Abstract

Combining underwater optical imaging principles and the level set, this paper proposes a novel type of level set method called optically guided level set. This novel method can transform optical challenges in underwater environments (such as the illumination bias and wavelength-selective absorption) into valuable guidance for underwater object segmentation. Using the underwater optical guidance, our novel method can generate accurate object segmentation results by suitable initialization and regular evolving of the level set. The optical guidance core lies in two observations pertaining to the underwater optical imaging process: (i) the overlap between the object region and optical collimation region and (ii) the correspondence between the object structure and irradiation distribution inside the optical collimation. The high accuracy of our proposed method is demonstrated via comparisons to the state-of-the-art level set and salient object detection methods for public underwater images collected in diverse environments. Moreover, by using the work presented in this paper, we plan to demonstrate optical principles’ potential for improving computer vision research, which is a promising research topic with many practical applications.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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2018 (2)

A. Jantzi, W. Jemison, A. Laux, L. Mullen, and B. Cochenour, “Enhanced underwater ranging using an optical vortex,” Opt. Express 26(3), 2668–2674 (2018).
[Crossref] [PubMed]

C. O. Ancuti, C. Ancuti, C. De Vleeschouwer, and P. Bekaert, “Color Balance and Fusion for Underwater Image Enhancement,” IEEE Trans. Image Process. 27(1), 379–393 (2018).
[Crossref] [PubMed]

2017 (2)

M. Twardowski and A. Tonizzo, “Scattering and absorption effects on asymptotic light fields in seawater,” Opt. Express 25(15), 18122–18130 (2017).
[Crossref] [PubMed]

Z. Chen, Z. Zhang, F. Dai, Y. Bu, and H. Wang, “Monocular Vision-Based Underwater Object Detection,” Sensors (Basel) 17(8), 1784–1796 (2017).
[Crossref] [PubMed]

2016 (6)

B. N. Li, J. Qin, R. Wang, M. Wang, and X. Li, “Selective level set segmentation using fuzzy region competition,” IEEE Access 4, 4777–4788 (2016).
[Crossref]

Y. Guo, H. Song, H. Liu, H. Wei, P. Yang, S. Zhan, H. Wang, H. Huang, N. Liao, Q. Mu, J. Leng, and W. Yang, “Model-based restoration of underwater spectral images captured with narrowband filters,” Opt. Express 24(12), 13101–13120 (2016).
[Crossref] [PubMed]

R. Gibson, R. Atkinson, and J. Gordon, “A review of underwater stereo-image measurement for marine biology and ecology applications,” Oceanogr. Mar. Biol. Annu. Rev. 47, 257–292 (2016).

Meng-Che Chuang, Jenq-Neng Hwang, and K. Williams, “A feature learning and object recognition framework for underwater fish images,” IEEE Trans. Image Process. 25(4), 1862–1872 (2016).
[PubMed]

Y. Li, H. Lu, J. Li, X. Li, Y. Li, and S. Serikawa, “Underwater image de-scattering and classification by deep neural network,” Comput. Electr. Eng. 54, 68–77 (2016).
[Crossref]

J. Zhang and S. Sclaroff, “Exploiting Surroundedness for Saliency Detection: A Boolean Map Approach,” IEEE Trans. Pattern Anal. Mach. Intell. 38(5), 889–902 (2016).
[Crossref] [PubMed]

2015 (1)

D. L. Rizzini, F. Kallasi, F. Oleari, and S. Caselli, “Investigation of vision-based underwater object detection with multiple datasets,” Int. J. Adv. Robot. Syst. 12(6), 77 (2015).
[Crossref]

2014 (2)

D. Kim, D. Lee, H. Myung, and H.-T. Choi, “Artificial landmark-based underwater localization for AUVs using weighted template matching,” Intell. Serv. Robot. 7(3), 175–184 (2014).
[Crossref]

X. Bai, Y. Fang, W. Lin, L. Wang, and B.-F. Ju, “Saliency-Based Defect Detection in Industrial Images by Using Phase Spectrum,” IEEE Trans. Industr. Inform. 10(4), 2135–2145 (2014).
[Crossref]

2013 (2)

J. Li, M. D. Levine, X. An, X. Xu, and H. He, “Visual Saliency Based on Scale-Space Analysis in the Frequency Domain,” IEEE Trans. Pattern Anal. Mach. Intell. 35(4), 996–1010 (2013).
[Crossref] [PubMed]

S. Balla-Arabé, X. Gao, and B. Wang, “GPU accelerated edge-region based level set evolution constrained by 2D gray-scale histogram,” IEEE Trans. Image Process. 22(7), 2688–2698 (2013).
[Crossref] [PubMed]

2012 (1)

D. Lee, G. Kim, D. Kim, H. Myung, and H. T. Choi, “Vision-based object detection and tracking for autonomous navigation of underwater robots,” Ocean Eng. 48, 59–68 (2012).
[Crossref]

2011 (3)

B. N. Li, C. K. Chui, S. Chang, and S. H. Ong, “Integrating spatial fuzzy clustering with level set methods for automated medical image segmentation,” Comput. Biol. Med. 41(1), 1–10 (2011).
[Crossref] [PubMed]

J. W. Kaeli, H. Singh, C. Murphy, and C. Kunz, “Improving color correction for underwater image surveys,” Oceans 11, 1 (2011).
[Crossref]

C. Li, R. Huang, Z. Ding, J. C. Gatenby, D. N. Metaxas, and J. C. Gore, “A level set method for image segmentation in the presence of intensity inhomogeneities with application to MRI,” IEEE Trans. Image Process. 20(7), 2007–2016 (2011).
[Crossref] [PubMed]

2010 (1)

C. Li, C. Xu, C. Gui, and M. D. Fox, “Distance regularized level set evolution and its application to image segmentation,” IEEE Trans. Image Process. 19(12), 3243–3254 (2010).
[Crossref] [PubMed]

2009 (1)

C. Kanan, M. H. Tong, L. Zhang, and G. W. Cottrell, “SUN: Top-down saliency using natural statistics,” Vis. Cogn. 17(6-7), 979–1003 (2009).
[Crossref] [PubMed]

2008 (1)

S. Lankton and A. Tannenbaum, “Localizing region-based active contours,” IEEE Trans. Image Process. 17(11), 2029–2039 (2008).
[Crossref] [PubMed]

2006 (1)

N. Bruce and J. Tsotsos, “Saliency based on information maximization,” Adv. Neural Inf. Process. Syst. 18, 155–169 (2006).

2003 (2)

D. R. Edgington, K. A. Salamy, M. Risi, R. E. Sherlock, D. Walther, and C. Koch, “Automated event detection in underwater video,” Oceans 5, 2749–2753 (2003).

P. M. Lee, B. H. Jeon, and S. M. Kim, “Visual servoing for underwater docking of an autonomous underwater vehicle with one camera,” Oceans 1, 677–682 (2003).

2001 (2)

S. C. Yu, T. Ura, T. Fujii, and H. Kondo, “Navigation of autonomous underwater vehicles based on artificial underwater landmarks,” Oceans 1, 409–416 (2001).

L. Itti and C. Koch, “Computational modelling of visual attention,” Nat. Rev. Neurosci. 2(3), 194–203 (2001).
[Crossref] [PubMed]

1997 (1)

D. Calloway, “Beer-lambert law,” J. Chem. Educ. 74(7), 744–761 (1997).
[Crossref]

1979 (1)

N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Syst. Man Cybern. 9(1), 62–66 (1979).
[Crossref]

1963 (1)

S. Q. Duntley, “Light in the sea,” JOSA 53(2), 214–233 (1963).
[Crossref]

An, X.

J. Li, M. D. Levine, X. An, X. Xu, and H. He, “Visual Saliency Based on Scale-Space Analysis in the Frequency Domain,” IEEE Trans. Pattern Anal. Mach. Intell. 35(4), 996–1010 (2013).
[Crossref] [PubMed]

Ancuti, C.

C. O. Ancuti, C. Ancuti, C. De Vleeschouwer, and P. Bekaert, “Color Balance and Fusion for Underwater Image Enhancement,” IEEE Trans. Image Process. 27(1), 379–393 (2018).
[Crossref] [PubMed]

Ancuti, C. O.

C. O. Ancuti, C. Ancuti, C. De Vleeschouwer, and P. Bekaert, “Color Balance and Fusion for Underwater Image Enhancement,” IEEE Trans. Image Process. 27(1), 379–393 (2018).
[Crossref] [PubMed]

Atkinson, R.

R. Gibson, R. Atkinson, and J. Gordon, “A review of underwater stereo-image measurement for marine biology and ecology applications,” Oceanogr. Mar. Biol. Annu. Rev. 47, 257–292 (2016).

Bai, X.

X. Bai, Y. Fang, W. Lin, L. Wang, and B.-F. Ju, “Saliency-Based Defect Detection in Industrial Images by Using Phase Spectrum,” IEEE Trans. Industr. Inform. 10(4), 2135–2145 (2014).
[Crossref]

Balla-Arabé, S.

S. Balla-Arabé, X. Gao, and B. Wang, “GPU accelerated edge-region based level set evolution constrained by 2D gray-scale histogram,” IEEE Trans. Image Process. 22(7), 2688–2698 (2013).
[Crossref] [PubMed]

Bekaert, P.

C. O. Ancuti, C. Ancuti, C. De Vleeschouwer, and P. Bekaert, “Color Balance and Fusion for Underwater Image Enhancement,” IEEE Trans. Image Process. 27(1), 379–393 (2018).
[Crossref] [PubMed]

Bruce, N.

N. Bruce and J. Tsotsos, “Saliency based on information maximization,” Adv. Neural Inf. Process. Syst. 18, 155–169 (2006).

Bu, Y.

Z. Chen, Z. Zhang, F. Dai, Y. Bu, and H. Wang, “Monocular Vision-Based Underwater Object Detection,” Sensors (Basel) 17(8), 1784–1796 (2017).
[Crossref] [PubMed]

Calloway, D.

D. Calloway, “Beer-lambert law,” J. Chem. Educ. 74(7), 744–761 (1997).
[Crossref]

Caselli, S.

D. L. Rizzini, F. Kallasi, F. Oleari, and S. Caselli, “Investigation of vision-based underwater object detection with multiple datasets,” Int. J. Adv. Robot. Syst. 12(6), 77 (2015).
[Crossref]

Chang, S.

B. N. Li, C. K. Chui, S. Chang, and S. H. Ong, “Integrating spatial fuzzy clustering with level set methods for automated medical image segmentation,” Comput. Biol. Med. 41(1), 1–10 (2011).
[Crossref] [PubMed]

Chen, Z.

Z. Chen, Z. Zhang, F. Dai, Y. Bu, and H. Wang, “Monocular Vision-Based Underwater Object Detection,” Sensors (Basel) 17(8), 1784–1796 (2017).
[Crossref] [PubMed]

Choi, H. T.

D. Lee, G. Kim, D. Kim, H. Myung, and H. T. Choi, “Vision-based object detection and tracking for autonomous navigation of underwater robots,” Ocean Eng. 48, 59–68 (2012).
[Crossref]

Choi, H.-T.

D. Kim, D. Lee, H. Myung, and H.-T. Choi, “Artificial landmark-based underwater localization for AUVs using weighted template matching,” Intell. Serv. Robot. 7(3), 175–184 (2014).
[Crossref]

Choi, S.

K. Jung, P. Youn, S. Choi, J. Lee, H. Kang, and H. Myung, “Development of retro-reflective marker and recognition algorithm for underwater environment,” 4th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI), 666–670 (2017).
[Crossref]

Chui, C. K.

B. N. Li, C. K. Chui, S. Chang, and S. H. Ong, “Integrating spatial fuzzy clustering with level set methods for automated medical image segmentation,” Comput. Biol. Med. 41(1), 1–10 (2011).
[Crossref] [PubMed]

Cochenour, B.

A. Jantzi, W. Jemison, A. Laux, L. Mullen, and B. Cochenour, “Enhanced underwater ranging using an optical vortex,” Opt. Express 26(3), 2668–2674 (2018).
[Crossref] [PubMed]

Cottrell, G. W.

C. Kanan, M. H. Tong, L. Zhang, and G. W. Cottrell, “SUN: Top-down saliency using natural statistics,” Vis. Cogn. 17(6-7), 979–1003 (2009).
[Crossref] [PubMed]

Dai, F.

Z. Chen, Z. Zhang, F. Dai, Y. Bu, and H. Wang, “Monocular Vision-Based Underwater Object Detection,” Sensors (Basel) 17(8), 1784–1796 (2017).
[Crossref] [PubMed]

De Vleeschouwer, C.

C. O. Ancuti, C. Ancuti, C. De Vleeschouwer, and P. Bekaert, “Color Balance and Fusion for Underwater Image Enhancement,” IEEE Trans. Image Process. 27(1), 379–393 (2018).
[Crossref] [PubMed]

Ding, Z.

C. Li, R. Huang, Z. Ding, J. C. Gatenby, D. N. Metaxas, and J. C. Gore, “A level set method for image segmentation in the presence of intensity inhomogeneities with application to MRI,” IEEE Trans. Image Process. 20(7), 2007–2016 (2011).
[Crossref] [PubMed]

Duntley, S. Q.

S. Q. Duntley, “Light in the sea,” JOSA 53(2), 214–233 (1963).
[Crossref]

Edgington, D. R.

D. R. Edgington, K. A. Salamy, M. Risi, R. E. Sherlock, D. Walther, and C. Koch, “Automated event detection in underwater video,” Oceans 5, 2749–2753 (2003).

Fang, Y.

X. Bai, Y. Fang, W. Lin, L. Wang, and B.-F. Ju, “Saliency-Based Defect Detection in Industrial Images by Using Phase Spectrum,” IEEE Trans. Industr. Inform. 10(4), 2135–2145 (2014).
[Crossref]

Fox, M. D.

C. Li, C. Xu, C. Gui, and M. D. Fox, “Distance regularized level set evolution and its application to image segmentation,” IEEE Trans. Image Process. 19(12), 3243–3254 (2010).
[Crossref] [PubMed]

Fujii, T.

S. C. Yu, T. Ura, T. Fujii, and H. Kondo, “Navigation of autonomous underwater vehicles based on artificial underwater landmarks,” Oceans 1, 409–416 (2001).

Gao, X.

S. Balla-Arabé, X. Gao, and B. Wang, “GPU accelerated edge-region based level set evolution constrained by 2D gray-scale histogram,” IEEE Trans. Image Process. 22(7), 2688–2698 (2013).
[Crossref] [PubMed]

Gatenby, J. C.

C. Li, R. Huang, Z. Ding, J. C. Gatenby, D. N. Metaxas, and J. C. Gore, “A level set method for image segmentation in the presence of intensity inhomogeneities with application to MRI,” IEEE Trans. Image Process. 20(7), 2007–2016 (2011).
[Crossref] [PubMed]

Gibson, R.

R. Gibson, R. Atkinson, and J. Gordon, “A review of underwater stereo-image measurement for marine biology and ecology applications,” Oceanogr. Mar. Biol. Annu. Rev. 47, 257–292 (2016).

Gordon, J.

R. Gibson, R. Atkinson, and J. Gordon, “A review of underwater stereo-image measurement for marine biology and ecology applications,” Oceanogr. Mar. Biol. Annu. Rev. 47, 257–292 (2016).

Gore, J. C.

C. Li, R. Huang, Z. Ding, J. C. Gatenby, D. N. Metaxas, and J. C. Gore, “A level set method for image segmentation in the presence of intensity inhomogeneities with application to MRI,” IEEE Trans. Image Process. 20(7), 2007–2016 (2011).
[Crossref] [PubMed]

Gui, C.

C. Li, C. Xu, C. Gui, and M. D. Fox, “Distance regularized level set evolution and its application to image segmentation,” IEEE Trans. Image Process. 19(12), 3243–3254 (2010).
[Crossref] [PubMed]

Guo, Y.

Y. Guo, H. Song, H. Liu, H. Wei, P. Yang, S. Zhan, H. Wang, H. Huang, N. Liao, Q. Mu, J. Leng, and W. Yang, “Model-based restoration of underwater spectral images captured with narrowband filters,” Opt. Express 24(12), 13101–13120 (2016).
[Crossref] [PubMed]

He, H.

J. Li, M. D. Levine, X. An, X. Xu, and H. He, “Visual Saliency Based on Scale-Space Analysis in the Frequency Domain,” IEEE Trans. Pattern Anal. Mach. Intell. 35(4), 996–1010 (2013).
[Crossref] [PubMed]

Huang, H.

Y. Guo, H. Song, H. Liu, H. Wei, P. Yang, S. Zhan, H. Wang, H. Huang, N. Liao, Q. Mu, J. Leng, and W. Yang, “Model-based restoration of underwater spectral images captured with narrowband filters,” Opt. Express 24(12), 13101–13120 (2016).
[Crossref] [PubMed]

Huang, R.

C. Li, R. Huang, Z. Ding, J. C. Gatenby, D. N. Metaxas, and J. C. Gore, “A level set method for image segmentation in the presence of intensity inhomogeneities with application to MRI,” IEEE Trans. Image Process. 20(7), 2007–2016 (2011).
[Crossref] [PubMed]

Itti, L.

L. Itti and C. Koch, “Computational modelling of visual attention,” Nat. Rev. Neurosci. 2(3), 194–203 (2001).
[Crossref] [PubMed]

Jantzi, A.

A. Jantzi, W. Jemison, A. Laux, L. Mullen, and B. Cochenour, “Enhanced underwater ranging using an optical vortex,” Opt. Express 26(3), 2668–2674 (2018).
[Crossref] [PubMed]

Jemison, W.

A. Jantzi, W. Jemison, A. Laux, L. Mullen, and B. Cochenour, “Enhanced underwater ranging using an optical vortex,” Opt. Express 26(3), 2668–2674 (2018).
[Crossref] [PubMed]

Jenq-Neng Hwang,

Meng-Che Chuang, Jenq-Neng Hwang, and K. Williams, “A feature learning and object recognition framework for underwater fish images,” IEEE Trans. Image Process. 25(4), 1862–1872 (2016).
[PubMed]

Jeon, B. H.

P. M. Lee, B. H. Jeon, and S. M. Kim, “Visual servoing for underwater docking of an autonomous underwater vehicle with one camera,” Oceans 1, 677–682 (2003).

Ju, B.-F.

X. Bai, Y. Fang, W. Lin, L. Wang, and B.-F. Ju, “Saliency-Based Defect Detection in Industrial Images by Using Phase Spectrum,” IEEE Trans. Industr. Inform. 10(4), 2135–2145 (2014).
[Crossref]

Jung, K.

K. Jung, P. Youn, S. Choi, J. Lee, H. Kang, and H. Myung, “Development of retro-reflective marker and recognition algorithm for underwater environment,” 4th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI), 666–670 (2017).
[Crossref]

Kaeli, J. W.

J. W. Kaeli, H. Singh, C. Murphy, and C. Kunz, “Improving color correction for underwater image surveys,” Oceans 11, 1 (2011).
[Crossref]

Kallasi, F.

D. L. Rizzini, F. Kallasi, F. Oleari, and S. Caselli, “Investigation of vision-based underwater object detection with multiple datasets,” Int. J. Adv. Robot. Syst. 12(6), 77 (2015).
[Crossref]

Kanan, C.

C. Kanan, M. H. Tong, L. Zhang, and G. W. Cottrell, “SUN: Top-down saliency using natural statistics,” Vis. Cogn. 17(6-7), 979–1003 (2009).
[Crossref] [PubMed]

Kang, H.

K. Jung, P. Youn, S. Choi, J. Lee, H. Kang, and H. Myung, “Development of retro-reflective marker and recognition algorithm for underwater environment,” 4th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI), 666–670 (2017).
[Crossref]

Kim, D.

D. Kim, D. Lee, H. Myung, and H.-T. Choi, “Artificial landmark-based underwater localization for AUVs using weighted template matching,” Intell. Serv. Robot. 7(3), 175–184 (2014).
[Crossref]

D. Lee, G. Kim, D. Kim, H. Myung, and H. T. Choi, “Vision-based object detection and tracking for autonomous navigation of underwater robots,” Ocean Eng. 48, 59–68 (2012).
[Crossref]

Kim, G.

D. Lee, G. Kim, D. Kim, H. Myung, and H. T. Choi, “Vision-based object detection and tracking for autonomous navigation of underwater robots,” Ocean Eng. 48, 59–68 (2012).
[Crossref]

Kim, S. M.

P. M. Lee, B. H. Jeon, and S. M. Kim, “Visual servoing for underwater docking of an autonomous underwater vehicle with one camera,” Oceans 1, 677–682 (2003).

Koch, C.

D. R. Edgington, K. A. Salamy, M. Risi, R. E. Sherlock, D. Walther, and C. Koch, “Automated event detection in underwater video,” Oceans 5, 2749–2753 (2003).

L. Itti and C. Koch, “Computational modelling of visual attention,” Nat. Rev. Neurosci. 2(3), 194–203 (2001).
[Crossref] [PubMed]

Kondo, H.

S. C. Yu, T. Ura, T. Fujii, and H. Kondo, “Navigation of autonomous underwater vehicles based on artificial underwater landmarks,” Oceans 1, 409–416 (2001).

Kunz, C.

J. W. Kaeli, H. Singh, C. Murphy, and C. Kunz, “Improving color correction for underwater image surveys,” Oceans 11, 1 (2011).
[Crossref]

Lankton, S.

S. Lankton and A. Tannenbaum, “Localizing region-based active contours,” IEEE Trans. Image Process. 17(11), 2029–2039 (2008).
[Crossref] [PubMed]

Laux, A.

A. Jantzi, W. Jemison, A. Laux, L. Mullen, and B. Cochenour, “Enhanced underwater ranging using an optical vortex,” Opt. Express 26(3), 2668–2674 (2018).
[Crossref] [PubMed]

Lee, D.

D. Kim, D. Lee, H. Myung, and H.-T. Choi, “Artificial landmark-based underwater localization for AUVs using weighted template matching,” Intell. Serv. Robot. 7(3), 175–184 (2014).
[Crossref]

D. Lee, G. Kim, D. Kim, H. Myung, and H. T. Choi, “Vision-based object detection and tracking for autonomous navigation of underwater robots,” Ocean Eng. 48, 59–68 (2012).
[Crossref]

Lee, J.

K. Jung, P. Youn, S. Choi, J. Lee, H. Kang, and H. Myung, “Development of retro-reflective marker and recognition algorithm for underwater environment,” 4th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI), 666–670 (2017).
[Crossref]

Lee, P. M.

P. M. Lee, B. H. Jeon, and S. M. Kim, “Visual servoing for underwater docking of an autonomous underwater vehicle with one camera,” Oceans 1, 677–682 (2003).

Leng, J.

Y. Guo, H. Song, H. Liu, H. Wei, P. Yang, S. Zhan, H. Wang, H. Huang, N. Liao, Q. Mu, J. Leng, and W. Yang, “Model-based restoration of underwater spectral images captured with narrowband filters,” Opt. Express 24(12), 13101–13120 (2016).
[Crossref] [PubMed]

Levine, M. D.

J. Li, M. D. Levine, X. An, X. Xu, and H. He, “Visual Saliency Based on Scale-Space Analysis in the Frequency Domain,” IEEE Trans. Pattern Anal. Mach. Intell. 35(4), 996–1010 (2013).
[Crossref] [PubMed]

Li, B. N.

B. N. Li, J. Qin, R. Wang, M. Wang, and X. Li, “Selective level set segmentation using fuzzy region competition,” IEEE Access 4, 4777–4788 (2016).
[Crossref]

B. N. Li, C. K. Chui, S. Chang, and S. H. Ong, “Integrating spatial fuzzy clustering with level set methods for automated medical image segmentation,” Comput. Biol. Med. 41(1), 1–10 (2011).
[Crossref] [PubMed]

Li, C.

C. Li, R. Huang, Z. Ding, J. C. Gatenby, D. N. Metaxas, and J. C. Gore, “A level set method for image segmentation in the presence of intensity inhomogeneities with application to MRI,” IEEE Trans. Image Process. 20(7), 2007–2016 (2011).
[Crossref] [PubMed]

C. Li, C. Xu, C. Gui, and M. D. Fox, “Distance regularized level set evolution and its application to image segmentation,” IEEE Trans. Image Process. 19(12), 3243–3254 (2010).
[Crossref] [PubMed]

Li, J.

Y. Li, H. Lu, J. Li, X. Li, Y. Li, and S. Serikawa, “Underwater image de-scattering and classification by deep neural network,” Comput. Electr. Eng. 54, 68–77 (2016).
[Crossref]

J. Li, M. D. Levine, X. An, X. Xu, and H. He, “Visual Saliency Based on Scale-Space Analysis in the Frequency Domain,” IEEE Trans. Pattern Anal. Mach. Intell. 35(4), 996–1010 (2013).
[Crossref] [PubMed]

Li, X.

Y. Li, H. Lu, J. Li, X. Li, Y. Li, and S. Serikawa, “Underwater image de-scattering and classification by deep neural network,” Comput. Electr. Eng. 54, 68–77 (2016).
[Crossref]

B. N. Li, J. Qin, R. Wang, M. Wang, and X. Li, “Selective level set segmentation using fuzzy region competition,” IEEE Access 4, 4777–4788 (2016).
[Crossref]

Li, Y.

Y. Li, H. Lu, J. Li, X. Li, Y. Li, and S. Serikawa, “Underwater image de-scattering and classification by deep neural network,” Comput. Electr. Eng. 54, 68–77 (2016).
[Crossref]

Y. Li, H. Lu, J. Li, X. Li, Y. Li, and S. Serikawa, “Underwater image de-scattering and classification by deep neural network,” Comput. Electr. Eng. 54, 68–77 (2016).
[Crossref]

Liao, N.

Y. Guo, H. Song, H. Liu, H. Wei, P. Yang, S. Zhan, H. Wang, H. Huang, N. Liao, Q. Mu, J. Leng, and W. Yang, “Model-based restoration of underwater spectral images captured with narrowband filters,” Opt. Express 24(12), 13101–13120 (2016).
[Crossref] [PubMed]

Lin, W.

X. Bai, Y. Fang, W. Lin, L. Wang, and B.-F. Ju, “Saliency-Based Defect Detection in Industrial Images by Using Phase Spectrum,” IEEE Trans. Industr. Inform. 10(4), 2135–2145 (2014).
[Crossref]

Liu, H.

Y. Guo, H. Song, H. Liu, H. Wei, P. Yang, S. Zhan, H. Wang, H. Huang, N. Liao, Q. Mu, J. Leng, and W. Yang, “Model-based restoration of underwater spectral images captured with narrowband filters,” Opt. Express 24(12), 13101–13120 (2016).
[Crossref] [PubMed]

Lu, H.

Y. Li, H. Lu, J. Li, X. Li, Y. Li, and S. Serikawa, “Underwater image de-scattering and classification by deep neural network,” Comput. Electr. Eng. 54, 68–77 (2016).
[Crossref]

Meng-Che Chuang,

Meng-Che Chuang, Jenq-Neng Hwang, and K. Williams, “A feature learning and object recognition framework for underwater fish images,” IEEE Trans. Image Process. 25(4), 1862–1872 (2016).
[PubMed]

Metaxas, D. N.

C. Li, R. Huang, Z. Ding, J. C. Gatenby, D. N. Metaxas, and J. C. Gore, “A level set method for image segmentation in the presence of intensity inhomogeneities with application to MRI,” IEEE Trans. Image Process. 20(7), 2007–2016 (2011).
[Crossref] [PubMed]

Mu, Q.

Y. Guo, H. Song, H. Liu, H. Wei, P. Yang, S. Zhan, H. Wang, H. Huang, N. Liao, Q. Mu, J. Leng, and W. Yang, “Model-based restoration of underwater spectral images captured with narrowband filters,” Opt. Express 24(12), 13101–13120 (2016).
[Crossref] [PubMed]

Mullen, L.

A. Jantzi, W. Jemison, A. Laux, L. Mullen, and B. Cochenour, “Enhanced underwater ranging using an optical vortex,” Opt. Express 26(3), 2668–2674 (2018).
[Crossref] [PubMed]

Murphy, C.

J. W. Kaeli, H. Singh, C. Murphy, and C. Kunz, “Improving color correction for underwater image surveys,” Oceans 11, 1 (2011).
[Crossref]

Myung, H.

D. Kim, D. Lee, H. Myung, and H.-T. Choi, “Artificial landmark-based underwater localization for AUVs using weighted template matching,” Intell. Serv. Robot. 7(3), 175–184 (2014).
[Crossref]

D. Lee, G. Kim, D. Kim, H. Myung, and H. T. Choi, “Vision-based object detection and tracking for autonomous navigation of underwater robots,” Ocean Eng. 48, 59–68 (2012).
[Crossref]

K. Jung, P. Youn, S. Choi, J. Lee, H. Kang, and H. Myung, “Development of retro-reflective marker and recognition algorithm for underwater environment,” 4th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI), 666–670 (2017).
[Crossref]

Oleari, F.

D. L. Rizzini, F. Kallasi, F. Oleari, and S. Caselli, “Investigation of vision-based underwater object detection with multiple datasets,” Int. J. Adv. Robot. Syst. 12(6), 77 (2015).
[Crossref]

Ong, S. H.

B. N. Li, C. K. Chui, S. Chang, and S. H. Ong, “Integrating spatial fuzzy clustering with level set methods for automated medical image segmentation,” Comput. Biol. Med. 41(1), 1–10 (2011).
[Crossref] [PubMed]

Otsu, N.

N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Syst. Man Cybern. 9(1), 62–66 (1979).
[Crossref]

Qin, J.

B. N. Li, J. Qin, R. Wang, M. Wang, and X. Li, “Selective level set segmentation using fuzzy region competition,” IEEE Access 4, 4777–4788 (2016).
[Crossref]

Risi, M.

D. R. Edgington, K. A. Salamy, M. Risi, R. E. Sherlock, D. Walther, and C. Koch, “Automated event detection in underwater video,” Oceans 5, 2749–2753 (2003).

Rizzini, D. L.

D. L. Rizzini, F. Kallasi, F. Oleari, and S. Caselli, “Investigation of vision-based underwater object detection with multiple datasets,” Int. J. Adv. Robot. Syst. 12(6), 77 (2015).
[Crossref]

Salamy, K. A.

D. R. Edgington, K. A. Salamy, M. Risi, R. E. Sherlock, D. Walther, and C. Koch, “Automated event detection in underwater video,” Oceans 5, 2749–2753 (2003).

Sclaroff, S.

J. Zhang and S. Sclaroff, “Exploiting Surroundedness for Saliency Detection: A Boolean Map Approach,” IEEE Trans. Pattern Anal. Mach. Intell. 38(5), 889–902 (2016).
[Crossref] [PubMed]

Serikawa, S.

Y. Li, H. Lu, J. Li, X. Li, Y. Li, and S. Serikawa, “Underwater image de-scattering and classification by deep neural network,” Comput. Electr. Eng. 54, 68–77 (2016).
[Crossref]

Sherlock, R. E.

D. R. Edgington, K. A. Salamy, M. Risi, R. E. Sherlock, D. Walther, and C. Koch, “Automated event detection in underwater video,” Oceans 5, 2749–2753 (2003).

Singh, H.

J. W. Kaeli, H. Singh, C. Murphy, and C. Kunz, “Improving color correction for underwater image surveys,” Oceans 11, 1 (2011).
[Crossref]

Song, H.

Y. Guo, H. Song, H. Liu, H. Wei, P. Yang, S. Zhan, H. Wang, H. Huang, N. Liao, Q. Mu, J. Leng, and W. Yang, “Model-based restoration of underwater spectral images captured with narrowband filters,” Opt. Express 24(12), 13101–13120 (2016).
[Crossref] [PubMed]

Tannenbaum, A.

S. Lankton and A. Tannenbaum, “Localizing region-based active contours,” IEEE Trans. Image Process. 17(11), 2029–2039 (2008).
[Crossref] [PubMed]

Tong, M. H.

C. Kanan, M. H. Tong, L. Zhang, and G. W. Cottrell, “SUN: Top-down saliency using natural statistics,” Vis. Cogn. 17(6-7), 979–1003 (2009).
[Crossref] [PubMed]

Tonizzo, A.

M. Twardowski and A. Tonizzo, “Scattering and absorption effects on asymptotic light fields in seawater,” Opt. Express 25(15), 18122–18130 (2017).
[Crossref] [PubMed]

Tsotsos, J.

N. Bruce and J. Tsotsos, “Saliency based on information maximization,” Adv. Neural Inf. Process. Syst. 18, 155–169 (2006).

Twardowski, M.

M. Twardowski and A. Tonizzo, “Scattering and absorption effects on asymptotic light fields in seawater,” Opt. Express 25(15), 18122–18130 (2017).
[Crossref] [PubMed]

Ura, T.

S. C. Yu, T. Ura, T. Fujii, and H. Kondo, “Navigation of autonomous underwater vehicles based on artificial underwater landmarks,” Oceans 1, 409–416 (2001).

Walther, D.

D. R. Edgington, K. A. Salamy, M. Risi, R. E. Sherlock, D. Walther, and C. Koch, “Automated event detection in underwater video,” Oceans 5, 2749–2753 (2003).

Wang, B.

S. Balla-Arabé, X. Gao, and B. Wang, “GPU accelerated edge-region based level set evolution constrained by 2D gray-scale histogram,” IEEE Trans. Image Process. 22(7), 2688–2698 (2013).
[Crossref] [PubMed]

Wang, H.

Z. Chen, Z. Zhang, F. Dai, Y. Bu, and H. Wang, “Monocular Vision-Based Underwater Object Detection,” Sensors (Basel) 17(8), 1784–1796 (2017).
[Crossref] [PubMed]

Y. Guo, H. Song, H. Liu, H. Wei, P. Yang, S. Zhan, H. Wang, H. Huang, N. Liao, Q. Mu, J. Leng, and W. Yang, “Model-based restoration of underwater spectral images captured with narrowband filters,” Opt. Express 24(12), 13101–13120 (2016).
[Crossref] [PubMed]

Wang, L.

X. Bai, Y. Fang, W. Lin, L. Wang, and B.-F. Ju, “Saliency-Based Defect Detection in Industrial Images by Using Phase Spectrum,” IEEE Trans. Industr. Inform. 10(4), 2135–2145 (2014).
[Crossref]

Wang, M.

B. N. Li, J. Qin, R. Wang, M. Wang, and X. Li, “Selective level set segmentation using fuzzy region competition,” IEEE Access 4, 4777–4788 (2016).
[Crossref]

Wang, R.

B. N. Li, J. Qin, R. Wang, M. Wang, and X. Li, “Selective level set segmentation using fuzzy region competition,” IEEE Access 4, 4777–4788 (2016).
[Crossref]

Wei, H.

Y. Guo, H. Song, H. Liu, H. Wei, P. Yang, S. Zhan, H. Wang, H. Huang, N. Liao, Q. Mu, J. Leng, and W. Yang, “Model-based restoration of underwater spectral images captured with narrowband filters,” Opt. Express 24(12), 13101–13120 (2016).
[Crossref] [PubMed]

Williams, K.

Meng-Che Chuang, Jenq-Neng Hwang, and K. Williams, “A feature learning and object recognition framework for underwater fish images,” IEEE Trans. Image Process. 25(4), 1862–1872 (2016).
[PubMed]

Xu, C.

C. Li, C. Xu, C. Gui, and M. D. Fox, “Distance regularized level set evolution and its application to image segmentation,” IEEE Trans. Image Process. 19(12), 3243–3254 (2010).
[Crossref] [PubMed]

Xu, X.

J. Li, M. D. Levine, X. An, X. Xu, and H. He, “Visual Saliency Based on Scale-Space Analysis in the Frequency Domain,” IEEE Trans. Pattern Anal. Mach. Intell. 35(4), 996–1010 (2013).
[Crossref] [PubMed]

Yang, P.

Y. Guo, H. Song, H. Liu, H. Wei, P. Yang, S. Zhan, H. Wang, H. Huang, N. Liao, Q. Mu, J. Leng, and W. Yang, “Model-based restoration of underwater spectral images captured with narrowband filters,” Opt. Express 24(12), 13101–13120 (2016).
[Crossref] [PubMed]

Yang, W.

Y. Guo, H. Song, H. Liu, H. Wei, P. Yang, S. Zhan, H. Wang, H. Huang, N. Liao, Q. Mu, J. Leng, and W. Yang, “Model-based restoration of underwater spectral images captured with narrowband filters,” Opt. Express 24(12), 13101–13120 (2016).
[Crossref] [PubMed]

Youn, P.

K. Jung, P. Youn, S. Choi, J. Lee, H. Kang, and H. Myung, “Development of retro-reflective marker and recognition algorithm for underwater environment,” 4th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI), 666–670 (2017).
[Crossref]

Yu, S. C.

S. C. Yu, T. Ura, T. Fujii, and H. Kondo, “Navigation of autonomous underwater vehicles based on artificial underwater landmarks,” Oceans 1, 409–416 (2001).

Zhan, S.

Y. Guo, H. Song, H. Liu, H. Wei, P. Yang, S. Zhan, H. Wang, H. Huang, N. Liao, Q. Mu, J. Leng, and W. Yang, “Model-based restoration of underwater spectral images captured with narrowband filters,” Opt. Express 24(12), 13101–13120 (2016).
[Crossref] [PubMed]

Zhang, J.

J. Zhang and S. Sclaroff, “Exploiting Surroundedness for Saliency Detection: A Boolean Map Approach,” IEEE Trans. Pattern Anal. Mach. Intell. 38(5), 889–902 (2016).
[Crossref] [PubMed]

Zhang, L.

C. Kanan, M. H. Tong, L. Zhang, and G. W. Cottrell, “SUN: Top-down saliency using natural statistics,” Vis. Cogn. 17(6-7), 979–1003 (2009).
[Crossref] [PubMed]

Zhang, Z.

Z. Chen, Z. Zhang, F. Dai, Y. Bu, and H. Wang, “Monocular Vision-Based Underwater Object Detection,” Sensors (Basel) 17(8), 1784–1796 (2017).
[Crossref] [PubMed]

Adv. Neural Inf. Process. Syst. (1)

N. Bruce and J. Tsotsos, “Saliency based on information maximization,” Adv. Neural Inf. Process. Syst. 18, 155–169 (2006).

Comput. Biol. Med. (1)

B. N. Li, C. K. Chui, S. Chang, and S. H. Ong, “Integrating spatial fuzzy clustering with level set methods for automated medical image segmentation,” Comput. Biol. Med. 41(1), 1–10 (2011).
[Crossref] [PubMed]

Comput. Electr. Eng. (1)

Y. Li, H. Lu, J. Li, X. Li, Y. Li, and S. Serikawa, “Underwater image de-scattering and classification by deep neural network,” Comput. Electr. Eng. 54, 68–77 (2016).
[Crossref]

IEEE Access (1)

B. N. Li, J. Qin, R. Wang, M. Wang, and X. Li, “Selective level set segmentation using fuzzy region competition,” IEEE Access 4, 4777–4788 (2016).
[Crossref]

IEEE Trans. Image Process. (6)

Meng-Che Chuang, Jenq-Neng Hwang, and K. Williams, “A feature learning and object recognition framework for underwater fish images,” IEEE Trans. Image Process. 25(4), 1862–1872 (2016).
[PubMed]

C. O. Ancuti, C. Ancuti, C. De Vleeschouwer, and P. Bekaert, “Color Balance and Fusion for Underwater Image Enhancement,” IEEE Trans. Image Process. 27(1), 379–393 (2018).
[Crossref] [PubMed]

C. Li, C. Xu, C. Gui, and M. D. Fox, “Distance regularized level set evolution and its application to image segmentation,” IEEE Trans. Image Process. 19(12), 3243–3254 (2010).
[Crossref] [PubMed]

C. Li, R. Huang, Z. Ding, J. C. Gatenby, D. N. Metaxas, and J. C. Gore, “A level set method for image segmentation in the presence of intensity inhomogeneities with application to MRI,” IEEE Trans. Image Process. 20(7), 2007–2016 (2011).
[Crossref] [PubMed]

S. Balla-Arabé, X. Gao, and B. Wang, “GPU accelerated edge-region based level set evolution constrained by 2D gray-scale histogram,” IEEE Trans. Image Process. 22(7), 2688–2698 (2013).
[Crossref] [PubMed]

S. Lankton and A. Tannenbaum, “Localizing region-based active contours,” IEEE Trans. Image Process. 17(11), 2029–2039 (2008).
[Crossref] [PubMed]

IEEE Trans. Industr. Inform. (1)

X. Bai, Y. Fang, W. Lin, L. Wang, and B.-F. Ju, “Saliency-Based Defect Detection in Industrial Images by Using Phase Spectrum,” IEEE Trans. Industr. Inform. 10(4), 2135–2145 (2014).
[Crossref]

IEEE Trans. Pattern Anal. Mach. Intell. (2)

J. Li, M. D. Levine, X. An, X. Xu, and H. He, “Visual Saliency Based on Scale-Space Analysis in the Frequency Domain,” IEEE Trans. Pattern Anal. Mach. Intell. 35(4), 996–1010 (2013).
[Crossref] [PubMed]

J. Zhang and S. Sclaroff, “Exploiting Surroundedness for Saliency Detection: A Boolean Map Approach,” IEEE Trans. Pattern Anal. Mach. Intell. 38(5), 889–902 (2016).
[Crossref] [PubMed]

IEEE Trans. Syst. Man Cybern. (1)

N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Syst. Man Cybern. 9(1), 62–66 (1979).
[Crossref]

Int. J. Adv. Robot. Syst. (1)

D. L. Rizzini, F. Kallasi, F. Oleari, and S. Caselli, “Investigation of vision-based underwater object detection with multiple datasets,” Int. J. Adv. Robot. Syst. 12(6), 77 (2015).
[Crossref]

Intell. Serv. Robot. (1)

D. Kim, D. Lee, H. Myung, and H.-T. Choi, “Artificial landmark-based underwater localization for AUVs using weighted template matching,” Intell. Serv. Robot. 7(3), 175–184 (2014).
[Crossref]

J. Chem. Educ. (1)

D. Calloway, “Beer-lambert law,” J. Chem. Educ. 74(7), 744–761 (1997).
[Crossref]

JOSA (1)

S. Q. Duntley, “Light in the sea,” JOSA 53(2), 214–233 (1963).
[Crossref]

Nat. Rev. Neurosci. (1)

L. Itti and C. Koch, “Computational modelling of visual attention,” Nat. Rev. Neurosci. 2(3), 194–203 (2001).
[Crossref] [PubMed]

Ocean Eng. (1)

D. Lee, G. Kim, D. Kim, H. Myung, and H. T. Choi, “Vision-based object detection and tracking for autonomous navigation of underwater robots,” Ocean Eng. 48, 59–68 (2012).
[Crossref]

Oceanogr. Mar. Biol. Annu. Rev. (1)

R. Gibson, R. Atkinson, and J. Gordon, “A review of underwater stereo-image measurement for marine biology and ecology applications,” Oceanogr. Mar. Biol. Annu. Rev. 47, 257–292 (2016).

Oceans (4)

P. M. Lee, B. H. Jeon, and S. M. Kim, “Visual servoing for underwater docking of an autonomous underwater vehicle with one camera,” Oceans 1, 677–682 (2003).

D. R. Edgington, K. A. Salamy, M. Risi, R. E. Sherlock, D. Walther, and C. Koch, “Automated event detection in underwater video,” Oceans 5, 2749–2753 (2003).

S. C. Yu, T. Ura, T. Fujii, and H. Kondo, “Navigation of autonomous underwater vehicles based on artificial underwater landmarks,” Oceans 1, 409–416 (2001).

J. W. Kaeli, H. Singh, C. Murphy, and C. Kunz, “Improving color correction for underwater image surveys,” Oceans 11, 1 (2011).
[Crossref]

Opt. Express (3)

Y. Guo, H. Song, H. Liu, H. Wei, P. Yang, S. Zhan, H. Wang, H. Huang, N. Liao, Q. Mu, J. Leng, and W. Yang, “Model-based restoration of underwater spectral images captured with narrowband filters,” Opt. Express 24(12), 13101–13120 (2016).
[Crossref] [PubMed]

A. Jantzi, W. Jemison, A. Laux, L. Mullen, and B. Cochenour, “Enhanced underwater ranging using an optical vortex,” Opt. Express 26(3), 2668–2674 (2018).
[Crossref] [PubMed]

M. Twardowski and A. Tonizzo, “Scattering and absorption effects on asymptotic light fields in seawater,” Opt. Express 25(15), 18122–18130 (2017).
[Crossref] [PubMed]

Sensors (Basel) (1)

Z. Chen, Z. Zhang, F. Dai, Y. Bu, and H. Wang, “Monocular Vision-Based Underwater Object Detection,” Sensors (Basel) 17(8), 1784–1796 (2017).
[Crossref] [PubMed]

Vis. Cogn. (1)

C. Kanan, M. H. Tong, L. Zhang, and G. W. Cottrell, “SUN: Top-down saliency using natural statistics,” Vis. Cogn. 17(6-7), 979–1003 (2009).
[Crossref] [PubMed]

Other (3)

J. Harel, C. Koch, and P. Perona, “Graph-based visual saliency,” NIPS, 545–552 (2006).

X. Hou and L. Zhang, “Saliency Detection: A Spectral Residual Approach,” IEEE Conference on Computer Vision and Pattern Recognition 1–8 (2007).
[Crossref]

K. Jung, P. Youn, S. Choi, J. Lee, H. Kang, and H. Myung, “Development of retro-reflective marker and recognition algorithm for underwater environment,” 4th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI), 666–670 (2017).
[Crossref]

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Figures (10)

Fig. 1
Fig. 1 Comparison of image deviation using Eq. (2). (a) Original images in the water, (b) deviation maps in the water, (c) original images on the ground, and (d) deviation maps on the ground. (b) and (d) are the results given by Eq. (2).
Fig. 2
Fig. 2 Illustration of underwater optical imaging. Light is emitted by the light source (denoted as A), reflected by the object (e.g., P), and enters the camera (C). The angle between the illuminating ray AP and the optical axis of the light source is denoted as φ. The angle between the imaging ray PC and the optical axis of the camera (i.e., DC) is denoted as θ. The projection of ray AP in the optical axis is denoted as AB and the length is denoted as z. During the imaging process, light scattered by particles in the water column (e.g., Q) enters the camera as well, thus blurring the image.
Fig. 3
Fig. 3 Illustration of underwater light field distribution. Plane S is perpendicular to the optical axis of the underwater light source, the distance between them being z. The distance between points P and B is denoted as r . For any perpendicular plane located at a distance z = z0 from the underwater light source, the irradiance E(λ) at any point generally decreases with its distance to the optical axis.
Fig. 4
Fig. 4 Optically guided ESF g , (a) original underwater image, (b) map of image deviations g, (c) map of the coefficient optical guidance ρ, and (d) map of g .
Fig. 5
Fig. 5 Segmentation process and results of our method: (a) Original image, (b) initial LSF, (c) final LSF, and (d) segmentation results.
Fig. 6
Fig. 6 Segmentation results of the DRLSE method with a fixed initial window (x = 25:35, y = 40:50).
Fig. 7
Fig. 7 Segmentation results with our optical collimation guidance. (a) Initial LSF under the optical collimation region guidance, (b) original ESF, (c) final contour by combining (a) and (b), (d) optical collimation distribution, (e) new ESF under the optical collimation distribution guidance, and (f) final contour by combining (a) and (e).
Fig. 8
Fig. 8 Segmentation results. (a) Local intensity clustering-based level set, (b) edge-region-based level set, (c) spatial fuzzy clustering-based level set, (d) fuzzy region competition-based level set, (e) localized region-based active contour, and (f) our method.
Fig. 9
Fig. 9 Manually initialized level set.
Fig. 10
Fig. 10 Object identification results with our method and salient object detection methods. (a) Ground-truth, (b) Itti, (c) SR, (d) PFT, (e) HFT, (f) AIM, (g) BMS, (h) SUN, (i) GBVS, and (j) our method.

Tables (4)

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Table 1 Correlations between different features.

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Table 2 Parameters controlling optically guided level set segmentation.

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Table 3 Initial parameter values in Fig. 8.

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Table 4 JSI values of the image segmentation results shown in Figs. 4 and 8.

Equations (28)

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Ε(ϕ)=u p (ϕ)+λ L g (ϕ)+α A g (ϕ),
g= 1 1+ | G σ ×I | 2 ,
Ε(ϕ)=u Ω 1 2 ( | ϕ1 | 2 ) dxdy+λ Ω gδ(ϕ) | ϕ |dxdy+α Ω gH(ϕ) dxdy,
H ω ( x )={ 0,x<ω 1,x>ω 1 2 [ 1+ x ω + 1 π sin( πx ω ) ],| x |ω
δ ω ( x )={ 0,| x |>ω 1 2ω [ 1+cos( πx ω ) ],| x |<ω
E(z,λ)= E 0 (λ) 1 (z+a) 2 e α(λ)z ,
E P (λ)=E(z,λ)f( r ),
L P (λ)= R P (λ) E P (λ)/ 4π .
E P' (λ)=A(λ)G(l) e α(λ)l L P (λ)+ E b (λ) e β(λ)l + E s (λ),
C x i = yΝ C( I x i , I y i ) = yΝ I x i - I y i ,
D x d =exp( D(x,m) )=exp( ( ξ 1 - ξ 2 ) 2 + ( γ 1 - γ 2 ) 2 ),
C x r = yΝ C( I x r , I y r ) = yΝ I x r - I y r .
V x c = V( I x c , I x i ) = ( I x r I x i ) 2 + ( I x g I x i ) 2 + ( I x b I x i ) 2 ,
S=corr2( C i ,(1 D d ))corr2( C i , C r )corr2( C i ,(1 V c ))corr2( D d , V c ).
L={ 1ifS>T 0otherwise ,
W=L( C i + C r D d V c ).
ϕ 0 ( x,y )=4ω( 0.5L ),
ρ(W)=β (2(W0.5)) 2 ,
g =gρ.
T=ave(S)+2var(S),
l= δ( ϕ 0 ) dxdy
= H ( ϕ 0 ) dxdy,
H ( ϕ 0 )={ 1, ϕ 0 0 0, ϕ 0 >0 .
ς=/l .
u= 0.2/ς .
λ=0.5ς.
α=2(0.5W)
JSI( R 1 , R 2 )= | R 1 R 2 | | R 1 R 2 | .

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