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Basics:

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parallelepiped. feature space. Unclassified Options. parametric rule. unclassified. Overlap Options ... Parallelepiped. Band A. Band B. cluster mean. Candidate ... – PowerPoint PPT presentation

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Title: Basics:


1
Basics
Notation
Sum
2
PARAMETERS
the statistical average the central
tendency the spread of the values about the
mean
MEAN Sample Variance Standard Deviation
3
Covariance
measures the tendencies of data file values for
the same pixel, but in different bands, to vary
with each other in relation to the means of their
respective bands.
4
Dimensionality
N the number of bands dimensions . an (n)
dimensional data (feature) space
Measurement Vector
Mean Vector
Feature Space - 2dimensions
190 85
Band B
Band A
5
Spectral Distance
a number that allows two measurement vectors to
be compared
6
terms
  • Parametric based upon statistical parameters
    (mean standard deviation)
  • Non-Parametric based upon objects (polygons) in
    feature space
  • Decision Rules rules for sorting pixels into
    classes

7
ClusteringMinimum Spectral Distance -
unsupervised
Band B
Band A
Band B
Band A
1st iteration cluster mean
2nd iteration cluster mean
8
Classification Decision Rules
  • Non-Parametric
  • parallelepiped
  • feature space
  • Unclassified Options
  • parametric rule
  • unclassified
  • Overlap Options
  • parametric rule
  • by order
  • unclassified
  • Parametric
  • minimum distance
  • Mahalanobis distance
  • maximum likelihood
  • If the non-parametric test results in one unique
    class, the pixel will be assigned to that class.
  • if the non-parametric test results in zero
    classes (outside the decision boundaries) the the
    unclassified rule applies either left
    unclassified or classified by the parametric rule
  • if the pixel falls into more than one class the
    overlap rule applies left unclassified, use the
    parametric rule, or processing order

9
Parallelepiped
  • Maximum likelihood
  • (bayesian)
  • probability
  • Bayesian, a prior (weights)

Band B
Band A
Minimum Distance
Band B
Band A
10
GeoStatistics
  • Univariate
  • Bivariate
  • Spatial Description

11
Univariate
  • One Variable
  • Frequency (table)
  • Histogram (graph)
  • Do the same thing (i.e count of observations in
    intervals or classes
  • Cumulative Frequency (total below cutoffs)

12
Summary of a histogram
  • Measurements of location (center of distribution
  • mean (m µ x )
  • median
  • mode
  • Measurements of spread (variability)
  • variance
  • standard deviation
  • interquartile range
  • Measurements of shape (symmetry length
  • coefficient of skewness
  • coefficient of variation

13
Bivariate
Scatterplots
Correlation
Linear Regression
slope constant
14
Spatial Description
- Data Postings symbol maps (if only 2 classes
indicator map - Contour Maps - Moving Windows
gt heteroscedasticity (values in some region
are more variable than in others) - Spatial
Continuity (h-scatterplots
Spatial lag h (0,1) same x, y1
h(0,0) h(0,3) h(0,5)
correlation coefficient (i.e the correlogram,
relationship of p with h
15
  • Correlogram p(h) the relationship of the
    correlation coefficient of an h-scatterplot and h
    (the spatial lag)
  • Covariance C(h) the relationship of
    thecoefficient of variation of an h-scatterplot
    and h
  • Semivariogram variogram moment of
    inertia

OR half the average sum difference between the x
and y pair of the h-scatterplot OR for a h(0,0)
all points fall on a line xy OR as h
points drift away from xy
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