The Application of the Getis Statistic to High Resolution Imagery to Detect Change in Tropical Corals Ellsworth F. LeDrew, Alan Lim Faculty of Environmental

The Application of the Getis Statistic to High Resolution Imagery to

Detect Change in Tropical Corals

Ellsworth F. LeDrew, Alan Lim

Faculty of Environmental Studies

University of Waterloo

Healthy Coral and Sun Healthy Coral and Sun AnemonesAnemones

Coral Reefs = Rainforests of the Coral Reefs = Rainforests of the SeaSea

Coral BleachingCoral Bleaching

50- 60% Permanently 50- 60% Permanently DamagedDamaged

Research IssuesResearch Issues

Remote Sensing corrections for water - minus– Refraction at surface in and out– Attenuation of signal with depth– Variation of Attenuation with Wavelength– Effect of Bottom Material

Explore Change Detection Procedure that Overrides these concerns - for the same window, the spatial pattern of depth is constant

Research StrategyResearch Strategy Use a Statistic of Spatial Homogeneity -

the Getis Statistic is One of Many If There is No Change Between Image

Dates, There will be No Change in Spatial Homogeneity

If There is an Increase in Stress, It is Probable that Spatial Homogeneity will Increase (e.g. massive bleaching or algae invasion)

A Change in the Getis Statistic Between Image Dates will Indicate the Degree of Change in Spatial Homogeneity

The Getis StatisticThe Getis Statistic The Getis statistic (Gi*) provides the

strength of pixel association within a region of spatial dependence.

Computation of Gi* generates values which relate to variations within patterns of spatial dependence.

large positive Gi* values denote a cluster of high DN values; large negative Gi* values denote a cluster of low DN values.

Similar Gi* values indicate a region of similar underlying spectral conditions

Getis Statistic Getis Statistic ComputationComputation

Gi* is computed as follows:

Where:– wij(d) is a spatial weight matrix

Wi* is the sum of the weights matrix

x is the mean of the entire images is the standard deviation of the entire imagen is the number of image pixels

Gi* = ∑j wij(d) xj - Wi

* xs[Wi (n - Wi

*) / (n - 1)]1/2

The Getis CalculationsThe Getis Calculations Getis statistic calculated at four distances: d=1

(3 X 3), d=2 (5 X 5), d=3 (7 X 7), d=4 (9 X 9)

Maximum Getis for all windows is retrieved, as well as distance ‘d’

Plot Maximum Getis to view spatial patterns of spatial dependence: subtract two dates to determine change in spatial dependence

Calculate change in distance between two dates to test homogeneity vs heterogeneity hypothesis:

– if Maximum Getis Distance (MGD) increases over time, homogeneity increases,

– if MGD decreases over time, heterogeneity increases.

Case StudiesCase Studies Savusavu, Fiji, Spot imagery for 1994 and 1996

– Open Water- no change benchmark– Two Major Cyanide damaged reefs– Not anniversary dates: June and October

Bunaken and Siladen, Indonesia– Spot Imagery for 1990, 1994, 1997, 2000– Ikonos Imagery for 2001– All anniversary dates in July– Siladen: only native use– Bunaken: Tourism

Palau, 0.6 m Aerial Photography, 1992, 1997, 2002– Damsel Fish manicured algae farms

Bunaken Region Spot Image, July 31, 1994

MARINE RAPID ASSESSMENT PROGRAM

IN THE BUNAKEN NATIONAL

MARINE PARK, NORTH SULAWESI

Roeroe, Allard,Yusuf 2000

Red= SciencePink= Water SupportGreen= Native Use

Blue= Tourist

July 14 SPOT 2000 Max Getis


West Bunaken

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Percent Change in Maximum Getis Distance

1996-1994 Damaged Reef B

1996-1994 Damaged Reef A

1996-1994 Open Water

The Change in Maximum Getis Distance The Change in Maximum Getis Distance for for FijiFiji

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2000-1997 East Bunaken

2000-1997 West Bunaken


The Change in Maximum Getis Distance for The Change in Maximum Getis Distance for BunakenBunaken


June 29 Ikonos 2001 Max Getis

West Bunaken

DIFFERENCES IN REAL AND SYNTHETIC SPATIAL RESOLUTION

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Siladen SPOT 4 M 00-90

Siladen IKONOS01- SPOT90

Siladen SPOT 20M 00-90

Siladen SPOT 20M 00- 4 m 90

: Siladen

PalauPalau

High spatial resolution (0.6m) digital aerial imagery of the Damsel Fish Farm on a coral reef in Palau for 1992, 1997,

2002 . Arrow points towards Damsel Fish Manicured Algae Turf for 92 and 97 and lack of Algae for 2002

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2003-1997 Palau Damsel Site



The Change in Maximum Getis Distance for The Change in Maximum Getis Distance for PalauPalau Damsel Fish Site Damsel Fish Site


1996-1994 Damaged Reef

A

2000-1997 East Bunaken

2003-1997 Palau Damsel

Site

2003-1992 Palau Damsel

Site1996-1994 Damaged Reef A 1.6731996-1994 Damaged Reef B 1.554 0.3592000-1997 East Bunaken 2.7492000-1997 West Bunaken 2.749 2.392003-1997 Palau Damsel Site 2.7492003-1992 Palau Damsel Site 2.151 0.5981997-1992 Palau Damsel Site 0.837 1.912 1.315

The Kolmogorov-Smirnov Statistics for the Shape Difference in Cummulative Histograms of the Temporal Difference in the Getis

Statistic. The Critical Value at 0.99 is 0.81.

For example, Damaged Reef A is NOT significantly different from Damaged Reef B Between 1994 and 1996, but the Difference between 1992 to 1997 of the Ngedarrach Reef IS Significantly

Different from the difference from 1997 to 2003.

All are Significantly Different from the Null Case of Open Water Between 1994 and 1996.

Summary of Getis Summary of Getis ResultsResults

Majority of change during past decade in Maximum Distance :MGD is positive = increase in homogeneity

This is an easily applied image structure measure that reflects changes in coral reef cover. It can be applied quickly to sequential images to identify ‘flash points’ of change that require in situ followup

The spatial structures may be useful in management zonation since they do reflect reef heterogeneity

Summary of Getis Summary of Getis ResultsResults

Ikonos data provides richer spatial detail than resampled SPOT, as expected, but aggregated statistics are consistent for the two image sets.

West Bunaken Siladen

East Bunaken

Maximum Getis from SPOT Maximum Getis from SPOT ImageryImagery

Examples of Spatial PatternsExamples of Spatial Patterns

The Change in Maximum Getis The Change in Maximum Getis Distance for Bunaken Marine Park, Distance for Bunaken Marine Park,

Indonesia, Indonesia, and Savusavu Bay, Fijiand Savusavu Bay, FijiQuickTime™ and aGraphics decompressorare needed to see this picture.

B B

B

B BB B B B B B B B B

J J

J

JJ

J J J J J J J J J

H H H

H H H H H H H H H H H

F F F

F

F F

F FF F F F

F F

Ñ Ñ Ñ Ñ

Ñ

ÑÑ

Ñ Ñ Ñ Ñ Ñ ÑÑ

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B East Bunaken SPOT 20M 97-94

J Siladen SPOT 20M 97-94

H Open Water SPOT 96-94

F Damaged Reef A SPOT 96-94

Ñ Damaged Reef B SPOT 96-94

Siladen, 1990 Siladen, 2000

SPOTenhanced

MaximumGetis

Statistic

-0.5 2.5 -0.5 2.5


June 29 Ikonos 2001 Max Getis

Siladen

Kolmogorov-Smirnov Kolmogorov-Smirnov TestTest

Non-Parametric Test for Significance in

Difference of Cumulative Histogram

DAMAGED

REEF A

DAMAGED

REEF B

WEST

BUNAKEN

EAST

BUNAKEN SILADEN

OPEN WATER 0.643 0.714 0.571 0.429 0.571

DAMAGED REEF A 0.214 0.214 0.571 0.357

DAMAGED REEF B 0.286 0.571 0.286

WEST BUNAKEN 0.571 0.429

EAST BUNAKEN 0.429

Location onFigure

Gmax1990

Gmax2000

MGD1990

MGD2000

CHANGE INMGD

A 0.69 1.06 2 5 3B 2.03 0.75 3 1 -2C 1.46 0.89 5 1 -4D 0.75 1.38 1 4 3E 1.35 1.68 1 3 2F 0.31 1.71 1 2 1G 0.33 1.2 1 4 3

Siladen, Maximum Getis Statistic 1990

-4.0 4.0

Siladen, Difference of Maximum Getis Distance:2000-1990

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Documents

The Application of the Getis Statistic to High Resolution Imagery to Detect Change in Tropical Corals Ellsworth F. LeDrew, Alan Lim Faculty of Environmental