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Unsupervised Change Detection on Synthetic Aperture Radar Images with Generalized Gamma Distributions by F. Crismer, G. Moser, V. A. Krylov, and S. B. Serpico University of Genoa, Italy

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Outline  SAR change detection  Generalized gamma distribution ratio model  Parameter estimation  Change detection  Experimental validation

 Conclusions

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SAR change detection • Multitemporal SAR – –

–

All-day and all-weather acquisitions. High resolution (up to 1 m) and short revisit time (up to 12 h). Appropriate for tracking of natural disatsters. Sample Cosmo-SkyMed (©ASI) image

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SAR change detection • Multitemporal SAR All-day and all-weather acquisitions. High resolution (up to 1 m) and short revisit time (up to 12 h). Appropriate for tracking of natural disatsters.

– –

–

• Objective –

Sample Cosmo-SkyMed (©ASI) image

Non-suprevised detection of changes on SAR image pairs.

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Generalized Gamma Distribution • Generalized Gamma Distribution (GΓD) [Stacy, 1962]

with Γ(.) – the gamma function , σ>0 - scale parameter, η>0 and ν≠0 shape paremeters.

• Special cases of GΓD – – – – –

Exponential, η=1, ν=1 Gamma, ν=1 Nakagami, ν = 0.5 Weibull, η=1 Lognormal, 𝜂 → ∞

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Generalized Gamma Distribution Ratio Assume that for two GΓDs the shape parameters η and ν take the same values: 𝜂 = 𝜂0 = 𝜂1 and 𝜈 = 𝜈0 = 𝜈1

then if we further assume the independence of the amplitudes 𝑟0 and 𝑟1 , and denote 𝑢 = 𝑟0 /𝑟1 , we get 1 0.9

and, finally, the GΓD-ratio model

λ=0.8

0.8

λ=1

p(u)

0.7 0.6

λ=1.5

0.5 0.4

λ=2

0.3

where 𝜆 = 𝜎0 /𝜎1 .

0.2

0.1 0 0

1

2

u

3

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Examples of GΓDR (η=1.3; ν=2) Università di Genova

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GΓD-ratio parameter estimation

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Method of log-cumulants (MoLC) for parameter estimation

• Consider the Mellin transform of a variable

• The log-moments of order

:

are defined as:

• The log-cumulants are defined as:

• The following connection with observations can be established for s=2,3,...:

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GΓD-ratio parameter estimation • Applied to GΓDR model the MoLC estimates are derived as: 𝑘1 𝑢 = ln 𝜆 2Ψ(1, 𝜂) 𝑘2 𝑢 = 𝜈2 2Ψ 3, 𝜂 𝑘4 𝑢 = 𝜈4

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characterized by 3 parameters - scale λ, - shape η and ν.

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GΓD-ratio parameter estimation • Applied to GΓDR model the MoLC estimates are derived as: 𝑘1 𝑢 = ln 𝜆 2Ψ(1, 𝜂) 𝑘2 𝑢 = 𝜈2 2Ψ 3, 𝜂 𝑘4 𝑢 = 𝜈4

characterized by 3 parameters - scale λ, - shape η and ν.

• The parameters are estimated as:

with

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strictly monotone with values in the range [0,6].

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GΓD-ratio parameter estimation • Applied to GΓDR model the MoLC estimates are derived as: 𝑘1 𝑢 = ln 𝜆 2Ψ(1, 𝜂) 𝑘2 𝑢 = 𝜈2 2Ψ 3, 𝜂 𝑘4 𝑢 = 𝜈4

characterized by 3 parameters - scale λ, - shape η and ν.

• The parameters are estimated as:

with

strictly monotone with values in the range [0,6].

• We prove the property of statistical consistency of the obtained MoLC estimates. Università di Genova

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Change detection • We employ the generanilzed Kittler thresholding to obtain the detection maps: – –

&

Illingworth

non-supervised automatic Bayesian approach; minimizes the following criterion function

where is an estimate of the prior probability of 𝐻𝑖 (change 𝐻1 and no-change 𝐻0 hypotheses), estimated as

and - normalized histogram, the ratio, and - parameter estimate.

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- parametric model of

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Experimental validation Pavia, Italy XSAR (band X), 25m resolution, 695 x 278 pixels 16 April 1994

•

18 April 1994

Changes due to the rice fields irrigation. Alessandria, Italy COSMO-SkyMed (band X), 2.5m resolution, 4963 x 2286 pixels 29 April 2009

•

1 May 2009

Changes due to a flood. Antispeckle filtering with SRAD (Speckle Reducing Anisotropic Diffusion).

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Experimental validation Experimetal analysis of the impact of image despeckling: Pavia Λ (SRAD)

Detection accuracy

False alarm rate

no SRAD

0.05%

0.02%

0.1

0.21%

0.01%

0.5

82.30%

0%

1.0

80.05%

0%

• Accuracies obtained by comparing the results with the available ground truth

Alessandria • Necessity to employ appropriate despeckling procedures.

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Λ (SRAD)

Detection accuracy

False alarm rate

no SRAD

0.34%

0.02%

0.1

0.69%

0.02%

0.5

82.59%

0.33%

1.0

89.00%

0.15%

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Experimental validation Results on the Pavia dataset: 82.3% accuracy No-change histogram with GΓD-ratio

Change histogram with GΓD-ratio

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Experimental validation Results on the Alessandria dataset: 89% accuracy No-change histogram with GΓD-ratio

Change histogram with GΓD-ratio

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Conclusions We have developed an automatic non-supervised method for change detection of SAR image pairs with the following properties: –

Accurate results after appropriate despeckling;

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Fast and consistent parameter estimation;

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Certain robustness with repect to possible multuple changes;

–

Further integration of the local information is necessary.

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