• Journal of Electronic Science and Technology
  • Vol. 22, Issue 4, 100286 (2024)
V. Sidda Reddy1,*, G. Ravi Shankar Reddy2,*, and K. Sivanagi Reddy3
Author Affiliations
  • 1Department of Information Technology, Stanley College of Engineering and Technology for Women, Hyderabad, 500001, India
  • 2Department of Electronics and Communication Engineering, CVR College of Engineering, Hyderabad, 501510, India
  • 3Department of Electronics and Communication Engineering, Sridevi Women’s Engineering College, Hyderabad, 500075, India
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    DOI: 10.1016/j.jnlest.2024.100286 Cite this Article
    V. Sidda Reddy, G. Ravi Shankar Reddy, K. Sivanagi Reddy. RUDIE: Robust approach for underwater digital image enhancement[J]. Journal of Electronic Science and Technology, 2024, 22(4): 100286 Copy Citation Text show less

    Abstract

    Processing underwater digital images is critical in ocean engineering, biology, and environmental studies, focusing on challenges such as poor lighting, image de-scattering, and color restoration. Due to environmental conditions on the sea floor, improving image contrast and clarity is essential for underwater navigation and obstacle avoidance. Particularly in turbid, low-visibility waters, we require robust computer vision techniques and algorithms. Over the past decade, various models for underwater image enrichment have been proposed to address quality and visibility issues under dynamic and natural lighting conditions. This research article aims to evaluate various image improvement methods and propose a robust model that improves image quality, addresses turbidity, and enhances color, ultimately improving obstacle avoidance in autonomous systems. The proposed model demonstrates high accuracy compared to traditional models. The result analysis indicates the proposed model produces images with greatly improved visibility and exceptional color accuracy. Furthermore, research can unlock new possibilities for underwater exploration, monitoring, and intervention by advancing the state-of-the-art models in this domain.
    $ {I}_{\lambda }\left(x{\mathrm{,}}\; y\right)=J\left(x{\mathrm{,}}\; y\right){t}_{\lambda }\left(x{\mathrm{,}}\;y\right)+\left(1-{t}_{\lambda }\left(x{\mathrm{,}}\;y\right)\right){A}_{\lambda } $(1)

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    $ {t}_{\lambda }\left(x{\mathrm{,}}\; y\right)={e}^{-\beta \left(\lambda \right)d\left(x{\mathrm{,}} \; y\right)} $(2)

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    $ {I}_{\lambda }\left(x{\mathrm{,}}\; y\right)={J}_{\lambda }\left(x{\mathrm{,}}\; y\right){N}_{\lambda }^{d\left(x{\mathrm{,}} \; y\right)}+\left(1-{N}_{\lambda }^{d\left(x{\mathrm{,}} \; y\right)}\right){A}_{\lambda } $(3)

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    $ {N}_{\lambda }=\left\{ 0.800.85,λ=650μm750μm(R)0.930.97,λ=490μm550μm(G)0.950.99,λ=400μm490μm(B)\right. $(4)

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    $ {A}_{\lambda }=\underset{\left(x{\mathrm{,}} \; y\right)\in I\left(i{\mathrm{,}} \; j\right)}{\mathrm{max}}{\text{min}}_{\in \Omega \left(x{\mathrm{,}}\;y\right)}{I}_{\lambda }\left(i{\mathrm{,}}\;j\right) {\mathrm{.}} $(5)

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    $ {I_\lambda }\left( {x{\mathrm{,}}\;y} \right) = ({J_\lambda }\left( {x{\mathrm{,}}\;y} \right) - {A_\lambda }) + {A_\lambda }N_\lambda ^{{{d}}\left( {x{\mathrm{,}}\;y} \right)} {\mathrm{.}} $(6)

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    $ {\text{log}}({I_\lambda }\left( {x{\mathrm{,}}\;y} \right) - {A_\lambda }) = {\text{log}}({J_\lambda }\left( {x{\mathrm{,}}\;y} \right) - {A_\lambda }) + {\text{log}}{N_\lambda }d\left( {x{\mathrm{,}}\;y} \right){\mathrm{.}} $(7)

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    $ d\left( {x{\mathrm{,}}\;y} \right) = 1/4\left[ {d\left( {x + 1{\mathrm{,}}\;y} \right) + d\left( {x - 1{\mathrm{,}}\;y} \right) + d\left( {x{\mathrm{,}}\;y + 1} \right) + d\left( {x{\mathrm{,}}\;y - 1} \right)} \right]{\mathrm{.}} $(8)

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    $ {\tilde J_\lambda }\left( {x{\mathrm{,}}\;y} \right) = {\tilde I_\lambda }\left( {x{\mathrm{,}}\;y} \right) + {\text{ln}}({N_\lambda }\left( {x{\mathrm{,}}\;y} \right) + c)d\left( {x{\mathrm{,}}\;y} \right) {\mathrm{.}} $(9)

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    $ {\nabla ^2}{\tilde J_\lambda }\left( {x{\mathrm{,}}\;y} \right) = {\nabla ^2}{\tilde I_\lambda }\left( {x{\mathrm{,}}\;y} \right) $(10)

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    $ {\tilde J^n}_\lambda (x{\mathrm{,}}\;y) = \frac{1}{4}\left( {{{\tilde J}_\lambda }^{n - 1}\left( {x - 1{\mathrm{,}}\;y} \right) + {{\tilde J}_\lambda }^{n - 1}\left( {x + 1{\mathrm{,}}\;y} \right) + {{\tilde J}_\lambda }^{n - 1}\left( {x{\mathrm{,}}\;y - 1} \right) + {{\tilde J}_\lambda }^{n - 1}\left( {x{\mathrm{,}}\;y + 1} \right) + {\nabla ^2}I\left( {x{\mathrm{,}}\;y} \right)} \right) $(11)

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    $ S_{{\text{max}}}^c = S_{{\text{mean}}}^c + \mu S_{{\text{Var}}}^c $(12)

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    $ S_{{\text{min}}}^c = S_{{\text{mean}}}^c - \mu S_{{\text{Var}}}^c $(13)

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    $ {S_{\mathrm{CR}}^c} = ({S^c} - S_{\mathrm{min}}^c)/({S_{\mathrm{max}}^c} - {S_{\mathrm{min}}^c})255{\mathrm{.}} $(14)

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    $ I\left( {x{\mathrm{,}}\;y} \right) = L\left( {x{\mathrm{,}}\;y} \right)R\left( {x{\mathrm{,}}\;y} \right) $(15)

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    $ \text{log }R\left(x{\mathrm{,}}\;y\right)=\mathrm{log} L\left(x{\mathrm{,}}\;y\right)+\mathrm{log} I\left(x{\mathrm{,}}\;y\right) {\mathrm{.}} $(16)

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    $ L\left(x{\mathrm{,}}\;y\right)=F\left(x{\mathrm{,}}\;y\right)I\left(x{\mathrm{,}}\;y\right) {\mathrm{.}} $(17)

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    $ F\left(x\mathrm{,}\; y\right)=Ke^{\left[\frac{-\left(x^2+y^2\right)}{\sigma^2}\right]}\mathrm{.} $(18)

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    $ \iint F\left(x{\mathrm{,}}\;y\right)\text{d}x\text{d}y=1{\mathrm{.}} $(19)

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    $ F\left( {x{\mathrm{,}}\;y} \right) = \frac{{ {\displaystyle\sum \limits_{m = i - p}^{i + p} } \displaystyle\sum \limits_{n = j - p}^{j + p} d\left( {m{\mathrm{,}}\;n} \right)\chi \psi }}{{ {\displaystyle\sum \limits_{m = i - p}^{i + p} }\; {\displaystyle\sum \limits_{n = j - p}^{j + p} } \chi \psi }} $(20)

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    $ \chi = {e^{ - {\sigma _d}\left( {{{\left( {i - m} \right)}^2} + {{\left( {j - n} \right)}^2}} \right)}} $(21)

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    $ \psi = {e^{ - {\sigma _l}{{\left( {d\left( {i{\mathrm{,}}\;j} \right) - d\left( {m{\mathrm{,}}\;n} \right)} \right)}^2}}}$(22)

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    $ \psi = {e^{ - {\sigma _l}{{\left( {\left| {d\left( {i{\mathrm{,}}\;j} \right) - d\left( {m{\mathrm{,}}\;n} \right)} \right| - \xi } \right)}^2}}} $(23)

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    $ {I}\left({x}{{{\mathrm{,}}}}\;{y}\right)=\sum _{{i}=1}^{{K}}{{W}}_{{i}}{{R}}_{{i}}\left({x}{{{\mathrm{,}}}}\;{y}\right) $(24)

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    $ {W_i}\left( {x{\mathrm{,}}\;y} \right) = {\mathrm{log}} \left[ {\alpha {f_i}\left( {x{\mathrm{,}}\;y} \right)} \right] - {\mathrm{log}} \left[ {{f_i}\left( {x{\mathrm{,}}\;y} \right)} \right] {\mathrm{.}}$(25)

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    $ {I}^{\prime }\left(x{\mathrm{,}}\;y\right)=b\left(I\left(x{\mathrm{,}}\;y\right)- {\text{Min}}_{i}\right)/{\varDelta }_{i} {\mathrm{.}} $(26)

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    $ \text{GIF}{\left(I\right)}_{P}=\frac{1}{\displaystyle \sum _{qϵ{W}_{k}}{W}_{{\text{GIF}}_{p{\mathrm{,}\;}q}}\left(G\right)}\displaystyle \sum _{qϵ{W}_{k}}{W}_{{\text{GIF}}_{p{\mathrm{,}\;}q}}\left(G\right) {I}_{q}{\mathrm{.}} $(27)

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    $ {W}_{{\text{GIF}}_{p{\mathrm{,}}\;q}}\left(G\right)=\frac{1}{{\left|w\right|}^{2}}\displaystyle \sum _{k\left(p{\mathrm{,}}\;q\right)ϵ{w}_{k}}\left(1+\frac{\left({G}_{p}-{\mu }_{k}\right)\left({G}_{q}-{\mu }_{k}\right)}{{\sigma }_{k}^{2}+\epsilon }\right) {\mathrm{.}} $(28)

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    $ \text{GIF}{\left(I\right)}_{P}=\displaystyle \sum _{qϵ{\omega }_{k}}{W}_{{\text{GIF}}_{p{\mathrm{,}}\;q}}\left(G\right) {I}_{q} {\mathrm{.}} $(29)

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    $ J\left( x \right) = \frac{{{I_c}\left( x \right) - {A_c}}}{{{\text{max}}\left( {t\left( x \right){\mathrm{,}}\;{t_0}} \right)}} + {A_c}. $(30)

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    $ {\text{ENTROPY}} = - \mathop \sum \limits_{i = 1}^n {p_i}\left( {{\text{lo}}{{\text{g}}_2}{p_i}} \right) $(31)

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    $ {\text{UCIQE}} = {c_1}{\sigma _c} + {c_2}{\text{co}}{{\text{n}}_l} + {c_3}{\mu _s} $(32)

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    $ {\text{PCQI}}\left( {x{\mathrm{,}}\;y} \right) = \frac{1}{M}\mathop \sum \limits_{j = 1}^M {q_i}\left( {x{\mathrm{,}}\;y} \right){q_c}\left( {x{\mathrm{,}}\;y} \right){q_s}\left( {x{\mathrm{,}}\;y} \right) $(33)

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    $ {\text{PSNR}} = 10{\text{lo}}{{\text{g}}_{10}}\frac{{{\mathrm{max}} {L^2}}}{{{\text{MSE}}}} {\mathrm{.}} $(34)

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    $ {\text{MSE}} = \frac{1}{{MN}}\mathop \sum \limits_{i = 1}^M \mathop \sum \limits_{j = 1}^N {(x(i{\mathrm{,}}\;j) - y(i{\mathrm{,}}\;j))^2} $(35)

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    V. Sidda Reddy, G. Ravi Shankar Reddy, K. Sivanagi Reddy. RUDIE: Robust approach for underwater digital image enhancement[J]. Journal of Electronic Science and Technology, 2024, 22(4): 100286
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