Inference Flow
V
Input pixel reflectance
If pixel reilectance in near-IR
If reflectance in red
band « 12€
If pixel reflectance in near-IR
band < 5%
True
Vegetation
If reflectance in red
band < 10%
Figure 5. Example of Decision Tree Classifier [1]
8. NEURAL NETWORK CLASSIFIERS
The Artificial Neural network based classifiers are used to
circumvent the complex class boundary problem. The most
widely used model is the Back Propagation model, which is a
supervised approach. The issues involved in applying ANN
models are :
e architecture of the ANN, like the number of hidden
layers , number of neurons in the hidden layer etc.
e degree of training , over training may make the
network mimic the pattern and not generalize it,
under training will cause error in classification
e feature to be used as inputs; gray levels, auxiliary
information, derived contextual information like
texture etc.
With regard to number of neurons in the hidden layer, Garson
[1] has suggested that the number of neurons in the hidden
layer should be equal to Ny(r(Nr-No), where
N, is the number of training samples
N, is the number of input features and
Np is the number of output classes
r is related to the noisiness of the data
For unsupervised classification Kohonen and ART models are
employed. For shape classification Hopfield type models are
better suited. For classification of highly correlated patterns an
iterative variant of Hopfield based on spin glass theory is used.
It is to be noted that ISODATA clustering is influenced by the
variance of the initial sample distribution to determine class
structures. Whereas in the case of Kohonen SOM cluster
structures depends on initial sample distribution.
IAPRS & SIS, Vol.34, Part 7, “Resource and Environmental Monitoring", Hyderabad, India,2002
8.1 Probabilistic Neural Networks [11]: Probabilistic neural
network (PNN) is based on statistical principles rather than
heuristic approach. The PNN uses Parzen or Parzen like
probability density function estimators, which asymptotically
tend towards parent density. PNN does this by using sums of
spherical Gaussian functions centered at each training sample
for probability density function estimation for that class. Hence
PNN is able to make a classification decision in accordance
with the Bayes principle , providing probability and reliability
measure for each class.
The decision function commonly used in PNN architecture is
M;
gi(x)= Eexp((Zy-1/0") (1)
j=l
and ((Zy-1Y/0?) s[G-x) (x)/20] (2)
which involves dot product Zi; and an exponential activation
function. © is smoothing factor which has same value
throughout the network, this is the only modification for
optimizing the network as classifier. Training involves finding
the optimal 6 for a set of training samples xij.
One of the properties of PNN is associative memory, i.e.
feature vectors are also stored unlike Back Propagation, where
only weights are stored.
Advantages of PNN are :
e Training is fast and easy and few passes are only
needed.
e As the number of training vectors increases the
decision surfaces will tend towards Bayes optimal
boundaries.
e Thesingle parameter, smoothing factor, is to be
modified to make the decision boundaries complex or
simple.
e For new training vectors the network need not be
retrained only smoothing factor is to be adjusted.
e Erroneous samples are tolerated.
e Network performance will not deteriorate if few
samples are only available.
Disadvantages of PNN are .
e New vectors are classified using all the vectors ,
hence all vectors are to be stored thus requiring a
large memory.
9. CONTEXTUAL CLASSIFIERS
It has been observed that pattern recognition tasks cannot be
treated as complete with out satisfactory induction of contextual
information either during classification process or as post
classification operation. Context, is defined as the local domain
from which observations were taken, and often includes
spatially or temporally related measurements. It is often
assumed that contextual relationships decay with distance as it
happens in the natural world.
Some techniques for incorporating contextual knowledge in the
classification process are
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