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9.1 Stacked Vector: The stacked vector approach attempts to
increase the classification accuracy by including structural
measurements, like texture measures, as an additional band to a
maximum likelihood classifier. The assumption of a normal
distribution is often violated by texture measures and may some
times cause difficulty.
9.2 Modelling context using Markov random fields (MRF):
In classical maximum likelihood decision rule, the prior
probability is set to be uniformly distributed due to lack of prior
knowledge or one does not know the true distributions. It may
be possible to improve classification results if prior pdf can be
modeled.
One source for modeling prior probability is context. The
premise for using context to model prior pdf is that adjacent
pixels in a image have reasonable degree of correlation. The
Markov random field (MRF) is useful to characterize
contextual information and Gibbs Random Field (GRF)
provides a practical way of using MRF model prior probability
density function.
Any pixel label with respect to its neighborhood is MRF if it
has the properties of positivity, Markovianity and
Homogeneity.
Marovianity property means that the label of a pixel depends on
its neighborhood pixel labels only.
Homogeneity property is that the conditional probability of a
pixel label, given the labels of the neighboring pixels is
independent of the location.
The equivalence of MRF and GRF is described by Hammersley
- Clifford theorem.
“A unique GRF exists for every MRF as long as the GRF is
defined terms of cliques on a neighborhood”.
The cliques are used to define the context in vertical, horizontal
and diagonal directions. On the ensemble of these cliques MRF
is defined and because of its equivalence to GRF in the
neighborhood the GRF is used to define posterior energy
function, the minimization of which is done using multi model
minimization techniques like simulated annealing.
10. FUZZY CLASSIFIERS
The traditional thematic map is used with a presumption that
every point on the ground can be labeled as belonging to one
and only one class. Although the discrete categorization is
convenient to handle because of its simplicity, it may not be an
accurate representation of the real world. The remotely sensed
data provides as many as 2H possible categories of data with k
bits per pixel per band and 1 bands.
The crisp classifiers compress nearly continuous measurements
into relatively few classes, thereby ignoring certain amount of
the information contained in the data to obtain easy to handle
simplistic thematic map. The decision-making by crisp
classifiers is deterministic.
Human language of decision-making is not generally
deterministic, rather characterized by certain level of
uncertainty or Fuzziness. The same thing holds good in the
classification of imagery. The mislabeling errors of crisp
classifiers are due to pixels that show affinity with several
IAPRS & SIS, Vol.34, Part 7, “Resource and Environmental Monitoring”, Hyderabad, India,2002
51
information classes. This type of pixel is often described as
“mixed” pixel. For example, in a image of agricultural areas
there will be some pixels representing more than one crop.
Fuzzy classification approach addresses the “mixed” pixel
problem by relaxing the discrete membership function of crisp
classifiers with the concept of partial membership such that
each pixel may simultaneously hold several non zero
membership grades for different labels. Thereby allowing
greater flexibility. The crisp classifiers discussed earlier are
modified to incorporate the fuzziness.
Commonly used fuzzy algorithms are: Fuzzy C- means, Fuzzy
maximum likelihood classification, Fuzzy rule base.
Advantage of Fuzzy over crisp classification techniques is " for
a given area if the features of interest are agricultural crops,
crisp classifier gives acreage estimate as a single number,
where as from a fuzzy classified out put based on fuzzy
membership grade it will be possible to estimate upper and
lower cut off acreage estimates for each crop."
All the techniques mentioned above have been used with
multispectral data with reasonable degree of success, but their
application to hyper spectral data is not straightforward.
11. HYPER SPECTRAL SENSOR DATA HANDLING
The large number of spectral bands complicates their use for
classification. The selection of a subset of bands or features is
desirable to keep the volume of data and parameter estimation
for classification. New methods and/or modification to the
existing ones is needed to make effective use of the information
available in the hyper spectral data sets.
11.1 Hughes Phenomena: In the case of MLC it was
mentioned that mean vector and covariance matrix of sample
data is used by the classifier. For n bands the number of
elements to be estimated is given by n(n-1)/2+2n.
Data Dimension Vs Number of Elements
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Data Dimensin
Figure 6. Number of Elements is mean
vector and co-variance matrix elements
It is often said that the performance of the classifier can be
improved by adding additional features. The performance does
improve upto a certain point as additional features (or bands)
are added and then deteriorates.
