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Abstract: “Contrast” is an generic denomination for “difference”. Measures of contrast are a powerful tool in image processing and analysis, e.g., in denoising, edge detection, segmentation, classification, parameter estimation, change detection, and feature selection. We present a survey on techniques that aim at measuring the contrast between (i) samples of SAR imagery, and (ii) samples and models, with emphasis on those that employ the statistical properties of the data.
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Key words:
- Contrast /
- Divergence /
- Entropy /
- Geodesic distance /
- Statistics /
- Synthetic Aperture Radar (SAR)
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Figure 2. Exponential densities with mean 1/2, 1, and 2 (red, black and blue, resp.) in linear and semilogarithmic scales
Figure 3. Unitary mean Gamma densities with 1, 3, and 8 looks (black, red, and blue, resp.) in linear and semilogarithmic scales
Figure 4. Densities in linear and semi-logarithmic scale of the
${\rm E}(1) $ (black) and$ {{\cal{G}}^0} $ distributions with unitary mean and$ \alpha\in\{-1.5,-3.0,-8.0\} $ in red, green, and blue, resp
Figure 5. Densities in linear and semilogarithmic scale
$ {\cal{G}}^0(-5,4,L) $ distributions with unitary mean and$ L\in\{1,3,8\} $ in red, green, and blue, resp
Figure 8. Strips of 10 × 500 pixels with samples from two
$ {\cal{G}}^0 $ distributionsTable 1. (
$h,\phi$ )-divergences and related functions$\phi$ and$h$ $(h,\phi)$-divergence $h(y)$ $\phi(x)$ Kullback-Leibler $y$ $x\ln(x)$ Rényi (order $\beta$) $\dfrac{1}{\beta-1}\ln\left((\beta-1)y+1\right),\;0\leq y < \dfrac{1}{1-\beta}$ $\dfrac{x^{\beta}-\beta(x-1)-1}{\beta-1},0 < \beta<1$ Hellinger ${y}/{2},0\leq y<2$ $(\sqrt{x}-1)^2$ Bhattacharyya $-\ln(1-y),0\leq y < 1$ $-\sqrt{x}+\dfrac{x+1}{2}$ Jensen-Shannon $y$ $x\ln\left(\dfrac{2x}{x+1}\right)$ Arithmetic-geometric $y$ $\left(\dfrac{x+1}{2}\right)\ln \dfrac{x+1}{2x}$ Triangular $y,\;0\leq y <2$ $\dfrac{(x-1)^2}{x+1}$ Harmonic-mean $-\ln\left(-\dfrac{y}{2}+1\right),\;0\leq y < 2$ $\dfrac{(x-1)^2}{x+1}$ 
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Table 2.
$h$ -$\phi$ entropies and related functions$(h,\phi)$-entropy $h(y)$ $\phi(x)$ Shannon[35] $y$ $-x\ln x$ Restricted Tsallis (order $\beta \in \mathbb{R}_{+}\,:\,\beta\neq 1$)[39] $y$ $\dfrac{x^\beta-x}{1-\beta} $ Rényi (order $\beta \in \mathbb{R}_+\,:\,\beta\neq 1$)[29] $\dfrac{\ln y}{1-\beta}$ $x^\beta$ Arimoto of order $\beta$ $\dfrac{\beta-1}{y^\beta-1}$ $x^{1/\beta}$ Sharma-Mittal of order $\beta$ $ \dfrac{\exp\{(\beta-1)y\} }{\beta-1}$ $ x\ln x$
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