ERS186: Environmental Remote Sensing

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ERS186Environmental Remote Sensing

• Lecture 14
• 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
Variable of Interest
Some relationship
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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
• Physical properties of the media scattering,
  transmission, absorption
• Geometric properties of the media position,
  size, shape, orientation, density

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What Have We Been Doing?
Remote Sensing Data
RT State Variables
Direct relationship
Some relationship
Variable of Interest
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Physical Interpretation of RS
Remote Sensing Data
RT State Variables
Direct 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
• 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!

Some relationship
Variable of Interest
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Physical 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
• Two categories of RT models
• 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 Interpretation of RS
Variable of Interest
Remote Sensing Data
Empirical relationship

• Empirical (statistical) relationships constitute
  the BULK of RS analysis.
• These analyses allow 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

• Common biophysical variables that directly affect
  RT
• Vegetation pigment concentration, biomass,
  foliar water content, APAR
• Temperature
• Soil moisture
• Surface roughness
• Evapotranspiration
• Atmosphere chemistry, temperature, water vapor,
  wind speed/direction, energy inputs,
  precipitation, cloud and aerosol properties
• BRDF
• Ocean color, phytoplankton, chemistry
• Snow and sea ice characteristics
• Spatial x,y, and potentially z
• Temporal time the image was acquired
• Directional sensor and sun angle
• Polarization in RADAR

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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. 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. 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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Hybrid Variables
Variable of Interest
Remote Sensing Data

• Many empirical relationships are functions of
  variables which can not be extracted from RS data
  (hidden variables).
• When hidden variables are present, for RS
  analysis to be useful the RT state variables must
  affect the hybrid variable more than the hidden
  variables do.
• These relationships are HIGHLY dependent on
  space, time, sensor, etc so extrapolation to
  other places and times must be done carefully!

Hidden variables
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Hybrid Variables

• These variable constitute a LARGE proportion of
  RS variables, and their wider applicability is
  usually VASTLY overstated!!!
• The applicability can be improved through a
  knowledge of the hidden variables and their
  impact on the variable of interest
• Example monetary value of farm land
• RS can help determine the soil type
• Type of crops which can be grown in that soil,
  under the local environmental conditions, and the
  value of those crops are needed to fully explore
  this question.
• Example species discrimination
• Most classifications, including the determination
  of what is a species? is a hidden variable in
  and of itself.

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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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Mapping LWP

• 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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Case Study Pixel Components

• 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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Mixed 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

• 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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LSU Results
Shadow
Soil
Vegetation
Greenberg, unpublished Each endmember fraction
gives different information about the landscape,
and is relatively easy to interpret. Shadow, in
particular, has some interesting properties. It
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

• The output of classification is a nominal hybrid
  variable
• Classification is one of the most widely used
  analysis techniques in RS (it is easy to collect
  class data relative to many continuous data).
• Good classification often relies on a good
  understanding of the RT state variables present
  and how they affect a class.
• If two classes have identical RT state variables,
  they can not be distinguished using RS data alone
  (this doesnt stop people from trying, though!)

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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 with a classifier algorithm
  to determine the spectral signature for each
  class.
• Using the classifier, label each pixel in an as
  one of the pre-determined classes (or,
  potentially, an other class).

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Classifier Algorithms

• There are a LOT of classifier algorithms.
• We will be covering some of these more explicitly
  next quarter, but it is worth covering some of
  them now.
• Table look up
• Parallelepiped
• Minimum distance
• Maximum likelihood

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Table Look Up

• 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
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Parallelepiped

• 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
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Minimum Distance

• 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

• Max likelihood uses the variance and covariance
  in class spectra to determine classification
  scheme.
• It assumes that the spectral responses for a
  given class are normally distributed.

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Maximum Likelihood

• We can then determine a probability surface,
  where for a given DN, being a member of a
  particular 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 inefficient,
  multimodal or non-normally distributed classes
  can be misclassified.