Abstract

Two methods based on factor graphs for reconstructing the three-dimensional (3D) shape of an object from a series of two-dimensional images are presented. First, a factor graph model is developed for image segmentation to obtain silhouettes from raw images; the shape-from-silhouette technique is then applied to yield the 3D reconstruction of the object. The second method presented is a direct 3D reconstruction of the object using a factor graph model for the voxels of the reconstruction. While both methods should be applicable to a variety of input data types, they will be developed and demonstrated for a particular application involving the LIDAR imaging of a submerged target. Results from simulations and from real LIDAR data are shown that detail the performance of the methods.

© 2004 Optical Society of America

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  1. I. Quidu, J. Ph. Malkasse, G. Burel, P. Vilbé, “Mine classification based on raw sonar data: an approach combining Fourier descriptors, statistical models, and genetic algorithms,” in Proceedings of Oceans 2000 MTS/IEEE Conf. and Exhibition (IEEE Press, Piscataway, N.J., 2000), Vol. 1, pp. 285–290.
  2. Q. Zheng, S. Z. Der, H. I. Mahmoud, “Model-based target recognition in pulsed ladar imagery,” IEEE Trans. Image Process. 10, 565–572 (2001).
    [CrossRef]
  3. P. J. Shargo, N. Çadalli, A. C. Singer, D. C. Munson, “A tomographic framework for LIDAR imaging,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE Press, Piscataway, N.J., 2001), Vol. 3, pp. 1893–1896.
  4. W. N. Martin, J. K. Aggarwal, “Volumetric descriptions of objects from multiple views,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-5, 150–158 (1983).
    [CrossRef]
  5. A. Laurentini, “How far 3D shapes can be understood from 2D silhouettes,” IEEE Trans. Pattern Anal. Mach. Intell. 17, 188–195 (1995).
    [CrossRef]
  6. A. Laurentini, “The visual hull concept for silhouette-based image understanding,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 150–162 (1994).
    [CrossRef]
  7. Lavakusha, A. K. Pujari, P. G. Reddy, “Linear octrees by volume intersection,” Comput. Vision Graph. Image Process. 45, 371–379 (1989).
    [CrossRef]
  8. M. Potemsil, “Generating octree models of 3D objects from their silhouettes in a sequence of images,” Comput. Vis. Graph. Image Process. 40, 1–29 (1987).
    [CrossRef]
  9. N. Ahuja, J. Veenstra, “Efficient octree generation from silhouettes,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Press, Piscataway, N.J., 1986), pp. 537–542.
  10. M. Jones, J. P. Oakley, “Efficient representation of object shape for silhouette intersection,” IEE Proc. Vision Image Signal Process. 142, 359–365 (1995).
    [CrossRef]
  11. J. C. Carr, W. R. Fright, A. H. Gee, R. W. Prager, K. J. Dalton, “3D shape reconstruction using volume intersection techniques,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE Press, Piscataway, N.J., 1998), pp. 1095–1100.
  12. Lavakusha, A. K. Pujari, P. G. Reddy, “Volume intersection algorithm with changing directions of view,” in Proceedings of the International Workshop on Industrial Applications of Machine Intelligence and Vision (IEEE Press, Piscataway, N.J., 1989), pp. 309–314.
  13. M. Kass, A. Witkin, D. Terzopoulos, “Snakes: active contour models,” Int. J. Comput. Vision 1, 321–331 (1988).
    [CrossRef]
  14. C. Xu, J. L. Prince, “Snakes, shapes, and gradient vector flow,” IEEE Trans. Image Process. 7, 959–969 (1998).
  15. A. K. Jain, Y. Zhong, S. Lakshmanan, “Object matching using deformable templates,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 267–278 (1996).
    [CrossRef]
  16. G. Poggi, A. R. P. Ragozini, “Image segmentation by tree-structured Markov random fields,” IEEE Signal Process. Lett. 6, 155–157 (1999).
    [CrossRef]
  17. R. A. Weisenseel, W. C. Karl, D. A. Casañon, R. C. Brower, “MRF-based algorithms for segmentation of SAR images,” in Proceedings of the International Conference on Image Processing (IEEE Computer Society Press, Los Alamitos, Calif., 1998), Vol. 3, pp. 770–774.
  18. M. Mignotte, C. Collet, P. Perez, P. Bouthemy, “Unsupervised Markovian segmentation of sonar images,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE Press, Piscataway, N.J., 1997), Vol. 4, pp. 2781–2784.
  19. D. Snow, P. Viola, R. Zabih, “Exact voxel occupancy with graph cuts,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 2000), Vol. 1, pp. 345–352.
  20. R. E. Walker, J. W. McLean, “LIDAR equations for turbid media with pulse stretching,” Appl. Opt. 38, 2384–2397 (1999).
    [CrossRef]
  21. J. W. McLean, J. D. Freeman, R. E. Walker, “Beam spread function with time dispersion,” Appl. Opt. 37, 4701–4711 (1998).
    [CrossRef]
  22. N. Çadalli, D. C. Munson, A. C. Singer, “Bistatic receiver model for airborne LIDAR returns incident on an imaging array from underwater objects,” Appl. Opt. 41, 3638–3649 (2002).
    [CrossRef] [PubMed]
  23. R. E. Walker, Marine Light Field Statistics (Wiley, New York, 1994).
  24. F. R. Kschischang, B. J. Frey, H.-A. Loeliger, “Factor graphs and the sum–product algorithm,” IEEE Trans. Inf. Theory 47, 498–519 (2001).
    [CrossRef]
  25. F. R. Kschischang, B. J. Frey, “Iterative decoding of compound codes by probability propagation in graphical models,” IEEE J. Sel. Areas Commun. 16, 219–230 (1998).
    [CrossRef]
  26. B. J. Frey, R. Koetter, N. Petrovic, “Codes on images and iterative phase unwrapping,” in Proceedings of the IEEE Information Theory Workshop (IEEE Press, Piscataway, N.J., 2001), pp. 9–11.
  27. S. M. Aji, G. B. Horn, R. J. McEliece, “Iterative decoding on graphs with a single cycle,” in Proceedings of the IEEE International Symposium on Information Theory (IEEE Press, Piscataway, N.J.), p. 276.
  28. G. Winkler, Image Analysis, Random Fields and Markov Chain Monte Carlo Methods: A Mathematical Introduction (Springer, New York, 2003).
  29. H. Elliot, H. Derin, R. Cristi, D. Geman, “Application of the Gibbs distribution to image segmentation,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE Press, Piscataway, N.J., 1984), Vol. 9, pp. 678–681.
  30. A. Minagawa, K. Uda, N. Tagawa, “Region extraction based on belief propagation for Gaussian model,” in Proceedings of the International Conference on Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 2002), Vol. 2, pp. 507–510.
  31. J. S. Lim, Two-Dimensional Signal and Image Processing (Prentice Hall, Englewood Cliffs, N.J., 1990).
  32. M. Wainwright, T. Jaakola, A. Willsky, “Tree-based reparameterization framework for approximate estimation of stochastic processes on graphs with cycles,” (Laboratory for Information and Decision Systems, MIT, Cambridge, Mass., 2001).

2002 (1)

2001 (2)

F. R. Kschischang, B. J. Frey, H.-A. Loeliger, “Factor graphs and the sum–product algorithm,” IEEE Trans. Inf. Theory 47, 498–519 (2001).
[CrossRef]

Q. Zheng, S. Z. Der, H. I. Mahmoud, “Model-based target recognition in pulsed ladar imagery,” IEEE Trans. Image Process. 10, 565–572 (2001).
[CrossRef]

1999 (2)

G. Poggi, A. R. P. Ragozini, “Image segmentation by tree-structured Markov random fields,” IEEE Signal Process. Lett. 6, 155–157 (1999).
[CrossRef]

R. E. Walker, J. W. McLean, “LIDAR equations for turbid media with pulse stretching,” Appl. Opt. 38, 2384–2397 (1999).
[CrossRef]

1998 (3)

F. R. Kschischang, B. J. Frey, “Iterative decoding of compound codes by probability propagation in graphical models,” IEEE J. Sel. Areas Commun. 16, 219–230 (1998).
[CrossRef]

J. W. McLean, J. D. Freeman, R. E. Walker, “Beam spread function with time dispersion,” Appl. Opt. 37, 4701–4711 (1998).
[CrossRef]

C. Xu, J. L. Prince, “Snakes, shapes, and gradient vector flow,” IEEE Trans. Image Process. 7, 959–969 (1998).

1996 (1)

A. K. Jain, Y. Zhong, S. Lakshmanan, “Object matching using deformable templates,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 267–278 (1996).
[CrossRef]

1995 (2)

M. Jones, J. P. Oakley, “Efficient representation of object shape for silhouette intersection,” IEE Proc. Vision Image Signal Process. 142, 359–365 (1995).
[CrossRef]

A. Laurentini, “How far 3D shapes can be understood from 2D silhouettes,” IEEE Trans. Pattern Anal. Mach. Intell. 17, 188–195 (1995).
[CrossRef]

1994 (1)

A. Laurentini, “The visual hull concept for silhouette-based image understanding,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 150–162 (1994).
[CrossRef]

1989 (1)

Lavakusha, A. K. Pujari, P. G. Reddy, “Linear octrees by volume intersection,” Comput. Vision Graph. Image Process. 45, 371–379 (1989).
[CrossRef]

1988 (1)

M. Kass, A. Witkin, D. Terzopoulos, “Snakes: active contour models,” Int. J. Comput. Vision 1, 321–331 (1988).
[CrossRef]

1987 (1)

M. Potemsil, “Generating octree models of 3D objects from their silhouettes in a sequence of images,” Comput. Vis. Graph. Image Process. 40, 1–29 (1987).
[CrossRef]

1983 (1)

W. N. Martin, J. K. Aggarwal, “Volumetric descriptions of objects from multiple views,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-5, 150–158 (1983).
[CrossRef]

Aggarwal, J. K.

W. N. Martin, J. K. Aggarwal, “Volumetric descriptions of objects from multiple views,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-5, 150–158 (1983).
[CrossRef]

Ahuja, N.

N. Ahuja, J. Veenstra, “Efficient octree generation from silhouettes,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Press, Piscataway, N.J., 1986), pp. 537–542.

Aji, S. M.

S. M. Aji, G. B. Horn, R. J. McEliece, “Iterative decoding on graphs with a single cycle,” in Proceedings of the IEEE International Symposium on Information Theory (IEEE Press, Piscataway, N.J.), p. 276.

Bouthemy, P.

M. Mignotte, C. Collet, P. Perez, P. Bouthemy, “Unsupervised Markovian segmentation of sonar images,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE Press, Piscataway, N.J., 1997), Vol. 4, pp. 2781–2784.

Brower, R. C.

R. A. Weisenseel, W. C. Karl, D. A. Casañon, R. C. Brower, “MRF-based algorithms for segmentation of SAR images,” in Proceedings of the International Conference on Image Processing (IEEE Computer Society Press, Los Alamitos, Calif., 1998), Vol. 3, pp. 770–774.

Burel, G.

I. Quidu, J. Ph. Malkasse, G. Burel, P. Vilbé, “Mine classification based on raw sonar data: an approach combining Fourier descriptors, statistical models, and genetic algorithms,” in Proceedings of Oceans 2000 MTS/IEEE Conf. and Exhibition (IEEE Press, Piscataway, N.J., 2000), Vol. 1, pp. 285–290.

Çadalli, N.

N. Çadalli, D. C. Munson, A. C. Singer, “Bistatic receiver model for airborne LIDAR returns incident on an imaging array from underwater objects,” Appl. Opt. 41, 3638–3649 (2002).
[CrossRef] [PubMed]

P. J. Shargo, N. Çadalli, A. C. Singer, D. C. Munson, “A tomographic framework for LIDAR imaging,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE Press, Piscataway, N.J., 2001), Vol. 3, pp. 1893–1896.

Carr, J. C.

J. C. Carr, W. R. Fright, A. H. Gee, R. W. Prager, K. J. Dalton, “3D shape reconstruction using volume intersection techniques,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE Press, Piscataway, N.J., 1998), pp. 1095–1100.

Casañon, D. A.

R. A. Weisenseel, W. C. Karl, D. A. Casañon, R. C. Brower, “MRF-based algorithms for segmentation of SAR images,” in Proceedings of the International Conference on Image Processing (IEEE Computer Society Press, Los Alamitos, Calif., 1998), Vol. 3, pp. 770–774.

Collet, C.

M. Mignotte, C. Collet, P. Perez, P. Bouthemy, “Unsupervised Markovian segmentation of sonar images,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE Press, Piscataway, N.J., 1997), Vol. 4, pp. 2781–2784.

Cristi, R.

H. Elliot, H. Derin, R. Cristi, D. Geman, “Application of the Gibbs distribution to image segmentation,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE Press, Piscataway, N.J., 1984), Vol. 9, pp. 678–681.

Dalton, K. J.

J. C. Carr, W. R. Fright, A. H. Gee, R. W. Prager, K. J. Dalton, “3D shape reconstruction using volume intersection techniques,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE Press, Piscataway, N.J., 1998), pp. 1095–1100.

Der, S. Z.

Q. Zheng, S. Z. Der, H. I. Mahmoud, “Model-based target recognition in pulsed ladar imagery,” IEEE Trans. Image Process. 10, 565–572 (2001).
[CrossRef]

Derin, H.

H. Elliot, H. Derin, R. Cristi, D. Geman, “Application of the Gibbs distribution to image segmentation,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE Press, Piscataway, N.J., 1984), Vol. 9, pp. 678–681.

Elliot, H.

H. Elliot, H. Derin, R. Cristi, D. Geman, “Application of the Gibbs distribution to image segmentation,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE Press, Piscataway, N.J., 1984), Vol. 9, pp. 678–681.

Freeman, J. D.

Frey, B. J.

F. R. Kschischang, B. J. Frey, H.-A. Loeliger, “Factor graphs and the sum–product algorithm,” IEEE Trans. Inf. Theory 47, 498–519 (2001).
[CrossRef]

F. R. Kschischang, B. J. Frey, “Iterative decoding of compound codes by probability propagation in graphical models,” IEEE J. Sel. Areas Commun. 16, 219–230 (1998).
[CrossRef]

B. J. Frey, R. Koetter, N. Petrovic, “Codes on images and iterative phase unwrapping,” in Proceedings of the IEEE Information Theory Workshop (IEEE Press, Piscataway, N.J., 2001), pp. 9–11.

Fright, W. R.

J. C. Carr, W. R. Fright, A. H. Gee, R. W. Prager, K. J. Dalton, “3D shape reconstruction using volume intersection techniques,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE Press, Piscataway, N.J., 1998), pp. 1095–1100.

Gee, A. H.

J. C. Carr, W. R. Fright, A. H. Gee, R. W. Prager, K. J. Dalton, “3D shape reconstruction using volume intersection techniques,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE Press, Piscataway, N.J., 1998), pp. 1095–1100.

Geman, D.

H. Elliot, H. Derin, R. Cristi, D. Geman, “Application of the Gibbs distribution to image segmentation,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE Press, Piscataway, N.J., 1984), Vol. 9, pp. 678–681.

Horn, G. B.

S. M. Aji, G. B. Horn, R. J. McEliece, “Iterative decoding on graphs with a single cycle,” in Proceedings of the IEEE International Symposium on Information Theory (IEEE Press, Piscataway, N.J.), p. 276.

Jaakola, T.

M. Wainwright, T. Jaakola, A. Willsky, “Tree-based reparameterization framework for approximate estimation of stochastic processes on graphs with cycles,” (Laboratory for Information and Decision Systems, MIT, Cambridge, Mass., 2001).

Jain, A. K.

A. K. Jain, Y. Zhong, S. Lakshmanan, “Object matching using deformable templates,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 267–278 (1996).
[CrossRef]

Jones, M.

M. Jones, J. P. Oakley, “Efficient representation of object shape for silhouette intersection,” IEE Proc. Vision Image Signal Process. 142, 359–365 (1995).
[CrossRef]

Karl, W. C.

R. A. Weisenseel, W. C. Karl, D. A. Casañon, R. C. Brower, “MRF-based algorithms for segmentation of SAR images,” in Proceedings of the International Conference on Image Processing (IEEE Computer Society Press, Los Alamitos, Calif., 1998), Vol. 3, pp. 770–774.

Kass, M.

M. Kass, A. Witkin, D. Terzopoulos, “Snakes: active contour models,” Int. J. Comput. Vision 1, 321–331 (1988).
[CrossRef]

Koetter, R.

B. J. Frey, R. Koetter, N. Petrovic, “Codes on images and iterative phase unwrapping,” in Proceedings of the IEEE Information Theory Workshop (IEEE Press, Piscataway, N.J., 2001), pp. 9–11.

Kschischang, F. R.

F. R. Kschischang, B. J. Frey, H.-A. Loeliger, “Factor graphs and the sum–product algorithm,” IEEE Trans. Inf. Theory 47, 498–519 (2001).
[CrossRef]

F. R. Kschischang, B. J. Frey, “Iterative decoding of compound codes by probability propagation in graphical models,” IEEE J. Sel. Areas Commun. 16, 219–230 (1998).
[CrossRef]

Lakshmanan, S.

A. K. Jain, Y. Zhong, S. Lakshmanan, “Object matching using deformable templates,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 267–278 (1996).
[CrossRef]

Laurentini, A.

A. Laurentini, “How far 3D shapes can be understood from 2D silhouettes,” IEEE Trans. Pattern Anal. Mach. Intell. 17, 188–195 (1995).
[CrossRef]

A. Laurentini, “The visual hull concept for silhouette-based image understanding,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 150–162 (1994).
[CrossRef]

Lavakusha,

Lavakusha, A. K. Pujari, P. G. Reddy, “Linear octrees by volume intersection,” Comput. Vision Graph. Image Process. 45, 371–379 (1989).
[CrossRef]

Lavakusha, A. K. Pujari, P. G. Reddy, “Volume intersection algorithm with changing directions of view,” in Proceedings of the International Workshop on Industrial Applications of Machine Intelligence and Vision (IEEE Press, Piscataway, N.J., 1989), pp. 309–314.

Lim, J. S.

J. S. Lim, Two-Dimensional Signal and Image Processing (Prentice Hall, Englewood Cliffs, N.J., 1990).

Loeliger, H.-A.

F. R. Kschischang, B. J. Frey, H.-A. Loeliger, “Factor graphs and the sum–product algorithm,” IEEE Trans. Inf. Theory 47, 498–519 (2001).
[CrossRef]

Mahmoud, H. I.

Q. Zheng, S. Z. Der, H. I. Mahmoud, “Model-based target recognition in pulsed ladar imagery,” IEEE Trans. Image Process. 10, 565–572 (2001).
[CrossRef]

Malkasse, J. Ph.

I. Quidu, J. Ph. Malkasse, G. Burel, P. Vilbé, “Mine classification based on raw sonar data: an approach combining Fourier descriptors, statistical models, and genetic algorithms,” in Proceedings of Oceans 2000 MTS/IEEE Conf. and Exhibition (IEEE Press, Piscataway, N.J., 2000), Vol. 1, pp. 285–290.

Martin, W. N.

W. N. Martin, J. K. Aggarwal, “Volumetric descriptions of objects from multiple views,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-5, 150–158 (1983).
[CrossRef]

McEliece, R. J.

S. M. Aji, G. B. Horn, R. J. McEliece, “Iterative decoding on graphs with a single cycle,” in Proceedings of the IEEE International Symposium on Information Theory (IEEE Press, Piscataway, N.J.), p. 276.

McLean, J. W.

Mignotte, M.

M. Mignotte, C. Collet, P. Perez, P. Bouthemy, “Unsupervised Markovian segmentation of sonar images,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE Press, Piscataway, N.J., 1997), Vol. 4, pp. 2781–2784.

Minagawa, A.

A. Minagawa, K. Uda, N. Tagawa, “Region extraction based on belief propagation for Gaussian model,” in Proceedings of the International Conference on Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 2002), Vol. 2, pp. 507–510.

Munson, D. C.

N. Çadalli, D. C. Munson, A. C. Singer, “Bistatic receiver model for airborne LIDAR returns incident on an imaging array from underwater objects,” Appl. Opt. 41, 3638–3649 (2002).
[CrossRef] [PubMed]

P. J. Shargo, N. Çadalli, A. C. Singer, D. C. Munson, “A tomographic framework for LIDAR imaging,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE Press, Piscataway, N.J., 2001), Vol. 3, pp. 1893–1896.

Oakley, J. P.

M. Jones, J. P. Oakley, “Efficient representation of object shape for silhouette intersection,” IEE Proc. Vision Image Signal Process. 142, 359–365 (1995).
[CrossRef]

Perez, P.

M. Mignotte, C. Collet, P. Perez, P. Bouthemy, “Unsupervised Markovian segmentation of sonar images,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE Press, Piscataway, N.J., 1997), Vol. 4, pp. 2781–2784.

Petrovic, N.

B. J. Frey, R. Koetter, N. Petrovic, “Codes on images and iterative phase unwrapping,” in Proceedings of the IEEE Information Theory Workshop (IEEE Press, Piscataway, N.J., 2001), pp. 9–11.

Poggi, G.

G. Poggi, A. R. P. Ragozini, “Image segmentation by tree-structured Markov random fields,” IEEE Signal Process. Lett. 6, 155–157 (1999).
[CrossRef]

Potemsil, M.

M. Potemsil, “Generating octree models of 3D objects from their silhouettes in a sequence of images,” Comput. Vis. Graph. Image Process. 40, 1–29 (1987).
[CrossRef]

Prager, R. W.

J. C. Carr, W. R. Fright, A. H. Gee, R. W. Prager, K. J. Dalton, “3D shape reconstruction using volume intersection techniques,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE Press, Piscataway, N.J., 1998), pp. 1095–1100.

Prince, J. L.

C. Xu, J. L. Prince, “Snakes, shapes, and gradient vector flow,” IEEE Trans. Image Process. 7, 959–969 (1998).

Pujari, A. K.

Lavakusha, A. K. Pujari, P. G. Reddy, “Linear octrees by volume intersection,” Comput. Vision Graph. Image Process. 45, 371–379 (1989).
[CrossRef]

Lavakusha, A. K. Pujari, P. G. Reddy, “Volume intersection algorithm with changing directions of view,” in Proceedings of the International Workshop on Industrial Applications of Machine Intelligence and Vision (IEEE Press, Piscataway, N.J., 1989), pp. 309–314.

Quidu, I.

I. Quidu, J. Ph. Malkasse, G. Burel, P. Vilbé, “Mine classification based on raw sonar data: an approach combining Fourier descriptors, statistical models, and genetic algorithms,” in Proceedings of Oceans 2000 MTS/IEEE Conf. and Exhibition (IEEE Press, Piscataway, N.J., 2000), Vol. 1, pp. 285–290.

Ragozini, A. R. P.

G. Poggi, A. R. P. Ragozini, “Image segmentation by tree-structured Markov random fields,” IEEE Signal Process. Lett. 6, 155–157 (1999).
[CrossRef]

Reddy, P. G.

Lavakusha, A. K. Pujari, P. G. Reddy, “Linear octrees by volume intersection,” Comput. Vision Graph. Image Process. 45, 371–379 (1989).
[CrossRef]

Lavakusha, A. K. Pujari, P. G. Reddy, “Volume intersection algorithm with changing directions of view,” in Proceedings of the International Workshop on Industrial Applications of Machine Intelligence and Vision (IEEE Press, Piscataway, N.J., 1989), pp. 309–314.

Shargo, P. J.

P. J. Shargo, N. Çadalli, A. C. Singer, D. C. Munson, “A tomographic framework for LIDAR imaging,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE Press, Piscataway, N.J., 2001), Vol. 3, pp. 1893–1896.

Singer, A. C.

N. Çadalli, D. C. Munson, A. C. Singer, “Bistatic receiver model for airborne LIDAR returns incident on an imaging array from underwater objects,” Appl. Opt. 41, 3638–3649 (2002).
[CrossRef] [PubMed]

P. J. Shargo, N. Çadalli, A. C. Singer, D. C. Munson, “A tomographic framework for LIDAR imaging,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE Press, Piscataway, N.J., 2001), Vol. 3, pp. 1893–1896.

Snow, D.

D. Snow, P. Viola, R. Zabih, “Exact voxel occupancy with graph cuts,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 2000), Vol. 1, pp. 345–352.

Tagawa, N.

A. Minagawa, K. Uda, N. Tagawa, “Region extraction based on belief propagation for Gaussian model,” in Proceedings of the International Conference on Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 2002), Vol. 2, pp. 507–510.

Terzopoulos, D.

M. Kass, A. Witkin, D. Terzopoulos, “Snakes: active contour models,” Int. J. Comput. Vision 1, 321–331 (1988).
[CrossRef]

Uda, K.

A. Minagawa, K. Uda, N. Tagawa, “Region extraction based on belief propagation for Gaussian model,” in Proceedings of the International Conference on Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 2002), Vol. 2, pp. 507–510.

Veenstra, J.

N. Ahuja, J. Veenstra, “Efficient octree generation from silhouettes,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Press, Piscataway, N.J., 1986), pp. 537–542.

Vilbé, P.

I. Quidu, J. Ph. Malkasse, G. Burel, P. Vilbé, “Mine classification based on raw sonar data: an approach combining Fourier descriptors, statistical models, and genetic algorithms,” in Proceedings of Oceans 2000 MTS/IEEE Conf. and Exhibition (IEEE Press, Piscataway, N.J., 2000), Vol. 1, pp. 285–290.

Viola, P.

D. Snow, P. Viola, R. Zabih, “Exact voxel occupancy with graph cuts,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 2000), Vol. 1, pp. 345–352.

Wainwright, M.

M. Wainwright, T. Jaakola, A. Willsky, “Tree-based reparameterization framework for approximate estimation of stochastic processes on graphs with cycles,” (Laboratory for Information and Decision Systems, MIT, Cambridge, Mass., 2001).

Walker, R. E.

Weisenseel, R. A.

R. A. Weisenseel, W. C. Karl, D. A. Casañon, R. C. Brower, “MRF-based algorithms for segmentation of SAR images,” in Proceedings of the International Conference on Image Processing (IEEE Computer Society Press, Los Alamitos, Calif., 1998), Vol. 3, pp. 770–774.

Willsky, A.

M. Wainwright, T. Jaakola, A. Willsky, “Tree-based reparameterization framework for approximate estimation of stochastic processes on graphs with cycles,” (Laboratory for Information and Decision Systems, MIT, Cambridge, Mass., 2001).

Winkler, G.

G. Winkler, Image Analysis, Random Fields and Markov Chain Monte Carlo Methods: A Mathematical Introduction (Springer, New York, 2003).

Witkin, A.

M. Kass, A. Witkin, D. Terzopoulos, “Snakes: active contour models,” Int. J. Comput. Vision 1, 321–331 (1988).
[CrossRef]

Xu, C.

C. Xu, J. L. Prince, “Snakes, shapes, and gradient vector flow,” IEEE Trans. Image Process. 7, 959–969 (1998).

Zabih, R.

D. Snow, P. Viola, R. Zabih, “Exact voxel occupancy with graph cuts,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 2000), Vol. 1, pp. 345–352.

Zheng, Q.

Q. Zheng, S. Z. Der, H. I. Mahmoud, “Model-based target recognition in pulsed ladar imagery,” IEEE Trans. Image Process. 10, 565–572 (2001).
[CrossRef]

Zhong, Y.

A. K. Jain, Y. Zhong, S. Lakshmanan, “Object matching using deformable templates,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 267–278 (1996).
[CrossRef]

Appl. Opt. (3)

Comput. Vis. Graph. Image Process. (1)

M. Potemsil, “Generating octree models of 3D objects from their silhouettes in a sequence of images,” Comput. Vis. Graph. Image Process. 40, 1–29 (1987).
[CrossRef]

Comput. Vision Graph. Image Process. (1)

Lavakusha, A. K. Pujari, P. G. Reddy, “Linear octrees by volume intersection,” Comput. Vision Graph. Image Process. 45, 371–379 (1989).
[CrossRef]

IEE Proc. Vision Image Signal Process. (1)

M. Jones, J. P. Oakley, “Efficient representation of object shape for silhouette intersection,” IEE Proc. Vision Image Signal Process. 142, 359–365 (1995).
[CrossRef]

IEEE J. Sel. Areas Commun. (1)

F. R. Kschischang, B. J. Frey, “Iterative decoding of compound codes by probability propagation in graphical models,” IEEE J. Sel. Areas Commun. 16, 219–230 (1998).
[CrossRef]

IEEE Signal Process. Lett. (1)

G. Poggi, A. R. P. Ragozini, “Image segmentation by tree-structured Markov random fields,” IEEE Signal Process. Lett. 6, 155–157 (1999).
[CrossRef]

IEEE Trans. Image Process. (2)

C. Xu, J. L. Prince, “Snakes, shapes, and gradient vector flow,” IEEE Trans. Image Process. 7, 959–969 (1998).

Q. Zheng, S. Z. Der, H. I. Mahmoud, “Model-based target recognition in pulsed ladar imagery,” IEEE Trans. Image Process. 10, 565–572 (2001).
[CrossRef]

IEEE Trans. Inf. Theory (1)

F. R. Kschischang, B. J. Frey, H.-A. Loeliger, “Factor graphs and the sum–product algorithm,” IEEE Trans. Inf. Theory 47, 498–519 (2001).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (4)

W. N. Martin, J. K. Aggarwal, “Volumetric descriptions of objects from multiple views,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-5, 150–158 (1983).
[CrossRef]

A. Laurentini, “How far 3D shapes can be understood from 2D silhouettes,” IEEE Trans. Pattern Anal. Mach. Intell. 17, 188–195 (1995).
[CrossRef]

A. Laurentini, “The visual hull concept for silhouette-based image understanding,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 150–162 (1994).
[CrossRef]

A. K. Jain, Y. Zhong, S. Lakshmanan, “Object matching using deformable templates,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 267–278 (1996).
[CrossRef]

Int. J. Comput. Vision (1)

M. Kass, A. Witkin, D. Terzopoulos, “Snakes: active contour models,” Int. J. Comput. Vision 1, 321–331 (1988).
[CrossRef]

Other (16)

B. J. Frey, R. Koetter, N. Petrovic, “Codes on images and iterative phase unwrapping,” in Proceedings of the IEEE Information Theory Workshop (IEEE Press, Piscataway, N.J., 2001), pp. 9–11.

S. M. Aji, G. B. Horn, R. J. McEliece, “Iterative decoding on graphs with a single cycle,” in Proceedings of the IEEE International Symposium on Information Theory (IEEE Press, Piscataway, N.J.), p. 276.

G. Winkler, Image Analysis, Random Fields and Markov Chain Monte Carlo Methods: A Mathematical Introduction (Springer, New York, 2003).

H. Elliot, H. Derin, R. Cristi, D. Geman, “Application of the Gibbs distribution to image segmentation,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE Press, Piscataway, N.J., 1984), Vol. 9, pp. 678–681.

A. Minagawa, K. Uda, N. Tagawa, “Region extraction based on belief propagation for Gaussian model,” in Proceedings of the International Conference on Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 2002), Vol. 2, pp. 507–510.

J. S. Lim, Two-Dimensional Signal and Image Processing (Prentice Hall, Englewood Cliffs, N.J., 1990).

M. Wainwright, T. Jaakola, A. Willsky, “Tree-based reparameterization framework for approximate estimation of stochastic processes on graphs with cycles,” (Laboratory for Information and Decision Systems, MIT, Cambridge, Mass., 2001).

J. C. Carr, W. R. Fright, A. H. Gee, R. W. Prager, K. J. Dalton, “3D shape reconstruction using volume intersection techniques,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE Press, Piscataway, N.J., 1998), pp. 1095–1100.

Lavakusha, A. K. Pujari, P. G. Reddy, “Volume intersection algorithm with changing directions of view,” in Proceedings of the International Workshop on Industrial Applications of Machine Intelligence and Vision (IEEE Press, Piscataway, N.J., 1989), pp. 309–314.

R. A. Weisenseel, W. C. Karl, D. A. Casañon, R. C. Brower, “MRF-based algorithms for segmentation of SAR images,” in Proceedings of the International Conference on Image Processing (IEEE Computer Society Press, Los Alamitos, Calif., 1998), Vol. 3, pp. 770–774.

M. Mignotte, C. Collet, P. Perez, P. Bouthemy, “Unsupervised Markovian segmentation of sonar images,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE Press, Piscataway, N.J., 1997), Vol. 4, pp. 2781–2784.

D. Snow, P. Viola, R. Zabih, “Exact voxel occupancy with graph cuts,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 2000), Vol. 1, pp. 345–352.

R. E. Walker, Marine Light Field Statistics (Wiley, New York, 1994).

P. J. Shargo, N. Çadalli, A. C. Singer, D. C. Munson, “A tomographic framework for LIDAR imaging,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE Press, Piscataway, N.J., 2001), Vol. 3, pp. 1893–1896.

I. Quidu, J. Ph. Malkasse, G. Burel, P. Vilbé, “Mine classification based on raw sonar data: an approach combining Fourier descriptors, statistical models, and genetic algorithms,” in Proceedings of Oceans 2000 MTS/IEEE Conf. and Exhibition (IEEE Press, Piscataway, N.J., 2000), Vol. 1, pp. 285–290.

N. Ahuja, J. Veenstra, “Efficient octree generation from silhouettes,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Press, Piscataway, N.J., 1986), pp. 537–542.

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Figures (18)

Fig. 1
Fig. 1

LIDAR data collection experiment: (a) experimental setup and (b) digital camera photograph of target.

Fig. 2
Fig. 2

Factor graph models for segmenting images with (a) no blurring and (b) a 2×2 blurring.

Fig. 3
Fig. 3

Approximate blur point-spread function.

Fig. 4
Fig. 4

Simulated target.

Fig. 5
Fig. 5

Image segmentation error in NB case: (a) in entire image, (b) away from edges, and (c) near edges.

Fig. 6
Fig. 6

Image segmentation error in SB case: (a) in entire image, (b) away from edges, and (c) near edges.

Fig. 7
Fig. 7

Image segmentation error in GB case: (a) in entire image, (b) away from edges, and (c) near edges.

Fig. 8
Fig. 8

Reconstruction error in (a) NB case, (b) SB case, and (c) GB case.

Fig. 9
Fig. 9

Silhouette formation from (a) in-air image: (b) with the WF method and (c) with the FG method.

Fig. 10
Fig. 10

Silhouette formation from (a) shadow image: (b) with the WF method and (c) with the FG method.

Fig. 11
Fig. 11

LIDAR reflection images used in reconstruction of target in air.

Fig. 12
Fig. 12

WF-SFS reconstruction from in-air data.

Fig. 13
Fig. 13

FG-SFS reconstruction from in-air data.

Fig. 14
Fig. 14

FG3D reconstruction from in-air data.

Fig. 15
Fig. 15

LIDAR shadow images used in reconstruction of submerged target.

Fig. 16
Fig. 16

WF-SFS reconstruction from shadow data.

Fig. 17
Fig. 17

FG-SFS reconstruction from shadow data.

Fig. 18
Fig. 18

FG3D reconstruction from shadow data.

Equations (25)

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

y[n1, n2]=x[n1, n2] ** h[n1, n2]+w[n1, n2],(n1, n2)I,
f(x1, x2,, xn)=XQgX(X),
μxg(x)=nN(x)\{g}μnx(x),
μgx(x)={x}g(X)nN(g)\{x}μng(n),
f(x|y)=f(y|x)f(x)f(y)=1Z f(y|x)f(x),
f(x)=1Zi,jψi,j(xi,j),
ψ(xi,j)
=1000ifxi,j=xi+1,j=xi,j+1=xi+1,j+11if(xi,j=xi+1,j+1)(xi+1,j=xi,j+1)10otherwise.
f(y|x)=i,jf(yi,j|x)=i,jf(yi,j|Xi,j).
f(x|y)=1Zi,jψ(xi,j)f(yi,j|Xi,j),
fyi,j(xi,j)
=12πσ2exp-12σ2 (yi,j-μ0)2ifxi,j=012πσ2exp-12σ2 (yi,j-μ1)2ifxi,j=1,
fyi,j(Xi,j)=12πσ2exp-12σ2 (yi,j-aTxi,j)2.
f(v|z)=1Z f(v)f(z|v),
ψ(vi, vj)=1ifvivjkifvi=vj,
f(z|v)=i,jf(zi,j|v)=i,jf(zi,j|vi).
f(zi,j|vi=0)=p 12πσ2exp-12σ2 (zi,j-μ0)2+(1-p) 12πσ2×exp-12σ2 (zi,j-μ1)2,
h[n1, n2]=1Zexp-12σ2 (n12+n22),
G(ω1, ω2)=Sxy(ω1, ω2)Syy(ω1, ω2)
=[Syy(ω1, ω2)-σ2]/H(ω1, ω2)Syy(ω1, ω2),
Hˆ(ω1, ω2)=H(ω1, ω2)if|H(ω1, ω2)|>γγ H(ω1, ω2)|H(ω1, ω2)|otherwise,
n1n2(x[n1, n2]-g[n1, n2]**y[n1, n2])2,
E(v)=iDzi(vi)+70i{j:vjN(vi)}12 (1-δ[vi-vj]),
Dzi(vi)=round40j[ξ(zi,j)]2ifvi=0300ifvi=1,
ξ(x)=0ifx<0xif0x<1.41.4ifx1.4,

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