Clustered point
processes are e.g. relevant for modelling of positions of weed plants or of
disease infected plants which
typically appear in clusters on the field. Inhomogeneous point processes
are models for point patterns where the intensity of points varies as a
function of the spatial location.
Space-time point processes are relevant when the point pattern changes
with time. In a forest one may e.g. observe births and deaths of trees
as time goes by. Space-time point processes have also been used to model
the space-time evolution of plant disease epidemics and weed plant occurrence
in a field.
Project links
Image analysis
Image analysis is an important area for the application of spatial statistics
as images are by their very nature spatial and their information spatially
correlated.
In image analysis one is usually concerned with extracting information
on the imaged object(s) from the images, althoug one can also be concerned
with the imaging process itself for example to be able to reduce image
noise. It may be of iterest to segment images into regions, for
example to distinguish between plants and soil in an image taken from a
camera mounted on an agricultural machine. It may further be of interest
to classify the regions, for example to distinguish weeds from crops.
The features needed for a classification could be provided by feature
detection, for example to identify points on leaves.
For some images and applications it can be relevant to model the image
as an observation of some underlying stochastic process and to attempt
to estimate the parameters of the model from the images (and here there
can be a close relation with the area stochastic geometry
and stereology.
Project links
Geostatistics
Geostatistics is mainly concerned with spatial prediction. On a field one
may e.g. have measured the clay content in the soil on a number of locations
and it may then be of interest to predict the clay content at remaining
unobserved locations given the observed clay contents.
A fundamental task in geostatistics is to model and estimate the spatial
correlation between the variables of interest as a function of their interdistance.
Often a Gaussian random field model is applied with a parametric model
for the covariance (or variogram).
For a Gaussian model, the optimal predictor is a linear function of
the available data, so that optimal prediction under a Gaussian model is
equivalent to the socalled kriging method of interpolation.
Links
Markov chain Monte Carlo
Models which are analytically intractable occur frequently in spatial statistics.
Monte Carlo methods are therefore important tools in the study and application
of spatial statistics.
Direct simulation of complex spatial models is typically not feasible,
but it is often quite easy to simulate an ergodic Markov chain whose stationary
distribution is the distribution of interest.
The samples required for the Monte Carlo calculations can thus be obtained
from a simulated Markov chain after the Markov chain has reached equilibrium.
Project links
People
At Dina Foulum
-
Kristian Kristensen (kk@dina.sp.dk)
-
Geostatistics.
-
Jørgen Nielsen (jorgenn@dina.sp.dk)
-
Stereology.
-
Frede Aakmann Tøgersen
(FredeA.Togersen@agrsci.dk)
-
Markov chain Monte Carlo, image analysis,
geostatistics.
At Dina Aalborg
-
Jesper Møller
(jm@math.auc.dk)
-
Markov chain Monte Carlo, stochastic
geometry, point processes.
-
Steffen L. Lauritzen
(steffen@math.auc.dk)
-
Ole Fredslund
Christensen (olefc@math.auc.dk)
-
Geostatistics, Markov chain Monte
Carlo.
-
Martin Bøgsted Hansen
(*) (mbh@math.auc.dk)
-
Point processes, image analysis,
Markov
chain Monte Carlo.
-
Claus Dethlefsen (*) (dethlef@math.auc.dk)
-
Image analysis.
-
Søren Lundbye - Christensen
(*) (s0ren@math.auc.dk)
-
Stochastic geometry, Markov chain
Monte Carlo.
-
Rasmus Waagepetersen (rw@math.auc.dk)
-
Markov chain Monte Carlo, stochastic
geometry, geostatistics.
(*): These people are strictly speaking not directly involved in Dina but
work closely with Dina people on projects in spatial statistics, some even
with applications in agriculture(!).
At Dina KVL
-
Mats Rudemo (mats@dina.kvl.dk)
-
Point processes, image analysis.
-
Morten Larsen (ml@dina.kvl.dk)
-
Image analysis.
At Dina Risø
-
Hanne Østergård
(hanne.oestergaard@risoe.dk)
-
Point processes.
-
Karsten Bjerre
(karsten.bjerre@risoe.dk)
-
Point processes.
-
Rasmus Nyholm Jørgensen
(rasmus.joergensen@risoe.dk)
-
Image analysis, Geostatistics.
Links
Preprints
Geostatistics and spatial statistics
Precision Agriculture
Spatial Decision Support Systems
Miscellaneous
About this page
This page is maintained by Morten
Larsen (ml@dina.kvl.dk).
to whom ypu can send updates and information
to be included on the page.
Author:
ml@dina.kvl.dk.
Updated: September 2002