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

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Typical image variogram (left),

Important quantities (right)

Some graphs of variogram models

NUGGET MODEL

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LINEAR MODEL

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SPHERICAL MODEL

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EXPONENTIAL MODEL

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A double or nested variogram

DOUBLE EXPONENTIAL MODEL

distance

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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

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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