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TRANSCRIPT
Relationships between Land Cover and Spatial Statistical Compression
in High-Resolution Imagery
James A. Shine1 and Daniel B. Carr2
34th Symposium on the Interface19 April 2002
1 George Mason University & US Army Topographic Engineering Center2 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)
0 10 20 30 40distance
0
20
40
60
80
100
120
140
gam
ma
Typical image variogram (left),
Important quantities (right)
Some graphs of variogram models
NUGGET MODEL
h
gam
ma
0 5 10 15 20 25 30
0.8
0.9
1.0
1.1
1.2
LINEAR MODEL
h
gam
ma
0 5 10 15 20 25 30
05
1015
2025
30
SPHERICAL MODEL
h
gam
ma
0 5 10 15 20 25 30
0.2
0.4
0.6
0.8
1.0
EXPONENTIAL MODEL
h
gam
ma
0 5 10 15 20 25 30
0.2
0.4
0.6
0.8
1.0
A double or nested variogram
DOUBLE EXPONENTIAL MODEL
distance
ga
mm
a
0 5 10 15 20 25 30
0.5
1.0
1.5
2.0
+
+
++
++ + + + + + + + + + + + + + + + + + + + + + + + +
o
oo
oo
oo
o o o o o o o o o o o o o o o o o o o o o o o
X
X
X
X
X
XX
XX
X X X X X X X X X X X X X X X X X X X X X
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
MOTIVATIONLarge 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
-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.
-Need to compare different types of imagery and hopefully make some inferences
DOUBLE EXPONENTIAL MODEL
distance
ga
mm
a
0 5 10 15 20 25 30
0.5
1.0
1.5
2.0
+
+
++
++ + + + + + + + + + + + + + + + + + + + + + + + +
o
oo
oo
oo
o o o o o o o o o o o o o o o o o o o o o o o
X
X
X
X
X
XX
XX
X X X X X X X X X X X X X X X X X X X X X
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 fields1202x1742=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 forest1325x1767=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, AZarid desert and mountains with dry drainage patterns2551x1806=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