Agriculture Reference
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The contextual approach to the extraction of information essentially concerns
the maximization of the posterior probability Pr(X/Y), where X is the unknown true
image and Y is the observed scene. This technique, known as MAP estimation, was
already described in Sect. 4.3 as a solution to the image restoration problem. Geman
and Geman ( 1984 ), Besag ( 1986 ), and Geman et al. ( 1990 ) have presented some
possible techniques for approximating a MAP estimate: simulated annealing
(SA) and iterated conditional modes (ICM). SA is a stochastic relaxation algorithm,
while ICM is deterministic. The two methods solve the optimization problem by
minimizing the energy function (Geman and Geman 1984 ; Geman et al. 1990 ).
The basic idea behind the SA algorithm was originally introduced to statistical
mechanics by Metropolis et al. ( 1953 ). Kirkpatrik et al. ( 1983 ) incorporated the
Metropolis scheme into a procedure analogous to chemical annealing to solve
combinatorial optimization problems such as the traveling salesman problem. SA
has an analogy with thermodynamics, specifically the way that metals cool and
crystallize, and is used to minimize a given cost function. The convergence of the
SA algorithm to the global optimum has been extensively analyzed (van Laarhoven
and Aarts 1987 ). Further details can be found in Geman and Geman ( 1984 ), where it
was shown that a necessary and sufficient condition to reach a global optimum is
that the temperature parameter decreases logarithmically with the number of
iterations. However, a study by Strenski and Kirkpatrick ( 1991 ) on finite length
cooling schedules found that geometric and linear cooling rates yielded a better
result than logarithmic designs.
ICM was originally proposed by Besag ( 1986 ), and represents a possible alter-
native to SA for solving complex combinatorial optimization problems that have a
prohibitively large computational burden. Thus, the ICM algorithm is particularly
suitable for large spatial data sets. It is a parsimonious procedure and can much
more efficiently solve the site-labeling problem. For more details about SA and
ICM, with applications to economic models, see Arbia et al. ( 1999 ) and Postiglione
et al. ( 2013 ).
4.7 GRASS for Analyzing Remotely Sensed Images
Software is crucial for analyzing RS images, and many software packages have
been developed. The objective of this section is not to review the different software,
but to present one possible example of a software application for image analysis.
We have chosen GRASS because it is free to use.
Within the last decade, GIS and image processing systems have undergone
evolutionary development. Future challenges require that these two technologies
be integrated, a process that has been implemented in GRASS.
Satellite images and orthophotos (aerial photographs) are processed as raster
maps in GRASS, and specialized tasks can be performed using the imagery
modules (i.e., command i. ) (Neteler and Mitasova 2008 ). All the general opera-
tions are handled by the raster modules.
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