Relationships between Land Cover
and Spatial Statistical Compression
in High-Resolution Imagery
James A. Shine1 and Daniel B. Carr2
34th Symposium on the Interface
19 April 2002
1 George Mason University & US Army Topographic Engineering Center
2 George Mason University
Outline of Talk
• The Variogram
•
•
•
•
•
Motivation and Procedure
Past Results
Present Results
Analysis and Conclusions
Future Work
Spatial Statistics: The Variogram
-A plot of average variance between points
vs. distance between those points (L2)
-If data are spatially uncorrelated, get a straight line
-If data are spatially correlated, variance generally
increases with distance
-Directional component also a consideration (N-S,
E-W, omnidirectional)
140
120
gamma
100
80
60
40
20
0
0
10
20
distance
30
40
Typical image variogram (left),
Important quantities (right)
Some graphs of
variogram models
LINEAR MODEL
20
10
15
g amma
1.0
0
0.8
5
0.9
g amma
1.1
25
1.2
30
NUGGET MODEL
5
10
15
20
25
30
0
10
15
20
25
h
h
SPHERICAL MODEL
EXPONENTIAL MODEL
1.0
30
0.4
0.6
g amma
0.8
0.8
0.6
0.4
0.2
0.2
g amma
5
1.0
0
0
5
10
15
h
20
25
30
0
5
10
15
h
20
25
30
A double or nested variogram
2.0
DOUBLE EXPONENTIAL MODEL
X
X
X
X X X X X X X
X X X X X X
X
X
X
X X
X
X
1.5
X
X
1.0
X
+ o
+ o
+ o
+
+ + + + + + + o
+ + + + + + + +
o o o o o o o o
+ + +
o
o
+
o
+
o o
+
o o
o
+
o o
X
+
o
o
+
o
o
+
o
X
o
+ o
X
0.5
gamma
X
o
0
5
10
15
distance
20
25
30
Variogram Applications
-Determination of range for
sampling applications:
ground truth
supervised classification
-Model for estimation/prediction
applications (forms of kriging)
Outline of Talk
• The Variogram
• Motivation and Procedure
•
•
•
•
Past Results
Present Results
Analysis and Conclusions
Future Work
MOTIVATION
Large data sets, computational challenges
(10^6-10^7 data points per km^2 at 1 m
resolution for pixels)
Large computation times not conducive to
real-world applications such as rapid
mapping
Compression will reduce computation time,
But how much can we reduce without losing
information?
PROCEDURE
Transfer data from imagery to text file
Compute variograms (FORTRAN code)
Format and plot the variograms
Compare variograms with full data sets vs
variograms with reduced data sets
Imagery
Ft. A.P. Hill, Ft. Story (both in Virginia) : 1-meter
resolution, 4-band CAMIS imagery, collected by
US Army Topographic Engineering Center
(TEC)
Others: 4-meter resolution, 4-band IKONOS
imagery, obtained from TEC’s imagery library
and also commercially available.
Bands:
1. Blue (~450 nm)
2. Green (~550 nm)
3. Red (~650 nm)
4. Near Infrared (~850 nm)
Outline of Talk
• The Variogram
• Motivation and Procedure
• Past Results
• Present Results
• Analysis and Conclusions
• Future Work
Previous Results: Ft. A.P. Hill, VA
(Shine, Interface 2001)
Mostly forest, some manmade
2196 x 2016=4.4x10^6 pixels
Compression works well for AP Hill
imagery; Band 1 (blue) variograms shown
below
Other A.P. Hill bands also
compressed well: Band 2
(Green), N-S at right,
E-W bottom left,
Average bottom right
Band 3 (Red), N-S at right,
E-W bottom left,
Average bottom right
Band 4 (IR), N-S at right,
E-W bottom left,
Average bottom right
Outline of Talk
• The Variogram
• Motivation and Procedure
• Past Results
• Present Results
• Analysis and Conclusions
• Future Work
Fort Story, VA results completed,
Plus some new imagery:
New York City
Ft. Stewart, GA
Ft. Moody, GA
Wright-Patterson AFB, OH
Ft. Huachuca, AZ
Fort Story, VA
New York City
Ft. Stewart, GA
Ft. Moody, GA
Wright-Patterson AFB, OH
Ft. Huachuca, AZ
Original Ft. Story
image:
Water, forest,
urban
3999x4999=
2.0x10^7 pixels
Ft. Story,original
Band One (Blue)
N-S at right,
E-W bottom left,
Average bottom
right
Ft. Story,original
Band Two(Green)
N-S at right,
E-W bottom left
Ft. Story Results
-Full variogram is very smooth
(exponential/spherical), but
compression is not good; compressed
variogram significantly different
from full variogram
-Need to compare different types of
imagery and hopefully make some
inferences
2.0
X
X
X
X X X X X X X
X X X X X X
X X X
X X
X
X
1.5
X
X
1.0
gamma
X
X
X
+
X
X
+
+
+
0.5
-Why does AP Hill compress well
and Story does not? Could be losing
a level on a nested model (right), but
perhaps different landcover or terrain
reacts differently to compression.
DOUBLE EXPONENTIAL MODEL
+
o
o
+ + + + + + + +
+ + +
+ + + + + + + +
o o o o o o o o o o o
+ + +
o o o o
+ +
o o o
o
o
o o
o
o
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o
+ o
o
0
5
10
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distance
20
25
30
Subarea from Ft. Story:
just forest
524x408=2.1x10^5 pixels
Ft. Story forest subimage
Band One (Blue)
N-S at right,
E-W bottom left
Average bottom right
Ft. Story forest subimage results
-Variograms seem to be unbounded (linear)
-Compression matches original pretty well, much
better than for the full image
-Do some more tests with other images and
landcovers
New Results:
Fort Story, VA
New York City
Ft. Stewart, GA
Ft. Moody, GA
Wright-Patterson AFB, OH
Ft. Huachuca, AZ
New York City
2000 x 2000
Urban, water,
smoke (9/12/01)
New York City
Blue
E-W,
N-S,
average
New York City
Green
E-W,
N-S,
average
New York City Results
-Variogram seems unbounded (linear)
-Almost no difference between the
full and compressed variograms
New Results:
Fort Story, VA
New York City
Ft. Stewart, GA
Ft. Moody, GA
Wright-Patterson AFB, OH
Ft. Huachuca, AZ
Fort Stewart
Mostly fields
2559x2559=
6.5x10^6 pixels
Ft. Stewart
Blue
E-W,
N-S,
average
Ft. Stewart
Green
E-W,
N-S,
average
Ft. Stewart
Red
E-W,
N-S,
average
Ft. Stewart
IR
E-W,
N-S,
average
Ft. Stewart Results
-Full variogram is very smooth
(exponential/spherical)
-Almost no difference between full
and compressed variograms, except
very slightly in Blue band
New Results:
Fort Story, VA
New York City
Ft. Stewart, GA
Ft. Moody, GA
Wright-Patterson AFB, OH
Ft. Huachuca, AZ
Ft. Moody fields
1202x1742=
2.1x10^6 pixels
Ft. Moody fields
Blue
E-W,
N-S,
average
Ft. Moody fields
Green
E-W,
N-S,
average
Ft. Moody fields
Red
E-W,
N-S,
average
Ft. Moody fields
IR
E-W,
N-S,
average
Ft. Moody forest
1325x1767=
2.3x10^6 pixels
Ft. Moody forest , Blue , E-W
(no spatial dependence after 3 pixels, so compression is useless;
all bands and directions give same non-dependence)
Ft. Moody Results
-Field subset variogram is mixed:
mostly linear in visible bands, mostly
spherical/exponential in IR band.
Compresses well although compressed
variogram is greater in magnitude than
full variogram for the Blue and Green
bands
-Forest subset shows no spatial
dependence, compression is irrelevant
New Results:
Fort Story, VA
New York City
Ft. Stewart, GA
Ft. Moody, GA
Wright-Patterson AFB, OH
Ft. Huachuca, AZ
Wright-Patterson AFB, Ohio
mostly fields, some urban
1385x1692=2.3x10^6 pixels
Wright-Patterson
Blue
E-W,
N-S,
average
Wright-Patterson
Green
E-W,
N-S,
average
Wright-Patterson
Red
E-W,
N-S,
average
Wright-Patterson
IR
E-W,
N-S,
average
Wright-Patterson Results
-A slight loss of variogram with
compression, especially in blue and
green
-Spherical/exponential variogram
New Results:
Fort Story, VA
New York City
Ft. Stewart, GA
Ft. Moody, GA
Wright-Patterson AFB, OH
Ft. Huachuca, AZ
Ft. Huachuca, AZ
arid desert and
mountains with dry
drainage patterns
2551x1806=
4.6x10^6 pixels
Ft. Huachuca
Blue
E-W,
N-S,
average
Ft. Huachuca
Green
E-W,
N-S,
average
Ft. Huachuca
Red
E-W,
N-S,
average
Ft. Huachuca
IR
E-W,
N-S,
average
Huachuca Results
-Almost no loss of variogram with
compression .
-Variogram is smooth
(spherical/exponential)
Computing Benchmarks
-Plots of overall execution time versus
total number of pixels to be processed:
without Ft. Story full
with Ft. Story full
Ratio of computation time (full/reduced)
increases as pixel size increases
Outline of Talk
•
•
•
•
The Variogram
Motivation and Procedure
Past Results
Present Results
• Analysis and Conclusions
• Future Work
Most losses occurred in the Blue and Green bands; Red
and IR seem to compress better. Checkered fields in
particular showed a slight loss in compression for Blue
and Green (Wright-Patterson and Ft. Stewart)
Most land cover types show a spherical/exponential
type of variogram. The exceptions seem to be pure
forest (linear or no spatial variation) and pure urban
(linear)
Mixtures in particular seem to show a
spherical/exponential type of variogram.
Still no definitive answer to the major loss of spatial
information for full Ft. Story image. Best theory: have
lost a level of variation in a nested spherical or
exponential model (low-level scale <= 20 meters).
Overall, spatial statistical compression works well for a
wide variety of land cover types; may lose some
information, but the range is pretty constant, and the
gain in computation is immense. (Be careful with
forests, though – further tests definitely needed there).
Outline of Talk
•
•
•
•
•
The Variogram
Motivation and Procedure
Past Results
Present Results
Analysis and Conclusions
• Future Work
Future Work
• Compare random,average compression
with systematic compression
• Test for further compression (64X) with
1 m imagery
• Improve software code and streamline
implementation
• Parallelize variogram computations
• Improve graphs