An Advanced Shape of Country Classifier

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An Advanced Shape of Country Classifier
The Extraction of Surface Features from DEMs

• Lee P. Herrington
• State University of New York
• College of Environmental Science Forestry
• Gerald Pellegrini
• Advanced Development, BAE Systems

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Overview

• What is shape of country
• What is it used for
• Previous methods
• Our method
• Need and method of smoothing the DEM
• Analytic method
• Results Conclusions

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What is Shape Of Country?

• The low resolution classification of a DEM into
  general features
• Peaks, ridges, saddles
• Pits, valleys
• Various classes of side hills
• Saddle, convex, concave, planar, etc
• Do NOT want high resolution bumps dips in the
  terrain!

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Scale of SOC
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Shape of Country(SOC)

• The TIN is a first approximation of SOC
• For our purposes we needed the following
  categories of SOC.

Description
Class
Description
Class
Concave upward
Concave hillside
Cell ht gt than surround
Peak
Convex upward
Convex hillside
Cell htlt than surround
Pit
curve orthog 2 - curve
Saddle
Line of adjacent peaks
Ridge
Hillside w/ no curvature
Flat sur
Line of adjacent pits
Valley
Surface no slope or curvature
Flat
Intersection of ridge and valley
Saddle pt
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Uses of SOC
Tractability estimate When SOC combined
with DEM Surficial Geo Got 80-90 correct
classification in Adirondack mts.

• Estimation of
• Soil physical properties
• Chemical properties
• Soil moisture content
• Expert systems
• Forest harvesting
• Hydrologic studies
• Engineering

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Overview

• What is shape of country
• What is it used for
• Previous methods and results
• Our method
• Need and method of smoothing the DEM
• Analytic method
• Results Conclusions

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Previous Methods for SOC

• Usually hierarchical methods based on
  relationships between adjacent cells of a DEM
• A peak would be defined as a cell surrounded by
  cells of lower elevation
• A valley was a line of adjacent cells that had
  cells of higher elevation on either side
• Etc.

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Previous Methods for SOC
Pit or Peak
Ridge or valley
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A 30 M DEM (unsmoothed)
Approximate Drainage path
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Hierarchical classification
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Comparison
?
A
A
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Where we are going
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Overview

• What is shape of country
• What is it used for
• Previous methods
• Our method
• Need and method of smoothing the DEM
• Analytic method
• Results Conclusions

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Smoothing the DEM

• Usual average filtering using 3x3 and 5x5 kernels
  
• Did not work
• Filter roll off was not sharp enough and too much
  short wavelength information leaked

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Roll off?
Sharp cutoff filter
1
Average Filter Roll off
Energy passed
Leakage
0
Spatial frequency (1/wavelength)
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Smoothing the DEM

• Usual average filtering using 3x3 and 5x5 kernels
  
• Did not work
• Filter roll off was not sharp enough and too much
  short wavelength information leaked
• Implemented a sharp roll off filter using the
  Fourier Transform actually the FFT
• FFT transforms data in the spatial domain (DEM)
  into the spatial frequency domain

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Domain idea
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Domain idea
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Surfaces as summations of sinusoids
Summation of sinusoids
Elevation
1 2 3
Distance ?
Spatial Frequency Domain
Distance domain
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Domain Change

• From the Distance domain
• To the Spatial frequency domain
• And back
• How?

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Fourier to the rescue!

• The FOURIER TRANSFORM is a mathematical process
  used to convert between domains
• You dont want to see the equations!!!
• The FAST FOURIER TRANSFORM or FFT is digital
  processing technique that makes the Fourier
  Transform practical
• Goes both ways
• Space to frequency FFT, frequency to space FFT-1

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Fourier Transform
INVERSE TRANSFORM
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Distance Domain
Raw 30m DEM (vertical Exaggeration )
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Processing
FFT
Raw 30m DEM
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Smoothed 30m DEM, Classified
Resulting Smoothed 30 m DEM (with SOC classes)
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Same information content!
Spatial Frequency domain
Distance domain
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OK, we have a smoothed DEM

• Now we need to create a classification of the
  surface
• And this is really Gerrys contribution

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Analytic (Continuous) Method

• Pass a 3x3 kernel over the DEM fitting a
  polynomial surface to the 9 points
• This yields a mathematical description
• Slope, aspect, and curvature (profile and plan
• Identify basic features based on above
• Construct terrain features based on comparison of
  properties of each cell

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Zevenbergen Thorns polynomial
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The problem

• Eigenvalue analysis used to generate the 1st
  estimate of shape
• BUT!
• Grid features may not be aligned with major SOC
  features
• If a ridge line does not pass exactly through the
  center of a cell then the cell will be seen as a
  side hill

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Alignment Problem
Fitted surface
elevation
All cell classed as side hills at center of the
cell
distance
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Solution

• Mathematically determine if there is a change in
  slope within the pixel from the equation fitted
  to the 3x3 kernel
• If so, generate new eigenvalues
• Use a table lookup routine based on both the
  original and recalculated eigenvalues to classify
  the cell

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Analysis Flow Chart
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Overview

• What is shape of country
• What is it used for
• Previous methods
• Our method
• Need and method of smoothing the DEM
• Analytic method
• Results Conclusions

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Results

• Smoothing and analysis technique applied to
• Analytic surfaces
• Real world DEMs
• It worked!

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Analytic Saddle
Saddle surface
Classification
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30m DEM
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Conclusions

• A combination of
• Smoothing with a sharp cutoff filter in the
  spatial frequency domain
• The use of a continuous analytic fitting process
• The determination of the actual location of the
  feature within a cell

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Conclusions

• A combination of this technique in with
  hierarchical processing and analysis of the
  original DEM may be a route to even better
  classifications.