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P(x1|Class) x P(x2|Class) x ... P(xi|Class).
This assumption of statistical independance is often
assumed in fuzzy logic schemas. Therefore these
methods are as weak as their assumptions.
Model based image analysis concentrates on the
estimation of model parameters from measurement
data under a minimum cost optimisation rule. Good
models have defined orthogonal parameters, so a first
step in feature extraction should be model inversion.
Each data source provides estimaters for its own model
with its specific parameters. For example, multispectral
data provides estimators for surface angle -> leaf angle
distribution, shading of slopes and spectral reflectance
-> the mixture of visible surfaces within a resolution
element -> leaf area index. A temperature / heat
balance model requires the complement of reflectance
= absorption of radiation. From thermal data the
emission can be measured and the temperature or
emittance can be estimated. The microwave reflection
model has parameters for surface normals, surface
roughness and dielectric properties.
Dependancies between models are initially estimated
on the bases of a dimension analysis and on the form
of the models involved. This is followed by an
estimation of the cooccurence of parameters. In the
end the total dependancy is represented by P(Class |
datal, data2, data2,..) or its inverse P(data-i,.. | Class).
The dependancy between class membership, context
and data is first modelled and then adjusted to
observed values for the model components. (context is
modelled through local priors).
Given the dependancies of all occuring (class, data),
the availability of only one, or few data sources at a
time can now be treated as a case of missing data !
4 Practice of multi source, multi class data.
4.1 GIS + RS data.
In the daily practice of RS data analysis and use of a
GIS the types of data available for hypothesis
evaluation and classification are : (old) maps or
GIS(t=0) -> status at time=0, + data ; emitted photon
data, reflected photon data, reflected (synthetic aper-
899
ture/ real aperture) electro magnetic waves -> GIS(t+1).
We assume that error correction and geo referencing
procedures have been applied and that the source
images have been segmented into surface objects ->
scene objects.
In model based scene analysis, a forward model is
defined as a relation between scene object parameters
and remotely sensed data. The analysis problem is
mostly a problem of model inversion: RS data -> object
parameters.
Objects in a scene are labelled by attributed class
names. The class names serve as a label indication
groups of objects which have something in common (
which need not be something observable by (all
sensors) remote sensing). This leads to the definition of
classes and subclasses connected by reasoning about
observability. The relation between an observable from a
certain source and class membership of the scene
object is the feature(vector). Features are often defined
through the definition of the interaction model between
object(class) and radiation -> data source. Feature
determination is in that case equivalent to parameter
estimation.
The general classification schema is :
maps, status of GIS -> class priors -> observable
sourcei -> feature 1 -> class (likelihood) observable
source2 -> feature 2 -> etc.
Old maps, GIS data: are very usefull in the definition of
prior probabitilies for classes per object, specially when
combined with a Markov state transition probability
algorithm [Middelkoop,1990,2]. It also helps in object
detection in combination with one of many area seg-
mentation procedures.
Digital elevation models (from the GIS) are used for the
prediction of shadow and shading effects via ray tracing
procedures.
Different sources lead to different features. Features are
often parameters of models linking observables to object
descriptors.
SE
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