Chapter 7 Part II Digital Image Processing

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Chapter 7Part IIDigital Image Processing
Geography 4260Remote Sensing
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• Image Classification

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• The classification of the feature types
  represented by digital images using visual image
  interpretation techniques relies on the same
  elements of interpretation used for air photo
  interpretation, i.e. shape, size, pattern, tone,
  texture, shadows, site, and association.
• Digital image interpretation relies mainly on
  color, i.e. on comparisons of digital numbers
  found in different bands in different parts of an
  image.

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• The objective of digital image classification
  procedures is to categorize the pixels in an
  image into land cover classes.
• The output is a thematic image with a limited
  number of feature classes as opposed to a
  continuous image with varying shades of gray or
  varying colors representing a continuous range of
  spectral reflectances.

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• The range of digital numbers in different bands
  for particular features is known as a spectral
  pattern or spectral signature.
• Pattern in this sense does not have a spatial
  component. A spectral pattern can be composed of
  adjacent pixels or widely separated pixels.

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• Spectral pattern recognition refers the
  classification procedures that can be used to
  group similar pixels into feature classes.
• Computerized spatial pattern recognition is much
  more complex, and is still in its infancy in
  spite of more than three decades of research.

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• Temporal pattern recognition can also be
  accomplished by digital methods. This involves
  detecting and interpreting changes in spectral
  responses at different times.
• Spectral, spatial and temporal classification
  methodologies can be applied simultaneously or
  sequentially to improve the overall success of an
  image classification process, and the visual
  interpretation of spatial relationships is often
  a prelude to digital image classification.

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• Digital image classification techniques can
  generally be classified into two types
• Unsupervised classification techniques,
• Supervised classification techniques, and
• Hybrid classification techniques.
• Often, however, these types are used sequentially
  or iteratively.

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• Unsupervised image classification techniques rely
  on the computer to classify spectrally-similar
  pixels into classes in such a way that the
  digital numbers in each class have values within
  all bands that are more similar to the values
  associated with other pixels in the same class
  than they are to the digital numbers of pixels in
  other classes.

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• Supervised classification techniques require the
  image analyst to define the classification
  categories and identify a representative samples
  of pixels to the computer.
• The computer then assign all of the remaining
  pixels to one of the predefined classes on the
  basis of the similarities between the digital
  number in the training pixels and the digital
  numbers in all other pixels.

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• Hybrid classification techniques are designed to
  improve the results of separately applied
  unsupervised and supervised classification
  techniques.
• All of these techniques are generally applied to
  multispectral images, but similar techniques have
  been developed for hyperspectral images.

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• Supervised Classification

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• Supervised classification is considered first
  because the methodology used is generally easier
  to understand. Supervised classification is
  accomplished in four steps
• The analyst defines a classification scheme,
• The analyst identifies pixels known to fall in
  each class for the computer,
• The computer put each image pixel into a class
  based on the multispectral data ranges of the
  training pixels, and then
• The computer generates a classified image.

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• The purpose of the image classification project
  dictates the classes into which the computer will
  be asked to categorize image pixels, and it is
  the analysts responsibility to define these
  classes.
• For example, a forestry application will require
  different classes than a hydrologic or
  agricultural application. However, general
  purpose classifications containing a large number
  of land cover classes are also common.

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• Once the classes are defined, the analyst must
  develop training classes, i.e. sets of pixels
  within each land cover class encapsulating the
  range of variability of the digital numbers in
  each band.
• This process will be described in more detail
  after a discussion of how the computer uses these
  data ranges.

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• The Classification Stage

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• The computer begins the process of image
  classification by arranging the digital numbers
  of each pixel along the range of digital numbers
  in each band, illustrated here with only two
  bands.

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• The clusters of pixels are normally arranged in
  multidimensional space since three or more bands
  will usually be utilized in a classification.

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• One of several possible classification
  strategies, or classifiers, will then be applied
  to assign the remaining pixels into one of the
  predefined classes. Three classifiers will
  considered here
• The minimum-distance-to-means classifier,
• The parallelepiped classifier, and
• The Gaussian maximum likelihood classifier.

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• The minimum-distance-to-means classifier compares
  each unclassified pixel to the mean digital
  number within each band and assigns the pixel to
  the class whose mean is the shortest distance
  away in hyperdimensional space.

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• The set of mean digital numbers for each cluster
  is known as the clusters mean vector. Pixels that
  are to be classified also have a set of digital
  numbers in each of the same bands.
• The software calculates each unclassified pixels
  distance from each mean vector and assigns the
  pixel to the class where this distance is a
  minimum. (Note The mean vector is not this
  distance it is the n-dimensional location of
  the cluster).

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• This distance between an unclassified pixel and
  each mean vector is easily visualized in two or
  three dimensions, but the computer can easily
  calculate the distance in any number of
  dimensions.

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• The minimum-distance-to-means classifier is
  computationally efficient because it involves
  only simple mathematical calculations, but it is
  based only on the means of each cluster and is
  not sensitive to the variances of the training
  data clusters.

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• The variance of a training class is a measure of
  the within-band dispersion of the digital
  numbers. A training class with high variance has
  a large range of digital numbers within one or
  more spectral bands.

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• It is not uncommon to find pixels that are closer
  to the mean of one cluster with limited variance
  which are actually members a second cluster with
  more variance whose mean is more distant.

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• Because of the potential for misclassification
  when nearby classes have high variances, the
  minimum-distance-to-mean classifier is not very
  suitable in these cases but is entirely
  acceptable when the classes have low variances
  and low correlation.

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• Parallelepiped Classifier

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• A parallelepiped classifier is sensitive to
  within class variance because it encloses all of
  the pixels within a training class in
  parallelepipeds, n-dimensional equivalents of the
  rectangles shown here.

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• Image pixels that fall outside of the
  parallelepipeds are classified as unknown.
  Pixels in overlapping parallelepipeds are
  classified as uncertain or are arbitrarily
  placed in one or both of the overlapping classes.

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• Like the minimum-distance-to-mean classifier, the
  parallelepiped classifier is computationally
  efficient (and therefore fast).
• Additionally, however, it avoids the problems
  associated with assigning pixels to adjacent
  classes when one of the classes has a high
  variance (as long as the classes dont overlap).

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• Training classes can have high correlation or
  high covariance, or both.
• The presence of training classes with high
  correlation or high covariance complicates the
  classification process therefore, an basic
  understanding of correlation and covariance is
  necessary to an understanding of the
  classification process.

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• Training classes with high correlation have
  overlapping clouds of training pixels. This makes
  it impossible to assign new pixels in the overlap
  area with any degree of certainty.

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• High correlation cannot occur with a single
  training class because it correlation describes
  the similarity (or lack of similarity) between
  two or more classes.

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• A training class with high covariance has a cloud
  of pixels that is elongated diagonally when
  plotted on a two-axes scatter diagram.

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• Covariance refers to the arrangement of digital
  numbers within two or more bands of a single
  training class and is independent of the digital
  numbers found within other training classes.

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• High covariance, however, increases the volume of
  the parallelepipeds, making it more likely that
  pixels will fall within overlap regions and
  therefore have higher correlations with other
  training classes.

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• Both high correlation and high covariance are
  common within spectral response categories.
• Parallelepiped classifiers can be modified to
  include stepped boundaries to reduce the amount
  of misclassification, but they cant eliminate
  overlap areas if they exist. The Gaussian maximum
  likelihood classifier was designed to overcome
  this limitation.

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• Gaussian Maximum Likelihood Classifier

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• The Gaussian maximum likelihood classifier
  assigns pixels to classes after considering both
  the variance and covariance within training
  classes.
• It does so by assuming that the distribution of
  the clouds of points representing the training
  data is normally distributed, i.e. exhibits a
  Gaussian distribution.

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• In one dimension, the frequency distribution of a
  Gaussian distribution forms a bell-shaped curve.

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• In two dimensions, probability ellipses define
  the likelihood that any particular point is
  associated with a particular distribution, with
  lower (but finite) probabilities beyond each
  ellipse.

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• These ellipses are defined here by
  equiprobability contours, lines along which the
  probability that a point falling at that location
  belongs to a particular class.

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• In three or more dimensions, probability space is
  represented by n-dimensional volumes. Visualizing
  more than three dimensional volumes is
  challenging for us, but not particularly
  difficult from a computational standpoint.

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• Even though n-dimensional equiprobability
  contours overlap, the probabilities that any
  particular unclassified pixel is associated with
  each class can be calculated.
• Pixels are then simply assigned to the class with
  the highest probability that they actually belong
  to that class. Although it is possible that
  pixels can be misclassified, probability theory
  suggests that any particular pixel is more likely
  to be correctly classified than it is to be
  misclassified.

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• An extension of the maximum likelihood classifier
  is the Bayesian classifier which depends on
• A priori knowledge of the land cover types that
  are most likely to occur, and
• The relative costs of misclassification.

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• A Bayesian classifier uses weighting factors to
  increase the likelihood that pixels will be
  assigned to more common land cover classes as
  long as the risks of misclassifying a pixel to a
  common class isnt going to cause too much of a
  problem.
• Less common classes are given lower weights as
  are classes where misclassification of a pixel
  into that class would produce more serious
  problems related to the objectives of the
  classification process.

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• A Bayesian classifier is superior to a simpler
  maximum likelihood classifier if the image
  analyst has sufficient information. But, this
  isnt usually the case.
• As a result, most maximum likelihood classifiers
  assume equal likelihood and equal costs
  associated with misclassification.

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• Maximum likelihood classifiers are much more
  computationally intensive than simpler
  classifiers, particularly with larger images
  containing more bands and with larger numbers of
  classes.
• Several techniques can be used to increase the
  efficiency of the classification process,
  including
• Using a lookup table to assign classes,
• Reducing the dimensionality of the data, and
• Using a stratified classifier or decision tree.

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• Lookup tables are database tables that contain
  the values of one variable associated with all
  possible unique values of another variable.

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• Without a lookup table
• The calculations necessary to determine the
  probabilities of a pixels belonging to each of
  the several classes must be performed, and then
• The probabilities must be sorted to determine
  the class to which that pixel should be assigned.
• Both of these steps have to be repeated for every
  unclassified pixel.

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• A lookup table containing all existing
  combinations of pixel values in each band and the
  class to which such a pixel should be assigned
  avoids repeating these calculations for every
  pixel.

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• In other words, the probabilities are calculated
  and sorted once for each unique set of digital
  numbers instead of once for each unclassified
  pixel.

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• A lookup table accelerates the classification
  process because the class to be assigned to
  multiple pixels with identical digital numbers
  can be found in the lookup table without having
  to recalculate and sort probabilities.

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• Note that it is not necessary to calculate the
  probabilities for possible combinations of
  digital numbers because the minimum and maximum
  digital numbers in each band can be determined
  ahead of time to limit the ranges of values that
  need to be included in the lookup table.

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• Increasing the number of bands included in the
  image classification process increases the number
  of calculations necessary to use a maximum
  likelihood classifier.
• Likewise, being able to reduce the number of
  bands would reduce the number of calculations and
  improve the speed of the classification. That can
  be accomplished through the application of
  principal or canonical components analysis prior
  to the application of the image classifier.

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• Landsat MSS data contains four bands, but the
  inherent dimensionality of the data is two bands.
  In other words, principal components analysis can
  be applied to the original data to produce two
  rasters that contain all of the information
  necessary to assign the data to land cover
  classes.
• Canonical component analysis achieves similar
  results.

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• Stratified classifiers (a.k.a. layered
  classifiers or decision tree classifiers) can
  also be used to reduce the number of calculations
  necessary.
• These classifiers assign pixels to more
  easily-identified classes first, leaving only a
  subset of the pixels to be classified with a
  maximum likelihood classifier later.

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• Because water has very low reflectance in
  infrared, pixels can often be easily classified
  as water or not water by looking at the
  digital numbers in an infrared band. Other land
  covers may require data from only two or three
  bands.
• Assigning easily identified pixels to classes
  with simpler classifiers reduces the number of
  pixels that need to be assigned to classes by a
  slower maximum likelihood classifier.

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• Classifiers are used to assign pixels to known
  land cover classes, but they require input data
  to produce results. The input data are used to
  create statistical measures of the digital
  numbers (in each band) that can be expected to be
  found within each class.
• These data are assembled by the image analyst
  during the preceding training stage.

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• The Training Stage

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• Supervised classification assigns unclassified
  pixels to classes defined by an image analyst
  using one of the previously-described
  classifiers
• A minimum-distance-to-means classifier,
• A parallelepiped classifier, or
• A Gaussian maximum likelihood classifier.
• However, it is the analysts job to identify the
  pixels within each class that the computer will
  use to assign other pixels to the classes.

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• During the training stage of image
  classification, an image analyst selects
  individual pixels that are believed to represent
  both the typical reflectance values for each land
  cover class and the range of values likely to be
  found in each class.
• This is an iterative process in that the analyst
  has the opportunity to improve the data by
  evaluating them and adding or removing individual
  pixels to improve the utility of a training class.

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• The success of the classification effort depends
  on
• The analysts understanding of the process,
• The analysts knowledge of the land cover types
  and their distribution in the particular
  geographic area, and
• The availability of reference data to fill gaps
  in the analysts knowledge.

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• The multidimensional clouds of data points that
  represent the spectral responses of individual
  pixels are spectral classes.

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• Each spectral class includes multiple pixels to
  represent the range of spectral responses within
  a land cover type in a particular image area.
• But, multiple spectral classes are often required
  within each land cover class to adequately
  represent a land cover class within the final
  classification scheme.

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• For example, a water class might include deep
  clear lakes and shallow muddy ponds in addition
  to other water areas.
• If the computer is expected to distinguish water
  and other land cover types, then all of the
  possible spectral classes of water and all of the
  possible spectral classes.

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• Other land cover classes may also contain
  multiple spectral classes, each of which must be
  included in the training data.
• Even a simple classification of cover types into
  broad classes can require a very large number of
  spectral classes selected from an even larger
  number of training sites.

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• Training sites are geographic areas within which
  all of the pixels are believed to belong to a
  single spectral class, i.e. uniform areas of
  known land cover types.

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• ERDAS IMAGINE uses areas of interest to enclose
  training sites. An area of interest is a polygon
  enclosing one or more pixels representing a land
  cover class in the proposed classification scheme.

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• The more general name for an area of interest
  used in this manner is a viewing window. All of
  the pixels within a viewing window should be
  representative of a particular spectral class.

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• Because all of the pixels in a viewing window
  represent a particular spectral class, viewing
  windows should avoid edge areas so that
  transition zones are not included in the class.

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• The pixels within each of the viewing windows
  used to define a particular spectral class
  provide the digital numbers that will be used by
  the image classifier.
• Depending of the type of classifier, these
  numbers will be used to calculate minimum
  distances to means, locate parallelepipeds, or
  define probability contours.

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• ERDAS IMAGINE allows an image analyst to create
  areas of interest by
• Dragging a mouse to enclose rectangular or oval
  areas,
• Clicking a series of points to define the
  boundaries of irregular polygons,
• Clicking a series of points to define line
  running through a series of adjacent pixels, or
• Selecting a single seed pixel whose digital
  numbers are used by the software to find
  statistically similar pixels.

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• Only a very small sample of pixels is needed to
  calculate the statistics for a statistics-based
  classifier such as a maximum likelihood
  classifier.
• However, supervised classifications are normally
  performed with tens to hundreds of pixels in each
  of several windows representing each training
  class

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• Increasing the number of representative pixels
  increases that statistical estimates of the mean
  vector and covariance which are needed to
  calculate the probabilities that unclassified
  pixels are members of particular classes.
• In general, using more pixels to define a
  spectral class improves the quality of the
  statistics for that class.

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• Selecting widely-dispersed multiple training
  sites for each spectral class also improves the
  statistical description of the variability within
  that class.
• In other words, selecting fewer pixels from
  multiple training sites dispersed throughout the
  image generally works better than selecting a
  large number of pixels from either a single
  training site or a small number of nearby
  training sites.

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• Using multiple training sites without limit,
  however, increases the time needed to
  characterize the class.
• The objective is to adequately capture the
  spectral variability within a training class
  without including too many redundant pixels and
  without creating redundant training classes.

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• ERDAS IMAGINE and other image processing software
  packages can produce and display graphs,
  statistics and images that allow an image analyst
  to recognize gaps and redundancies in the
  training data. An analyst can then use this
  information to refine the data before they are
  used for classification.
• Training set refinement refers to the process of
  using these information resources to improve the
  training data.

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• Training set refinement tools and processes
  include
• Histograms and other graphical views of the
  data,
• Quantitative measures of category separability,
• Self-classification of the training set data,
• Interactive preliminary classification of pixels
  that were not included in the training classes,
  and
• Classification of a representative image
  subscene.

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• Graphical Representations of the Training Data

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• Graphical representations of the training data
  include
• Histograms,
• Coincident spectral plots, and
• Two-dimensional scatter diagrams.

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• Histograms

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• A histogram is a graph of the number of
  observations for each pixel value within a
  spectral band (or within a training class).
• Pixel values are on the horizontal axis and pixel
  counts are on the vertical axis.

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• In ERDAS IMAGINE, histograms include the median
  pixel value (as a digital number and graphically
  as a red line) and the minimum and maximum pixel
  values.

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• Histograms of training sites are useful because
  they provide a visual indication of the normality
  of the distribution.
• This is especially important when a Gaussian
  maximum likelihood classifier is to be employed
  because this classifier assumes that the training
  data are normally distributed.

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• This histogram illustrates a bimodal
  distribution.
• If these data represented a training class, they
  would be unacceptable for use with a maximum
  likelihood classifier.

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• A bimodal histogram indicates that a class
  contains two different spectral subclasses and
  suggests that two different training classes
  should be developed to differentiate them.

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• This is true even if the subclasses will be
  recombined in the final land cover classification
  because it makes it less likely that other land
  use types will be assigned to the resultant
  unimodal spectral subclasses.

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• Histograms illustrate the distribution of digital
  numbers within a band, but they dont make it
  easy to compare the distributions of digital
  numbers for different cover types in multiple
  bands.
• Coincident spectral plots are designed to
  overcome this shortcoming of histograms.

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• Coincident Spectral Plots

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• Coincident spectral plots display the mean and
  variance of the digital numbers associated with
  each spectral class in each band. (Standard
  deviation is one measure of the variance of a
  distribution).

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• The coincident spectral plots illustrated here
  suggest that classification of the features
  represented by these training classes can be
  accomplished with some degree of confidence in
  spite of significant overlap.

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• Two-Dimensional Scatter Plots

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• Two-dimensional scatter plots are used to compare
  the spectral response patterns of one or more
  training classes in two spectral bands and are
  useful for providing a visual indication of the
  separability of training classes utilizing only
  those two bands.

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• Scatter plots can also be used to visualize the
  degree of correlation between two bands
• Bands that are highly correlated (either
  negatively or positively) are not very useful for
  separating features from one another, but
• Bands that show poor correlation usually
  contains data that will allow the separation of
  different feature types from one another.

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• Histograms, coincident spectral plots, and
  scatter diagrams provide qualitative information
  that an image analyst can use to subjectively
  evaluate spectral classes, but they dont provide
  quantitative measures that can be used to assess
  signatures.

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• Quantitative Measures of
• Category Separability

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• Quantitative measures of category separability
  attempt to objectively summarize the ability of
  training classes to distinguish between the
  feature types they represent.
• ERDAS IMAGINE provides four such quantitative
  measures, including the Euclidean distance
  between training class means in n-dimensional
  space.

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• The results of all of these measures are normally
  presented in matrix format. The zeros along the
  diagonal within this matrix of Euclidean
  distances indicate that classes cannot be
  separated from themselves, while higher values
  indicate a higher level of separability.

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• Note that the numbers on opposite sides of the
  diagonal are mirror images of themselves.
• This is simply a result of the fact that the
  distances between spectral class means can be
  measured in either direction. Matrices of other
  quantitative measures of separability are also
  symmetrical.

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• Euclidean distances doesnt include a measure of
  the variance within training classes because it
  only considers the mean of each spectral class.
• The second quantitative measure provided by ERDAS
  IMAGINE, divergence, does include the variance in
  the calculation.

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• The formula used to calculate divergence is
  complex, but it is normally used by computer
  software rather than image analysts making it
  simple to apply.

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• Higher divergence numbers, like higher Euclidean
  distances, indicate higher separability while
  zeros are again found along the diagonals.
• Divergence values have no fixed range. Therefore,
  they are used to make relative comparisons of
  separability.

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• Transformed divergence, a third quantitative
  measure of separability, weights the covariance
  of the pairs by their distances in such a way
  that the values range from 0 to 2000.

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• The following general rules apply
• Spectral classes can be separated using only two
  bands if their transformed divergence of the two
  spectral classes between for those two bands is
  greater than 1900,
• Separability is fairly good if the transformed
  divergence is between 1700 and 1900, and
• Separability is poor if the transformed
  divergence is below 1700.

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• The same training classes were used to generate
  these transformed divergence values as were used
  in the earlier example.
• An obvious advantage of transformed divergence is
  that it normalizes the data for easy comparisons.

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• The maximized values for most of the pairs of
  spectral classes indicate that these signatures
  are suitable for separating these classes.
  Complete separability is made possible by the
  high quality of Thematic Mapper data and the fact
  that all seven bands were included in the
  signatures.

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• However, such high quality signatures cannot be
  produced without very careful selection of pixels
  within each training class regardless of the
  quality of the image data.

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• The Jefferies-Matusita (JM) distance, a final
  quantitative measure of spectral separability, is
  produced in a manner that is similar to the
  transformed divergence and is interpreted
  similarly, but it has a maximum value of 1414.

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• Self-Classification of Training Data Sets

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• Self-classification uses the training data to
  classify the pixels that were used to generate
  the training data.
• Although it might seem that all of the pixels
  will necessarily be correctly classified, that is
  not always the case. Some pixels may end up being
  incorrectly classified if there are overlaps in
  the ranges of digital numbers used to create the
  classes.

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• The percentage of misclassified pixels in each
  training class is normally presented in the form
  of a error matrix.

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• Training class signatures that arent able to
  accurately classify the pixels used to create
  them arent likely to accurately classify the
  remaining pixels in an image.
• However, the converse is not necessarily true
  Training classes that successfully classify their
  component pixels arent necessarily able to
  accurately classify the remaining pixels in an
  image because those remaining pixels may not be
  represented by any of the available signatures.

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• Training classes that exclude signatures
  representing one or more land cover types can
  only put those land covers into an existing class
  or into an unknown class.
• Therefore, self-classification is useful for
  determining if signatures are poorly developed,
  but it cant be used to show that the training
  classes are complete or that they will do a good
  job of classifying all of the pixels omitted from
  their development.

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• Interactive Preliminary Classification

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• As the name implies, interactive preliminary
  classification allows an analyst to test the
  accuracy and completeness of training classes
  during their development.
• Usually, the preliminary classification uses a
  computationally efficient classifier such as a
  parallelepiped classifier even when a more
  sophisticated classifier will be used to perform
  the final classification.

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• During this process, the analyst is able to add
  or remove pixels from the preliminary training
  classes to immediately see the results of the
  modified classification.
• This interactive process easily identifies
  individual pixels that either improve or degrade
  the quality of the classification, resulting in
  final spectral classes that produce good results.

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• Representative Subscene Classification

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• Representative subscene classification is similar
  to interactive preliminary classification except
  that the classification is performed with the
  type of classifier that the analyst plans to use
  in the final classification step and only part of
  the entire image is classified.
• Using part of the full image allows the analyst
  to concentrate on areas where the cover types are
  already well known and makes the process less
  time consuming.

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• Final Comments on the Training Stage

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• Image classifiers are designed for efficiency
  (speed) and accuracy.
• The training stage, however, must be conducted in
  a manner that produces maximum accuracy.
  Introducing shortcuts at the training stage is
  likely to produce poor results in the final
  classification.

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• The most difficult part of the training process
  is not the development of spectral classes for
  distinctly different land cover types such as
  water, forest and agriculture.
• Instead, the problems arise in developing
  spectral classes that will assign pixels in
  transition zones and areas of mixed cover types
  to the appropriate land cover classes.

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• By definition, transition zones are areas
  containing elements of the cover types that are
  more homogenous on either side of the transition
  zone.
• As a result, spectral signatures often have to be
  developed separately for transition zones and the
  analyst needs to develop a consistent
  classification scheme that will either assign
  these areas to one or another primary cover type
  or to a transitional cover type.

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• Refining spectral classes is often a
  trial-and-error process where the analyst adds or
  removes pixels from a developing training class
  to test the effect that the modification has on
  the ability of the classifier to produce
  acceptable results.
• Sometimes it is necessary to remove
  rarely-occurring land cover type from the
  classification scheme in order to avoid
  misclassifying pixels that belong to more common
  land cover types.

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• The training stage may also make it apparent that
  some of the originally-proposed land cover
  classes will need to be combined into more
  general classes because the spectral responses of
  the proposed classes are indistinguishable.
• For example, the data may not make it possible to
  distinguish individual tree species even though
  they are adequate to classify trees into more
  general categories such as evergreen, deciduous
  and mixed forests.

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• Sometimes, the inherent spectral responses of
  similar cover types may make it impossible to
  separate them using a single multiband image.
• In these cases, it may be necessary to acquire
  additional data in the form of field data or
  images acquired on other dates or with other
  sensors, or to use other classification
  techniques such as visual interpretation of the
  digital image or of other images including higher
  resolution digital images or aerial photography.

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• Unsupervised Classification

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• Unsupervised classification differs from
  supervised classification in that
• The image analyst does not design the
  classification scheme nor develop training
  classes, and
• The computer uses algorithms that aggregate
  similar pixels into classes based on their
  similarity with each other and their
  dissimilarity to the remaining pixels rather than
  their likely land cover types.

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• With unsupervised classification, the land cover
  types associated with each class are initially
  unknown and the computer produces no information
  to aid in their identity.
• It is the image analysts job to associate the
  classes defined by the computer with the land
  cover types in the image that these classes
  represent.

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• The procedural steps are reversed in these two
  classification methodologies
• In supervised classification, the analyst
  defines land cover types and then develops
  spectral classes that can be used by the computer
  to identify those pixels that are members of each
  class.
• In unsupervised classification, the computer
  develops spectral classes and then the analyst
  associates the spectral classes with land cover
  types.

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• Unsupervised classification has two significant
  advantages over supervised classification
• The computer can assign pixels to
  spectrally-distinct classes which an analyst
  might not recognize as existing, and
• The computer can identify a much larger number
  of spectrally-distinct classes than an analyst
  might consider to exist.

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• Even if an analyst recognizes that distinct
  subclasses exist, unsupervised classification
  techniques allow the analyst to avoid developing
  spectral classes for each unique class and
  subclass.
• Instead, the computer creates a large number of
  distinct classes and then the analyst can combine
  them into final classes as deemed appropriate.

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• The methods used in both supervised and
  unsupervised classification require the
  assignment of individual pixels into a finite
  number of spectral classes. Each of these
  spectral classes is presumed to represent a
  unique land cover type.

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• Unsupervised classification uses one of many
  available clustering algorithms to determine
  natural groups of spectrally-similar pixels. Most
  of these fall into two general types
• K-means algorithms have the computer
  more-or-less arbitrarily select a number of
  pixels as the starting points for defining
  clusters, and
• Moving window algorithms that use a moving
  window to identify small groups of
  spectrally-similar pixels to use as starting
  points for defining clusters.

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• K-Means Algorithms

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• Standard k-means algorithms require the analyst
  to set the number of clusters to be defined.
• The computer then selects one pixel to initially
  represent each class. These seed pixels are
  arbitrarily scattered throughout the
  multidimensional image space defined by the
  digital numbers in each available band for each
  pixel. In other words, the seed pixels have large
  differences in most of their digital numbers.

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• After selecting seed pixels, the computer uses
  the mean vector of each seed pixel to assign the
  remaining pixels to clusters around the nearest
  mean vector.
• New mean vectors are then calculated using all of
  the pixels in each of these new clusters. All of
  the pixels in the image are then reassigned to
  the nearest of these new mean vectors.

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• The process of calculating new mean vectors and
  reassigning pixels to the nearest mean vector is
  repeated until only a limited number of pixels
  need to be shifted to other classes because there
  is little movement of the mean vectors.
• The threshold percentage of pixels reassigned is
  another variable controlled by the image analyst,
  i.e. the inputs to the computer include a
  percentage of reassigned pixels below which the
  process stops.

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• A final input provided by the analyst is the
  number of iterations allowed.
• The computer stops calculating new mean vectors
  and reassigning pixels when
• Fewer pixels than the input threshold are being
  reassigned, or
• The maximum number of iterations has been
  completed.

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• ERDAS IMAGINE provides a variant of the k-means
  approach known as Iterative Self-Organizing Data
  Analysis or ISODATA.
• The ISODATA algorithm is similar to other k-means
  algorithms, but a significant difference is that
  the ISODATA algorithm allows the computer to
  determine the final number of clusters while this
  value is set by the image analyst in other
  k-means applications.

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• The number of classes can change because the
  computer is allowed to merge spectrally-similar
  preliminary clusters (i.e. clusters whose mean
  vectors are nearby) and to split clusters whose
  standard deviation within any single band is
  larger than a predefined threshold.

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• If splitting a cluster with a large standard
  deviation produces clusters that are smaller than
  an analyst-specified threshold, the new clusters
  are simply eliminated and their constituent
  pixels are reassigned to the remaining cluster
  whose mean vector is nearest.
• As stated earlier, the process then repeats until
  either few pixels are being reassigned or a
  maximum number of iterations has been completed.

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• Moving Window Algorithms

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• Unsupervised classification algorithms that use a
  moving window to identify initial clusters are
  predicated on the idea that the initial sets of
  pixels used to define preliminary classes should
  be spectrally similar because the final clusters
  will contain spectrally-similar pixels.

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• No such algorithms are provided by ERDAS IMAGINE,
  but they are widely used and are the basis of
  many unsupervised classifications discussed in
  the remote sensing literature.
• Therefore, a basic understanding of the
  methodology used by these algorithms is important
  to the correct interpretation of research
  conclusions.

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• The algorithms take into consideration the
  texture or roughness of the pixels within a
  moving window passed through the image.
• Texture is defined by the multi-dimensional
  variance of the digital numbers within a moving
  window passed through the image.

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• The analyst inputs a threshold variance below
  which the pixels within the window are considered
  smooth, and the computer then moves a window
  through the image until it encounters a smooth
  window.
• The mean of these pixels then becomes the center
  of the first preliminary cluster.

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• The computer then continues searching for other
  smooth windows and defines the mean of each
  newly-found smooth window as the next cluster
  center.
• The analyst is required to specify the maximum
  number of initial clusters. This number is
  usually relatively large (e.g. 50) because the
  computer will eventually combine many of these
  into a smaller number of spectrally-similar
  clusters.

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• When the analyst-defined number of preliminary
  cluster centers has been reached, the computer
  calculates the distances between each pair of
  preliminary clusters and merges the two clusters
  that are separated by the smallest distance.
• New statistics are then calculated and the two
  then-nearest clusters are merged. This process is
  repeated until all of the remaining clusters are
  more spectrally-distinct than an analyst-defined
  threshold.

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• The clusters that werent eliminated by merging
  are used to classify all of the remaining pixels
  using one of the classifiers that are used for
  supervised classifications (e.g. a
  minimum-distance-to-means classifier or a maximum
  likelihood classifier).

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• In a sense, this process is similar to a
  supervised classification except that the
  computer selects the training classes by
  identifying the spectrally-smoothest areas of the
  input image.
• The final classification uses the computers
  training classes instead of an analysts training
  classes, but the final classification uses the
  same types of classifiers.

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• Disadvantages of this approach result from the
  facts that some important land cover classes may
  not be included in the classification because
• They are inherently rough at certain scales
  (e.g. rivers or roads), or
• They exist in areas that werent processed
  before maximum number of smooth clusters was
  found.

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• A final variation of this procedure overcomes
  these limitations by involving the analyst in the
  selection of some of the initial clusters.
• This involves elements of both supervised and
  unsupervised classification, and many other
  hybrid classification methodologies are commonly
  used in image classification.

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• Final Comments on Unsupervised Classification

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• Unsupervised classification procedures are
  designed to identify spectrally-similar classes
  of pixels.
• They are incapable, however, of associating these
  classes with landcover classes. This associative
  process can be as difficult as the process of
  developing and refining the spectral classes that
  are used in supervised classifications.

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• There are four possible relationships between
  spectral classes and land cover classes
• A one-to-one relationship,
• A many-to-one relationship, and
• A many-to-one relationship.
• Many-to-one and one-to-many relationships are
  more common and are relatively easy to deal with.
  One-to-many relationships, though, are especially
  problematic.

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• A one-to-one relationship exists when each of the
  spectral classes represents a distinct landcover
  class.
• If this type of relationship exists, the analyst
  only needs to recognize the relationships and
  assign appropriate class names.

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• In a many-to-one relationship, two or more
  spectral classes are logically grouped to define
  a single landcover class.
• For example, an unsupervised classification might
  produce distinct spectral classes that the
  analyst recognizes as deep clear water, slightly
  turbid lakes, and shallow muddy ponds. These can
  conveniently be assigned to a water landcover
  class unless the analyst is especially interested
  in the differences between these water features.

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• The analysts job is more difficult, however, if
  one to many relationships exist.
• For example, the analyst may wish to produce a
  classification that separates deciduous and
  evergreen forest types in a forestry application.
  If the computer generates three spectral classes
  which the analyst recognizes as deciduous,
  evergreen and mixed forest, these spectral
  classes dont provide any method to achieve the
  analysts objective.

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• Next Chapter 8
• Microwave and Lidar Remote Sensing Systems