<span style="text-wrap: wrap;">Stochastic Contrast Measures for SAR Data: A Survey</span>

doi:10.12000/JR19108

Stochastic Contrast Measures for SAR Data: A Survey

DOI: 10.12000/JR19108

Alejandro C. Frery^,

Funds: This work was partially founded by CNPq (Brazilian National Council for Scientific and Technological Development) and Fapeal (the State Science Foundation-Alagoas State, Brazil)

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Author Bio:
Alejandro C. Frery (S’92–SM’03) received a B.Sc. degree in Electronic and Electrical Engineering from the Universidad de Mendoza, Mendoza, Argentina. His M.Sc. degree was in Applied Mathematics (Statistics) from the Instituto de Matemática Pura e Aplicada (IMPA, Rio de Janeiro) and his Ph.D. degree was in Applied Computing from the Instituto Nacional de Pesquisas Espaciais (INPE, São José dos Campos, Brazil). He is currently the leader of LaCCAN – Laboratório de Computação Científica e Análise Numérica, Universidade Federal de Alagoas, Maceió, Brazil, and holds a Huashan Scholar position (2019–2021) with the Key Lab of Intelligent Perception and Image Understanding of the Ministry of Education, Xidian University, Xi’an, China. His research interests are statistical computing and stochastic modeling

Corresponding author: Laboratório de Computação Científica e Análise Numérica – LaCCAN, Universidade Federal de Alagoas – Ufal, 57072-900 Maceió, AL – Brazil, and the Key Lab of Intelligent Perception and Image Understanding of the Ministry of Education, Xidian University, Xi’an, China. Email: acfrery@laccan.ufal.br

摘要

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.
- Contrast /
- Divergence /
- Entropy /
- Geodesic distance /
- Statistics /
- Synthetic Aperture Radar (SAR)

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Figure 1. Mind map of this review contents

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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

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Figure 3. Unitary mean Gamma densities with 1, 3, and 8 looks (black, red, and blue, resp.) in linear and semilogarithmic scales

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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

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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

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Figure 6. Equalized intensity data with grid

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Figure 7. Regression analysis for the estimation of the equivalent number of looks

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Figure 8. Strips of 10 × 500 pixels with samples from two ${\cal{G}}^0$ distributions

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Figure 9. Illustration of edge detection by maximum likelihood

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Figure 10. Illustration of parameter estimation by distance minimization

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Figure 11. Illustration of the Nonlocal Means approach

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Table 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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