ERS186: Environmental Remote Sensing

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ERS186Environmental Remote Sensing

• Lecture 11
• The remote sensing process and the analysis of
  continuous and nominal variables

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Outline

• Conceptual basis of remote sensing research
• Physical interpretation of RS data
• Empirical interpretation of RS data
• Continuous variables
• Simple regression models
• Linear spectral unmixing
• Nominal variables
• Classification techniques

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The Goal of Remote Sensing
Remote Sensing Data
Two types of models
Information
physical and empirical
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The state variable approach to modeling...a
physical approach
Model based on State Variables
Some relationship
Data
Knowledge
Estimation of the variable of interest
Output (information)
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Radiative Transfer State Variables
Remote Sensing Data
RT State Variables
Direct relationship

• RT state variables the smallest set of variables
  needed to fully describe the RS data
• Type(s) of media atmosphere, vegetation, soil,
  etc
• Factor 1 Spectral scattering, transmission,
  absorption properties of media (These are
  functions of time!)
• Factor 2 Architectural properties of the media
  position, size, shape, orientation, density
  (These are functions of time!)
• Factor 3 View and illumination directions

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Aside Why is time involved?Examples...

• - At the onset of moisture stress soybean and
  cotton leaves droop, corn leaves roll into
  vertical cylinders.
• - With the onset of a strong wind, the
  irradiance on a deciduous forest floor increases
  dramatically as leaves minimize aerodynamic drag
  rather than maximize light interception.
• In general, plant canopies grow and develop
  during a growing season thus, their architecture
  and often the spectral properties of their
  components change over time.

In general Factors 1 and 2 are stochastic
variables i.e. functions of time.
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An physical RT modeling approach
Remotely Sensed Data
RT State Variable Model
Direct relationship
knowledge
Estimation of Variable of Interest
Output (information)
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Physical RT Models
Remote Sensing Data
RT State Variable model
Direct relationship
Some relationship

• If the variable of interest does NOT directly
  affect the RT state variables, RS alone is not
  sufficient to retrieve information on the
  variable of interest from a physical
  interpretation. Examples
• Bird nesting locations
• Human population densities
• Rooting depth of plants
• Tsetse fly infestations
• Note most of variables of interest we have
  covered in this class DO directly affect the RT
  state variables or ARE state variables
  themselves, which is why we covered them!

Estimation of Variable of Interest
Output
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Physical RT Models
Remote Sensing Data
RT State Variables
RT Models
Invertible models

• Radiative transfer models
• Try to predict RS data based on a function of the
  RT state variables
• RT models can be
• -Economically invertible models typically
  designed for simple scenes, have a few number of
  state variables
• -Non-economically invertible models typically
  designed for complex scenes, have a large number
  of state variables

Some relationship
Variable of Interest
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Empirical Models
Variable of Interest
Remote Sensing Data
Empirical relationship

• Empirical (statistical) relationships constitute
  the BULK of RS analysis.
• These analyses allow us to determine IF there is
  a relationship, not WHY there is a relationship.
• Two types of variables of interest
• Biophysical variables RT state variables and
  functions of RT state variables (most the
  variables covered in this class)
• Hybrid variables function of at least 1 non-RT
  state variable

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Biophysical Variables

• Examples of common biophysical variables that
  affect RT
• Vegetation Factor 1 pigment concentration,
  foliar water content, Factor 2 LAI, biomass
• Temperature
• Soil moisture Factor 1
• Surface roughness Factor 2
• Evapotranspiration
• Atmosphere chemistry, temperature, water vapor,
  wind speed/direction, energy inputs,
  precipitation, cloud and aerosol properties
• Ocean color, phytoplankton, chemistry
• Snow and sea ice characteristics
• Spatial x,y, and potentially z
• BRDF Factor 3
• Temporal time during (day, season, year) that
  the image was acquired

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Biophysical Variables

• These variables WILL affect RS data, but not
  necessarily in a repeatable or useful way because
  other state variables are present affecting the
  RS data.
• Repeatability limitations. Example - Liquid
  water content in cotton changes in LAI, leaf
  orientation, background soil properties,
  atmospheric affects will make an empirically
  determined relationship between liquid water
  content and RS data extracted from scene
  difficult to apply to another scene without
  controlling for those other RT state variables.
• Usefulness limitations. Example - LAI we know
  LAI affects RS data, but we can not reliably
  estimate high LAIs using current analysis
  technology and techniques.

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Continuous Relationships

• Question How much of (some variable of interest)
  is present in a pixel?
• Methods
• Collect field data on variable of interest
• Determine empirical relationship between RS data
  to field data
• Relationship determination can take an extremely
  wide range of methods, from regression to neural
  network to complex model formulation, etc
• Invert relationship on entire RS scene

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Case Study Cotton Water

• Question what is the canopy water content of a
  pixel of cotton?
• Methods
• Collected leaf water potential (LWP) on cotton
  leaves and GPS coordinates of those leaves.
• Determined the continuum of the water absorption
  feature at 975nm and 1150nm and regressed this
  against LWP data for the appropriate pixels.
• The regression gives me a model (f) of LWPf(CR),
  so I can apply the model to an entire AVIRIS
  scene, and each pixel will be the estimated LWP.

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Biophysical Variable
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Field vs. RS Relationship

• Found a relationship (albeit tenuous) between the
  field measurements and the RS measurements.
• The deeper the absorption feature, the higher the
  LWP.
• We generate an equation of the line that fits the
  data, which can be inverted on the image data to
  produce LWP from a given CR value.

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Cotton field LWP

• Cooler colors indicate higher LWP, hotter colors
  indicate lower LWP.
• Notice the variation in the cotton field. A
  farmer might want to water the center of the
  field more than the top and bottom.

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Limitations

• Can I apply these results to a different species?
• Can I apply these results to cotton at different
  ages?
• Can I apply these results to cotton at different
  times of the day?

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Unmixing

• Question what are the media present in a pixel,
  and how much of a pixel is comprised of a given
  media?

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Pure vs. Mixed Pixels

• In the class, so far, we have mainly dealt with
  pure pixels (e.g. pixels in which there is one
  type of material).
• When do you find pure pixels?
• When the spatial extent of the material is larger
  than the size of the pixel. Examples
• Large clouds and 1 km. GOES pixels
• Mineral deposits and 20 m. AVIRIS pixels
• Leaves and an integrating sphere spectrometer

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Pure vs. Mixed Pixels

• Types of mixtures (from Geology lecture)
• Areal
• Intimate
• Coating
• Molecular
• Mixed pixels typically refer to areal or intimate
  mixtures

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This mixed pixel contains ...
square pixel
Bare Soil
Tree
River
Tree shadow
Grass
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Unmixing Pixels

• We want to determine the fraction of each
  endmember in a potentially mixed pixel.
• Endmember pure reflectance spectra of a pixel
  component, measured in the lab, in the field, or
  from the image itself.
• Examples of commonly used endmembers green
  vegetation, soil, shadow, water, clouds,
  non-photosynthetic vegetation (NPV, wood,
  decayed leaves, etc.)

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Linear Spectral Unmixing

• Basic assumption the reflectance of a pixel is a
  linear combination of the endmember spectra times
  their relative cover fraction.
• Two parts to the algorithm
• Fifraction of endmember i in pixel (usually
  0Fi1)
• DN?the pixel reflectance for band ?
• DN?,ithe reflectance for band ? of endmember I
• E?error term

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Linear Spectral Unmixing, LSU

• For each spectral band, there is a different
  version of equation (2)
• If the number of bands 1 is equal to the number
  of endmembers, we can solve the set of equations
  without an error term.
• If the number of bands 1 is greater than the
  number of endmembers, we can solves the set of
  equations and generate an error term.
• This set of equations does not have a unique
  solution if there are more endmembers than bands.
• Since DN? is known (from the image) and DN?,i are
  known (from lab, field, or image spectra), we can
  determine Fi and E? (if i lt (B 1))!

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Linear Spectral Unmixing, Results
Shadow
Soil
Vegetation
Greenberg, unpublished Endmember fractions of
Vegetation, Shadow, Soil. Shadow is related to
the structure of the pixel more heterogenous
canopies yield greater shadow. Nearly all
human-affected pixels (regardless of type!) will
have LOW shadow. Old forests will have HIGH
shadow.
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LSU Shortcomings

• Because of multiple scattering, BRDF factors, and
  other issues, rarely are pixels composed of
  linear mixtures of individual components. These
  are mainly 3-d structural factors.
• The higher the vertical complexity in a pixel,
  the less likely the fractions will represent
  cover. Vegetation cover is often overestimated
  in LSU.

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Classification

• Classification is one of the most widely used
  analysis techniques in RS.
• Spectral space ltgtInformation space
• Good classification often relies on a good
  understanding of the RT state variables present
  and how they affect a class.
• If two classes are identical in spectral space,
  then classification accuracy will be low.

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Classification

• Three types of classification
• Supervised
• Requires training pixels, pixels where both the
  spectral values and the class is known.
• Unsupervised
• No extraneous data is used classes are
  determined purely on difference in spectral
  values.
• Hybrid
• Use unsupervised and supervised classification
  together
• Useful fact we arent limited to using only raw
  DNs, radiance, or reflectance in our classifier.
  We can use ratio or difference indices, LSU
  fractions, spatial data (distance from some
  target) or any other data transformation we might
  think would be appropriate in the classifier.

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Supervised Classification

• Steps
• Decide on classes.
• Choose training pixels which represent these
  classes.
• Use the training data to train the classifier.
• Then classify each pixel in the image using the
  trained classifier.
• The result? Each pixel is labeled as belonging
  to one of classes - or to other.

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Many types of Classifiers

• A short list of examples (We will cover some of
  these in more detail next quarter).
• Table look up
• Parallelepiped
• Minimum distance
• Maximum likelihood
• Layer
• Spatial

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Table Look Up Classifier
How it works ...

• For each class, a table of band DNs are produced
  with their corresponding classes.
• For each image pixel, the image DNs are matched
  against the table to generate the class.
• If the combination of band DNs is not found, the
  class can not be determined.
• Benefits conceptually easy and computationally
  fast.
• Drawbacks relatively useless, unless every
  potential combination of band DNs and their class
  is known.

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Table Look Up Classifier...
How it works ...
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Parallelepiped Classifier
How it works ...

• The minimum and maximum DNs for each class are
  determined and are used as thresholds for
  classifying the image.
• Benefits simple to train and use,
  computationally fast
• Drawbacks pixels in the gaps between the
  parallelepipes can not be classified pixels in
  the region of overlapping parallelepipes can not
  be classified.

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Parallelepiped Classifier
How it works ...
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Minimum Distance Classifier
How it works ...

• A centroid for each class is determined from
  the data by calculating the mean value by band
  for each class. For each image pixel, the
  distance in n-dimensional distance to each of
  these centroids is calculated, and the closest
  centroid determines the class.
• Benefits mathematically simple and
  computationally efficient
• Drawback insensitive to different degrees of
  variance in spectral response data.

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Maximum Likelihood Classifier
How it works ...

• Max likelihood uses the variance and covariance
  in class spectra to determine classification
  scheme.
• It often, but not always, assumes that the
  spectral responses for a given class are normally
  distributed.

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Maximum Likelihood Classifier
How it works ...

• We can then determine a probability that a given
  DN is a member of each class. The pixel is
  classified by using the most likely class or
  Other if the probability isnt over some
  threshold.
• Benefits takes variation in spectral response
  into consideration.
• Drawbacks computationally intensive multimodal
  or non-normally distributed classes require extra
  care when training the classifier, if high
  accuracy is to be achieved.

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Study question Use each of the first four
classifiers to establish decision boundaries for
each class shown. Case 1, separate means, equal
variance
Spectral band 2. NIR, 0.8 to 0.9 um
Spectral band 1. For example, red, 0.6 to 0.7 um
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Study question Use each of the first four
classifiers to establish decision boundaries for
each class shown. Case 2, equal means, unequal
variances
Spectral band 2. NIR, 0.8 to 0.9 um
Spectral band 1. For example, red, 0.6 to 0.7 um
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Study question Use each of the first four
classifiers to establish decision boundaries for
each class shown. Case 3, bimodal distribution
Spectral band 2. NIR 0.8 to 0.9 um
Spectral band 1. For example, red, 0.6 to 0.7 um
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Study question Use each of the first four
classifiers to establish decision boundaries for
each class shown. Case 4, separate means,
highly correlated data
Spectral band 2. NIR, 0.8 to 0.9 um
Spectral band 1. For example, red, 0.6 to 0.7 um
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Study question Use each of the first four
classifiers to establish decision boundaries for
each class shown. Case 5, separate means,
uncorrelated data
Spectral band 2. NIR, 0.8 to 0.9 um
Spectral band 1. For example, red, 0.6 to 0.7 um