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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
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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
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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;
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Further integration of the local information is necessary.
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