Chapter 2 EMR

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Digital Image Processing A Remote Sensing
Perspective FW 5560 Per- Pixel Classification
Algorithms
Per-pixel Supervised Classification Algorithms
Parallelepiped Classification Algorithm Minimum
Distance to Mean
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Using a one-standard deviation threshold a
PARALLELEPIPED algorithm decides BVijk is in
class c if, and only if where c 1, 2, 3, ,
m, number of classes, and k 1, 2, 3, , n,
number of bands. Therefore, if the low and high
decision boundaries are defined as
and the parallelepiped algorithm becomes
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Minimum Distance to Means Classification Algorithm
The minimum distance to means is computationally
simple. User provides the mean vectors for each
class in each band µck from the training data. To
perform a minimum distance classification, the
program must calculate the distance to each mean
vector µck from each unknown pixel (BVijk).
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Mahalanobis Distance Classification Is similar to
minimum distance, except that the covariance
matrix is utilized. Variance and covariance are
figured in so that clusters that are highly
varied lead to similarly varied classes, and vice
versa. For example, when classifying urban
areastypically a class whose pixels vary
widelycorrectly classified pixels may be farther
from the mean than those of a class for water,
which is usually not a highly varied class T. The
equation is D (X-Mc)T (Covc -1)
(X-Mc) Where D Mahalanobis distance c a
particular class X the measurement vector of
the candidate pixel Mc the mean vector of the
signature of class c Covc the covariance
matrix of the pixels in the signature of class
c Covc-1 inverse of Covc The pixel is
assigned to the class, c, for which D is the
lowest.
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Maximum Likelihood Classification Algorithm

• The aforementioned classifiers are based on
  identifying decision boundaries in feature space
  using multispectral distance measurements. The
  maximum likelihood decision rule is based on
  probability.
• It assigns each pixel having pattern
  measurements or features X to the class i whose
  units are most probable or likely to have given
  rise to feature vector X.
• In other words, the probability of a pixel
  belonging to each of a predefined set of m
  classes is calculated, and the pixel is then
  assigned to the class for which the probability
  is the highest.
• The maximum likelihood decision rule is one of
  the most widely used supervised classification
  algorithms.

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The maximum likelihood procedure assumes that the
training data statistics for each class in each
band are normally distributed (Gaussian). Trainin
g data with bi- or n-modal histograms in a single
band are not ideal. The individual modes probably
represent unique classes that should be trained
upon individually and labeled as separate
training classes. Produces unimodal, Gaussian
training class statistics that fulfill the normal
distribution requirement.
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For example, consider the hypothetical histogram
(data frequency distribution) of forest training
data obtained in band k. We could choose to store
the values contained in this histogram in the
computer, but a more elegant solution is to
approximate the distribution by a normal
probability density function (curve), as shown
superimposed on the histogram.
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The estimated probability density function for
class wi with one band of data is computed using
the equation Where exp is e (the base
of the natural logarithms) raised to the
computed power, x is one of the brightness
values on the x-axis, is the
estimated mean of all the values in the forest
training class, is the estimated
variance of all the measurements in this class.
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If the training data consists of multiple bands
of remote sensor data for the classes of
interest, we compute an n-dimensional
multivariate normal density function
using Where is the
determinant of the covariance matrix,
is the inverse of the covariance matrix,
is the transpose of the vector
The mean vectors (Mi) and covariance matrix
(Vi) for each class are estimated from the
training data.
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ISODATA Unsuperived Classification
Algorithm The Iterative Self-Organizing Data
Analysis Technique (ISODATA) - a comprehensive
set of heuristic (rule of thumb) procedures that
have been incorporated into an iterative
classification algorithm. The ISODATA algorithm
includes a) merging clusters if their separation
distance in multispectral feature space is below
a user-specified threshold and b) rules for
splitting a single cluster into two clusters.
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ISODATA is iterative- makes a large number of
passes through the dataset. ISODATA- initial
arbitrary assignment of all Cmax clusters takes
place along an n-dimensional vector that runs
between very specific points in feature
space. The region in feature space is defined
using the mean, µk, and standard deviation, sk,
of each band in the analysis. This method of
automatically seeding the original Cmax vectors
makes sure that the first few lines of data do
not bias the creation of clusters.
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ISODATA is self-organizing because it requires
relatively little human input. Normally requires
the analyst to specify the following criteria
Cmax the maximum number of clusters to be
identified by the algorithm (e.g., 20
clusters). T the maximum percentage of pixels
whose class values are allowed to be unchanged
between iterations. When this number is reached,
the ISODATA algorithm terminates. M the
maximum number of times ISODATA is to classify
pixels and recalculate cluster mean vectors. The
ISODATA algorithm terminates when this number is
reached.
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Minimum members in a cluster () If a cluster
contains less than the minimum percentage of
members, it is deleted and the members are
assigned to an alternative cluster. Maximum
standard deviation (smax) When the standard
deviation for a cluster exceeds the specified
maximum standard deviation and the number of
members in the class is greater than twice the
specified minimum members in a class, the cluster
is split into two clusters. The mean vectors for
the two new clusters are the old class centers
1s. Minimum distance between cluster means
(C) Clusters with a weighted distance less than
this value are merged.
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