Stochastic Contrast Measures for SAR Data: A Survey

Alejandro C. Frery

null doi: 10.12000/JR19108
Citation: null doi: 10.12000/JR19108

Stochastic Contrast Measures for SAR Data: A Survey

doi: 10.12000/JR19108
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
  • Figure  1.  Mind map of this review contents

    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  6.  Equalized intensity data with grid

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

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

    Figure  9.  Illustration of edge detection by maximum likelihood

    Figure  10.  Illustration of parameter estimation by distance minimization

    Figure  11.  Illustration of the Nonlocal Means approach

    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 $-\ln\left(-\dfrac{y}{2}+1\right),\;0\leq y < 2$ $\dfrac{(x-1)^2}{x+1}$
    下载: 导出CSV

    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$
    下载: 导出CSV
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  • 收稿日期:  2019-12-05
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