Abstract

We address an image segmentation method to detect concealed objects captured by passive millimeter wave (MMW) imaging. Passive MMW imaging can create interpretable imagery on the objects concealed under clothing, which gives the great advantage to the security system. In this paper, we propose the multi-level expectation maximization (EM) method to separate the concealed objects from the other area in the image. We apply the EM method to obtain a Gaussian mixture model (GMM) of the acquired image. In the experiments, we evaluate the performance by the average probability of error. We will show that the consecutive EM processes separates the object area more accurately than the conventional EM method.

© 2010 OSA

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References

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  1. H.-M. Chen, S. Lee, R. M. Rao, M.-A. Slamani, and P. K. Varshney, “Imaging for concealed weapon detection: a tutorial overview of development in imaging sensors and processing,” IEEE Signal Process. Mag. 22(2), 52–61 (2005).
    [CrossRef]
  2. R. Appleby and R. N. Anderton, “Millimeter-wave and submillimeter-wave imaging for security and surveillance,” Proc. IEEE 95(8), 1683–1690 (2007).
    [CrossRef]
  3. T. W. Du Bosq, J. M. Lopez-Alonso, and G. D. Boreman, “Millimeter wave imaging system for land mine detection,” Appl. Opt. 45(22), 5686–5692 (2006).
    [CrossRef] [PubMed]
  4. L. Yujiri, M. Shoucri, and P. Moffa, “Passive millimeter-wave imaging,” IEEE Microw. Mag. 4(3), 39–50 (2003).
    [CrossRef]
  5. J. Son, V. P. Guschin, A. G. Denisov, S. Yeom, and D. Jung, “Comparisons of 3 dimensional temperature distributions of mm and IR images,” Proceedings of IEEE Conference on Microwaves, Radar and Remote Sensing Symposium, MRRS, Kiev, 132–135 (2008).
  6. F. Buersgens, G. Acuna, and R. Kersting, “Millimeter wave probing of the acoustic phase for concealed object detection,” Opt. Express 15(14), 8838–8843 (2007).
    [CrossRef] [PubMed]
  7. M. R. Fetterman, J. Grata, G. Jubic, W. L. Kiser, and A. Visnansky, “Simulation, acquisition and analysis of passive millimeter-wave images in remote sensing applications,” Opt. Express 16(25), 20503–20515 (2008).
    [CrossRef] [PubMed]
  8. K. B. Cooper, R. J. Dengler, N. Llombart, T. Bryllert, G. Chattopadhyay, I. Mehdi, and P. H. Siegel, “An approach for sub-second imaging of concealed objects using terahertz (THz) radar,” Int. J. Infrared Millim. Waves 30, 1297–1307 (2009).
  9. A. Denisov, V. Gorishnyak, S. Kuzmin, V. Miklashevich, V. Obolonskv, V. Radzikhovsky, B. Shevchuk, B. Yshenko, V. Uliz'ko, and J. Son, “Some experiments concerning resolution of 32 sensors passive 8 mm wave imaging system,” Proceedings of the 20th International Symposium on Space Terahertz Technology, Charlottesville, 227–229 (2009).
  10. M.-K. Jung, Y.-S. Chae, S.-K. Kim, M. Koji, and J.-K. Rhee, “Studies on the millimeter-wave passive imaging system,” J. Korean Inst. Electr. and Electro. Mater. Eng. 43, 182–188 (2006).
  11. R. C. Gonzalez, Digital Image Processing 2/E (Prentice-Hall Inc., 2003).
  12. T. Fabritius, S. Makita, M. Miura, R. Myllylä, and Y. Yasuno, “Automated segmentation of the macula by optical coherence tomography,” Opt. Express 17(18), 15659–15669 (2009).
    [CrossRef] [PubMed]
  13. T. Collier, P. Shen, B. de Pradier, K.-B. Sung, R. Richards-Kortum, M. Follen, and A. Malpica, “Near real time confocal microscopy of amelanotic tissue: dynamics of aceto-whitening enable nuclear segmentation,” Opt. Express 6(2), 40–48 (2000).
    [CrossRef] [PubMed]
  14. D.-S. Lee, S. Yeom, J. Son, and S.-H. Kim, “Image segmentation of concealed objects detected by a PMMW imaging system,” presented at the 34th International Conference on Infrared, Millimeter, and Terahertz Waves, Paradise Hotel, Busan, Korea, 21–25 (2009).
  15. X. Shen, C. R. Dietlein, E. Grossman, Z. Popovic, and F. G. Meyer, “Detection and segmentation of concealed objects in terahertz images,” IEEE Trans. Image Process. 17(12), 2465–2475 (2008).
    [CrossRef] [PubMed]
  16. C. D. Haworth, Y. Saint-Pern, D. Clark, E. Trucco, and Y. R. Petillot, “Detection and tracking of multiple metallic objects in millimeter-wave images,” Int. J. Comput. Vis. 71(2), 183–196 (2007).
    [CrossRef]
  17. A. Dempster, N. Laird, and D. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc., B 39, 1–38 (1977).
  18. S. Yeom, B. Javidi, P. Ferraro, D. Alfieri, S. Denicola, and A. Finizio, “Three-dimensional color object visualization and recognition using multi-wavelength computational holography,” Opt. Express 15(15), 9394–9402 (2007).
    [CrossRef] [PubMed]
  19. R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification (John Wiley & Sons, 2001).
  20. K. Fukunaga, Introduction to Statistical Pattern Recognition 2nd (Academic Press, Boston, 1990).
  21. W. A. Yasnoff, J. K. Mui, and J. W. Bacus, “Error measures for scene segmentation,” Pattern Recognit. 9(4), 217–231 (1977).
    [CrossRef]

2009 (2)

K. B. Cooper, R. J. Dengler, N. Llombart, T. Bryllert, G. Chattopadhyay, I. Mehdi, and P. H. Siegel, “An approach for sub-second imaging of concealed objects using terahertz (THz) radar,” Int. J. Infrared Millim. Waves 30, 1297–1307 (2009).

T. Fabritius, S. Makita, M. Miura, R. Myllylä, and Y. Yasuno, “Automated segmentation of the macula by optical coherence tomography,” Opt. Express 17(18), 15659–15669 (2009).
[CrossRef] [PubMed]

2008 (2)

X. Shen, C. R. Dietlein, E. Grossman, Z. Popovic, and F. G. Meyer, “Detection and segmentation of concealed objects in terahertz images,” IEEE Trans. Image Process. 17(12), 2465–2475 (2008).
[CrossRef] [PubMed]

M. R. Fetterman, J. Grata, G. Jubic, W. L. Kiser, and A. Visnansky, “Simulation, acquisition and analysis of passive millimeter-wave images in remote sensing applications,” Opt. Express 16(25), 20503–20515 (2008).
[CrossRef] [PubMed]

2007 (4)

C. D. Haworth, Y. Saint-Pern, D. Clark, E. Trucco, and Y. R. Petillot, “Detection and tracking of multiple metallic objects in millimeter-wave images,” Int. J. Comput. Vis. 71(2), 183–196 (2007).
[CrossRef]

S. Yeom, B. Javidi, P. Ferraro, D. Alfieri, S. Denicola, and A. Finizio, “Three-dimensional color object visualization and recognition using multi-wavelength computational holography,” Opt. Express 15(15), 9394–9402 (2007).
[CrossRef] [PubMed]

R. Appleby and R. N. Anderton, “Millimeter-wave and submillimeter-wave imaging for security and surveillance,” Proc. IEEE 95(8), 1683–1690 (2007).
[CrossRef]

F. Buersgens, G. Acuna, and R. Kersting, “Millimeter wave probing of the acoustic phase for concealed object detection,” Opt. Express 15(14), 8838–8843 (2007).
[CrossRef] [PubMed]

2006 (2)

T. W. Du Bosq, J. M. Lopez-Alonso, and G. D. Boreman, “Millimeter wave imaging system for land mine detection,” Appl. Opt. 45(22), 5686–5692 (2006).
[CrossRef] [PubMed]

M.-K. Jung, Y.-S. Chae, S.-K. Kim, M. Koji, and J.-K. Rhee, “Studies on the millimeter-wave passive imaging system,” J. Korean Inst. Electr. and Electro. Mater. Eng. 43, 182–188 (2006).

2005 (1)

H.-M. Chen, S. Lee, R. M. Rao, M.-A. Slamani, and P. K. Varshney, “Imaging for concealed weapon detection: a tutorial overview of development in imaging sensors and processing,” IEEE Signal Process. Mag. 22(2), 52–61 (2005).
[CrossRef]

2003 (1)

L. Yujiri, M. Shoucri, and P. Moffa, “Passive millimeter-wave imaging,” IEEE Microw. Mag. 4(3), 39–50 (2003).
[CrossRef]

2000 (1)

1977 (2)

W. A. Yasnoff, J. K. Mui, and J. W. Bacus, “Error measures for scene segmentation,” Pattern Recognit. 9(4), 217–231 (1977).
[CrossRef]

A. Dempster, N. Laird, and D. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc., B 39, 1–38 (1977).

Acuna, G.

Alfieri, D.

Anderton, R. N.

R. Appleby and R. N. Anderton, “Millimeter-wave and submillimeter-wave imaging for security and surveillance,” Proc. IEEE 95(8), 1683–1690 (2007).
[CrossRef]

Appleby, R.

R. Appleby and R. N. Anderton, “Millimeter-wave and submillimeter-wave imaging for security and surveillance,” Proc. IEEE 95(8), 1683–1690 (2007).
[CrossRef]

Bacus, J. W.

W. A. Yasnoff, J. K. Mui, and J. W. Bacus, “Error measures for scene segmentation,” Pattern Recognit. 9(4), 217–231 (1977).
[CrossRef]

Boreman, G. D.

Bryllert, T.

K. B. Cooper, R. J. Dengler, N. Llombart, T. Bryllert, G. Chattopadhyay, I. Mehdi, and P. H. Siegel, “An approach for sub-second imaging of concealed objects using terahertz (THz) radar,” Int. J. Infrared Millim. Waves 30, 1297–1307 (2009).

Buersgens, F.

Chae, Y.-S.

M.-K. Jung, Y.-S. Chae, S.-K. Kim, M. Koji, and J.-K. Rhee, “Studies on the millimeter-wave passive imaging system,” J. Korean Inst. Electr. and Electro. Mater. Eng. 43, 182–188 (2006).

Chattopadhyay, G.

K. B. Cooper, R. J. Dengler, N. Llombart, T. Bryllert, G. Chattopadhyay, I. Mehdi, and P. H. Siegel, “An approach for sub-second imaging of concealed objects using terahertz (THz) radar,” Int. J. Infrared Millim. Waves 30, 1297–1307 (2009).

Chen, H.-M.

H.-M. Chen, S. Lee, R. M. Rao, M.-A. Slamani, and P. K. Varshney, “Imaging for concealed weapon detection: a tutorial overview of development in imaging sensors and processing,” IEEE Signal Process. Mag. 22(2), 52–61 (2005).
[CrossRef]

Clark, D.

C. D. Haworth, Y. Saint-Pern, D. Clark, E. Trucco, and Y. R. Petillot, “Detection and tracking of multiple metallic objects in millimeter-wave images,” Int. J. Comput. Vis. 71(2), 183–196 (2007).
[CrossRef]

Collier, T.

Cooper, K. B.

K. B. Cooper, R. J. Dengler, N. Llombart, T. Bryllert, G. Chattopadhyay, I. Mehdi, and P. H. Siegel, “An approach for sub-second imaging of concealed objects using terahertz (THz) radar,” Int. J. Infrared Millim. Waves 30, 1297–1307 (2009).

de Pradier, B.

Dempster, A.

A. Dempster, N. Laird, and D. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc., B 39, 1–38 (1977).

Dengler, R. J.

K. B. Cooper, R. J. Dengler, N. Llombart, T. Bryllert, G. Chattopadhyay, I. Mehdi, and P. H. Siegel, “An approach for sub-second imaging of concealed objects using terahertz (THz) radar,” Int. J. Infrared Millim. Waves 30, 1297–1307 (2009).

Denicola, S.

Dietlein, C. R.

X. Shen, C. R. Dietlein, E. Grossman, Z. Popovic, and F. G. Meyer, “Detection and segmentation of concealed objects in terahertz images,” IEEE Trans. Image Process. 17(12), 2465–2475 (2008).
[CrossRef] [PubMed]

Du Bosq, T. W.

Fabritius, T.

Ferraro, P.

Fetterman, M. R.

Finizio, A.

Follen, M.

Grata, J.

Grossman, E.

X. Shen, C. R. Dietlein, E. Grossman, Z. Popovic, and F. G. Meyer, “Detection and segmentation of concealed objects in terahertz images,” IEEE Trans. Image Process. 17(12), 2465–2475 (2008).
[CrossRef] [PubMed]

Haworth, C. D.

C. D. Haworth, Y. Saint-Pern, D. Clark, E. Trucco, and Y. R. Petillot, “Detection and tracking of multiple metallic objects in millimeter-wave images,” Int. J. Comput. Vis. 71(2), 183–196 (2007).
[CrossRef]

Javidi, B.

Jubic, G.

Jung, M.-K.

M.-K. Jung, Y.-S. Chae, S.-K. Kim, M. Koji, and J.-K. Rhee, “Studies on the millimeter-wave passive imaging system,” J. Korean Inst. Electr. and Electro. Mater. Eng. 43, 182–188 (2006).

Kersting, R.

Kim, S.-K.

M.-K. Jung, Y.-S. Chae, S.-K. Kim, M. Koji, and J.-K. Rhee, “Studies on the millimeter-wave passive imaging system,” J. Korean Inst. Electr. and Electro. Mater. Eng. 43, 182–188 (2006).

Kiser, W. L.

Koji, M.

M.-K. Jung, Y.-S. Chae, S.-K. Kim, M. Koji, and J.-K. Rhee, “Studies on the millimeter-wave passive imaging system,” J. Korean Inst. Electr. and Electro. Mater. Eng. 43, 182–188 (2006).

Laird, N.

A. Dempster, N. Laird, and D. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc., B 39, 1–38 (1977).

Lee, S.

H.-M. Chen, S. Lee, R. M. Rao, M.-A. Slamani, and P. K. Varshney, “Imaging for concealed weapon detection: a tutorial overview of development in imaging sensors and processing,” IEEE Signal Process. Mag. 22(2), 52–61 (2005).
[CrossRef]

Llombart, N.

K. B. Cooper, R. J. Dengler, N. Llombart, T. Bryllert, G. Chattopadhyay, I. Mehdi, and P. H. Siegel, “An approach for sub-second imaging of concealed objects using terahertz (THz) radar,” Int. J. Infrared Millim. Waves 30, 1297–1307 (2009).

Lopez-Alonso, J. M.

Makita, S.

Malpica, A.

Mehdi, I.

K. B. Cooper, R. J. Dengler, N. Llombart, T. Bryllert, G. Chattopadhyay, I. Mehdi, and P. H. Siegel, “An approach for sub-second imaging of concealed objects using terahertz (THz) radar,” Int. J. Infrared Millim. Waves 30, 1297–1307 (2009).

Meyer, F. G.

X. Shen, C. R. Dietlein, E. Grossman, Z. Popovic, and F. G. Meyer, “Detection and segmentation of concealed objects in terahertz images,” IEEE Trans. Image Process. 17(12), 2465–2475 (2008).
[CrossRef] [PubMed]

Miura, M.

Moffa, P.

L. Yujiri, M. Shoucri, and P. Moffa, “Passive millimeter-wave imaging,” IEEE Microw. Mag. 4(3), 39–50 (2003).
[CrossRef]

Mui, J. K.

W. A. Yasnoff, J. K. Mui, and J. W. Bacus, “Error measures for scene segmentation,” Pattern Recognit. 9(4), 217–231 (1977).
[CrossRef]

Myllylä, R.

Petillot, Y. R.

C. D. Haworth, Y. Saint-Pern, D. Clark, E. Trucco, and Y. R. Petillot, “Detection and tracking of multiple metallic objects in millimeter-wave images,” Int. J. Comput. Vis. 71(2), 183–196 (2007).
[CrossRef]

Popovic, Z.

X. Shen, C. R. Dietlein, E. Grossman, Z. Popovic, and F. G. Meyer, “Detection and segmentation of concealed objects in terahertz images,” IEEE Trans. Image Process. 17(12), 2465–2475 (2008).
[CrossRef] [PubMed]

Rao, R. M.

H.-M. Chen, S. Lee, R. M. Rao, M.-A. Slamani, and P. K. Varshney, “Imaging for concealed weapon detection: a tutorial overview of development in imaging sensors and processing,” IEEE Signal Process. Mag. 22(2), 52–61 (2005).
[CrossRef]

Rhee, J.-K.

M.-K. Jung, Y.-S. Chae, S.-K. Kim, M. Koji, and J.-K. Rhee, “Studies on the millimeter-wave passive imaging system,” J. Korean Inst. Electr. and Electro. Mater. Eng. 43, 182–188 (2006).

Richards-Kortum, R.

Rubin, D.

A. Dempster, N. Laird, and D. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc., B 39, 1–38 (1977).

Saint-Pern, Y.

C. D. Haworth, Y. Saint-Pern, D. Clark, E. Trucco, and Y. R. Petillot, “Detection and tracking of multiple metallic objects in millimeter-wave images,” Int. J. Comput. Vis. 71(2), 183–196 (2007).
[CrossRef]

Shen, P.

Shen, X.

X. Shen, C. R. Dietlein, E. Grossman, Z. Popovic, and F. G. Meyer, “Detection and segmentation of concealed objects in terahertz images,” IEEE Trans. Image Process. 17(12), 2465–2475 (2008).
[CrossRef] [PubMed]

Shoucri, M.

L. Yujiri, M. Shoucri, and P. Moffa, “Passive millimeter-wave imaging,” IEEE Microw. Mag. 4(3), 39–50 (2003).
[CrossRef]

Siegel, P. H.

K. B. Cooper, R. J. Dengler, N. Llombart, T. Bryllert, G. Chattopadhyay, I. Mehdi, and P. H. Siegel, “An approach for sub-second imaging of concealed objects using terahertz (THz) radar,” Int. J. Infrared Millim. Waves 30, 1297–1307 (2009).

Slamani, M.-A.

H.-M. Chen, S. Lee, R. M. Rao, M.-A. Slamani, and P. K. Varshney, “Imaging for concealed weapon detection: a tutorial overview of development in imaging sensors and processing,” IEEE Signal Process. Mag. 22(2), 52–61 (2005).
[CrossRef]

Sung, K.-B.

Trucco, E.

C. D. Haworth, Y. Saint-Pern, D. Clark, E. Trucco, and Y. R. Petillot, “Detection and tracking of multiple metallic objects in millimeter-wave images,” Int. J. Comput. Vis. 71(2), 183–196 (2007).
[CrossRef]

Varshney, P. K.

H.-M. Chen, S. Lee, R. M. Rao, M.-A. Slamani, and P. K. Varshney, “Imaging for concealed weapon detection: a tutorial overview of development in imaging sensors and processing,” IEEE Signal Process. Mag. 22(2), 52–61 (2005).
[CrossRef]

Visnansky, A.

Yasnoff, W. A.

W. A. Yasnoff, J. K. Mui, and J. W. Bacus, “Error measures for scene segmentation,” Pattern Recognit. 9(4), 217–231 (1977).
[CrossRef]

Yasuno, Y.

Yeom, S.

Yujiri, L.

L. Yujiri, M. Shoucri, and P. Moffa, “Passive millimeter-wave imaging,” IEEE Microw. Mag. 4(3), 39–50 (2003).
[CrossRef]

Appl. Opt. (1)

IEEE Microw. Mag. (1)

L. Yujiri, M. Shoucri, and P. Moffa, “Passive millimeter-wave imaging,” IEEE Microw. Mag. 4(3), 39–50 (2003).
[CrossRef]

IEEE Signal Process. Mag. (1)

H.-M. Chen, S. Lee, R. M. Rao, M.-A. Slamani, and P. K. Varshney, “Imaging for concealed weapon detection: a tutorial overview of development in imaging sensors and processing,” IEEE Signal Process. Mag. 22(2), 52–61 (2005).
[CrossRef]

IEEE Trans. Image Process. (1)

X. Shen, C. R. Dietlein, E. Grossman, Z. Popovic, and F. G. Meyer, “Detection and segmentation of concealed objects in terahertz images,” IEEE Trans. Image Process. 17(12), 2465–2475 (2008).
[CrossRef] [PubMed]

Int. J. Comput. Vis. (1)

C. D. Haworth, Y. Saint-Pern, D. Clark, E. Trucco, and Y. R. Petillot, “Detection and tracking of multiple metallic objects in millimeter-wave images,” Int. J. Comput. Vis. 71(2), 183–196 (2007).
[CrossRef]

Int. J. Infrared Millim. Waves (1)

K. B. Cooper, R. J. Dengler, N. Llombart, T. Bryllert, G. Chattopadhyay, I. Mehdi, and P. H. Siegel, “An approach for sub-second imaging of concealed objects using terahertz (THz) radar,” Int. J. Infrared Millim. Waves 30, 1297–1307 (2009).

J. Korean Inst. Electr. and Electro. Mater. Eng. (1)

M.-K. Jung, Y.-S. Chae, S.-K. Kim, M. Koji, and J.-K. Rhee, “Studies on the millimeter-wave passive imaging system,” J. Korean Inst. Electr. and Electro. Mater. Eng. 43, 182–188 (2006).

J. R. Stat. Soc., B (1)

A. Dempster, N. Laird, and D. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc., B 39, 1–38 (1977).

Opt. Express (5)

Pattern Recognit. (1)

W. A. Yasnoff, J. K. Mui, and J. W. Bacus, “Error measures for scene segmentation,” Pattern Recognit. 9(4), 217–231 (1977).
[CrossRef]

Proc. IEEE (1)

R. Appleby and R. N. Anderton, “Millimeter-wave and submillimeter-wave imaging for security and surveillance,” Proc. IEEE 95(8), 1683–1690 (2007).
[CrossRef]

Other (6)

R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification (John Wiley & Sons, 2001).

K. Fukunaga, Introduction to Statistical Pattern Recognition 2nd (Academic Press, Boston, 1990).

R. C. Gonzalez, Digital Image Processing 2/E (Prentice-Hall Inc., 2003).

D.-S. Lee, S. Yeom, J. Son, and S.-H. Kim, “Image segmentation of concealed objects detected by a PMMW imaging system,” presented at the 34th International Conference on Infrared, Millimeter, and Terahertz Waves, Paradise Hotel, Busan, Korea, 21–25 (2009).

A. Denisov, V. Gorishnyak, S. Kuzmin, V. Miklashevich, V. Obolonskv, V. Radzikhovsky, B. Shevchuk, B. Yshenko, V. Uliz'ko, and J. Son, “Some experiments concerning resolution of 32 sensors passive 8 mm wave imaging system,” Proceedings of the 20th International Symposium on Space Terahertz Technology, Charlottesville, 227–229 (2009).

J. Son, V. P. Guschin, A. G. Denisov, S. Yeom, and D. Jung, “Comparisons of 3 dimensional temperature distributions of mm and IR images,” Proceedings of IEEE Conference on Microwaves, Radar and Remote Sensing Symposium, MRRS, Kiev, 132–135 (2008).

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Figures (7)

Fig. 1
Fig. 1

Passive millimeter wave imaging system.

Fig. 2
Fig. 2

Image segmentation procedure for concealed object detection.

Fig. 3
Fig. 3

EM algorithm.

Fig. 4
Fig. 4

Visual images (a) with concealment, (b) without concealment, PMMW image of (c) 8 mm-vertical polarization with the GSF, (d) 8 mm-horizontal polarization with the GSF.

Fig. 5
Fig. 5

GMM fitting results of, (a) the 1st EM (b) the 2nd EM, segmented images after, (c) the 1st EM, (d) the 2nd EM.

Fig. 6
Fig. 6

Experimental results, axe, (a) without concealment, (b) PMMW image, segmented images after, (c) 1st EM, (d) 2nd EM, gun, (e) without concealment, (f) PMMW image, segmented images after, (g) 1st EM (h) 2nd EM, skin-aid, (i) without concealment, (j) PMMW image, segmented images after, (k) 1st EM, (l) 2nd EM, water-pack, (m) without concealment, (n) PMMW image, segmented images after, (o) 1st EM, (p) 2nd EM.

Fig. 7
Fig. 7

Performance comparison between the conventional EM and the multi-level EM.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

p(xt)=k=1NkN(xt|μk,Σk)P(Gk),t=1,...,Nt,
N(xt;μk,Σk)=12πΣk1/2e12(xtμk)tΣk1(xtμk),
P(Gk|xt)=N(xt;μk,Σk)P(Gk)k=1NkN(xt;μk,Σk)P(Gk),
μk=t=1NtP(Gk|xt)xtt=1NtP(Gk|xt),
Σk=t=1NtP(Gk|xt)(xtμk)(xtμk)tt=1NtP(Gk|xt),
P(Gk)=1Ntt=1NtP(Gk|xt).
P(G1|xt)G2G1P(G2|xt),t=1,...,Nt.
Pe=P(D1|H0)P(H0)+P(D0|H1)P(H1),
P(D1|H0)=|FSFO||BO|,
P(H0)=|BO||BOFO|,
P(D0|H1)=|FOFS||FO|,
P(H1)=|FO||BOFO|,
Pe=|FSFO|+|FOFS||BOFO|.

Metrics