Abstract

We present a novel image acquisition technique for Optical Coherence Tomography (OCT) that enables manual lateral scanning. The technique compensates for the variability in lateral scan velocity based on feedback obtained from correlation between consecutive A-scans. Results obtained from phantom samples and biological tissues demonstrate successful assembly of OCT images from manually-scanned datasets despite non-uniform scan velocity and abrupt stops encountered during data acquisition. This technique could enable the acquisition of images during manual OCT needle-guided biopsy or catheter-based imaging, and for assembly of large field-of-view images with hand-held probes during intraoperative in vivo OCT imaging.

©2009 Optical Society of America

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  1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
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    [Crossref] [PubMed]
  4. R. Huber, M. Wojtkowski, and J. G. Fujimoto, “Fourier domain mode locking (FDML): A new laser operating regime and applications for optical coherence tomography,” Opt. Express 14, 3225–3237 (2006).
    [Crossref] [PubMed]
  5. Z. Chen, Z. Yonghua, S. M. Srinivas, J. S. Nelson, N. Prakash, and R. D. Frostig, “Optical Doppler tomography,” IEEE J. Sel. Top. Quantum Electron. 5, 1134–1142 (1999).
    [Crossref]
  6. J. J. Pasquesi, S. C. Schlachter, M. D. Boppart, E. J. Chaney, S. J. Kaufman, and S. A. Boppart, “In vivo detection of exercise-induced ultrastructural changes in genetically-altered murine skeletal muscle using polarization-sensitive optical coherence tomography,” Opt. Express 14, 1547–1556 (2006).
    [Crossref] [PubMed]
  7. A. L. Oldenburg, V. Crecea, S. A. Rinne, and S. A. Boppart, “Phase-resolved magnetomotive OCT for imaging nanomolar concentrations of magnetic nanoparticles in tissues,” Opt. Express 16, 11525–11539 (2008).
    [PubMed]
  8. S. A. Boppart, W. Luo, D. L. Marks, and K. W. Singletary, “Optical coherence tomography: feasibility for basic research and image-guided surgery of breast cancer,” Breast Cancer Res. Treatment 84, 85–97 (2004).
    [Crossref]
  9. S. Radhakrishnan, A. M. Rollins, J. E. Roth, S. Yazdanfar, V. Westphal, D. S. Bardenstein, and J. A. Izatt, “Real-time optical coherence tomography of the anterior segment at 1310 nm,” Arch. Ophthalmol. 119, 1179–1185 (2001).
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  12. S. A. Boppart, B. E. Bouma, C. Pitris, G. J. Tearney, J. G. Fujimoto, and M. E. Brezinski, “Forward-imaging instruments for optical coherence tomography,” Opt. Lett. 22, 1618–1620 (1997).
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  13. S. Han, M. V. Sarunic, J. Wu, M. Humayun, and C. Yang, “Handheld forward-imaging needle endoscope for ophthalmic optical coherence tomography inspection,” J. Biomed. Opt 13, 020505 (2008).
    [Crossref] [PubMed]
  14. P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
    [Crossref]
  15. R. L. Galloway, “The process and development of image guided procedures,” Annu. Rev. Biomed. Eng 3, 83–108 (2001).
    [Crossref] [PubMed]
  16. A. H. Gee, R. James Housden, P. Hassenpflug, G. M. Treece, and R. W. Prager, “Sensorless freehand 3D ultrasound in real tissue: Speckle decorrelation without fully developed speckle,” Med. Image Anal 10, 137–149 (2006).
    [Crossref]
  17. L. Mercier, T. Langø, F. Lindseth, and D. L. Collins, “A review of calibration techniques for freehand 3-D ultrasound systems,” Ultrasound Med. Biol 31, 449–471 (2005).
    [Crossref] [PubMed]
  18. P. Hassenpflug, R. W. Prager, G. M. Treece, and A. H. Gee, “Speckle classification for sensorless freehand 3-D ultrasound,” Ultrasound Med. Biol 31, 1499–1508 (2005).
    [Crossref] [PubMed]
  19. T. A Tuthill, J. F. Krucker, J. B. Fowlkes, and P. L. Carson, “Automated three-dimensional US frame positioning computed from elevational speckle decorrelation,” Radiology 209, 575–582 (1998).
    [PubMed]
  20. L. Pai-Chi, C. Chong-Jing, and Y. Chih-Kuang, “On velocity estimation using speckle decorrelation” IEEE. Trans. Ultrason. Ferroelectr. Freq. Control 48, 1084–1091 (2001).
    [Crossref]
  21. R. W. Prager, A. H. Gee, G. M. Treece, C. J. C. Cash, and L. H. Berman, “Sensorless freehand 3-D ultrasound using regression of the echo intensity,” Ultrasound Med. Biol 29, 437–446 (2003).
    [Crossref] [PubMed]
  22. A. Krupa, G. Fichtinger, and G. D. Hager, “Full Motion Tracking in Ultrasound Using Image Speckle Information and Visual Servoing,” in Proceedings of IEEE International Conference on Robotics and Automation (2007), pp. 2458–2464.
    [Crossref]
  23. P. C. Li, C. Y. Li, and W. C. Yeh, “Tissue motion and elevational speckle decorrelation in freehand 3D ultrasound,” Ultrason. Imaging 24, 1–12 (2002).
    [PubMed]
  24. K. W. Gossage, T. S. Tkaczyk, J. J. Rodriguez, and J. K. Barton, “Texture analysis of optical coherence tomography images: feasibility for tissue classification,” J. Biomed. Opt 8, 570–575 (2003).
    [Crossref] [PubMed]
  25. S. J. Kirkpatrick, R. K. Wang, and D. D. Duncan, “OCT-based elastography for large and small deformations,” Opt. Express 14, 11585–11597 (2006).
    [Crossref] [PubMed]
  26. D. D. Duncan and S. J. Kirkpatrick, ”Processing algorithms for tracking speckle shifts in optical elastography of biological tissues,” J. Biomed. Opt 6, 418–426 (2001).
    [Crossref] [PubMed]
  27. D. D. Duncan and S. J. Kirkpatrick, ”Performance analysis of a maximum-likelihood speckle motion estimator,” Opt. Express 10, 927–941 (2002).
    [PubMed]
  28. H.-J. Ko, W. Tan, R. Stack, and S. A. Boppart, ”Optical coherence elastography of engineered and developing tissue,” Tissue Eng 12, 63–73 (2006).
    [Crossref] [PubMed]
  29. S. H. Yun, G. J. Tearney, J. F. de Boer, and B. E. Bouma, ”Motion artifacts in optical coherence tomography with frequency-domain ranging,” Opt. Express 12, 2977–2998 (2004).
    [Crossref] [PubMed]
  30. R. J. Zawadzki, S. S. Choi, S. M. Jones, S. S. Oliver, and J. S. Werner, ”Adaptive optics-optical coherence tomography: optimizing visualization of microscopic retinal structures in three dimensions,” J. Opt. Soc. Am. A 24, 1373–1383 (2007).
    [Crossref]
  31. J. M. Schmitt, S. H. Xiang, and K. M. Yung, ”Speckle in optical coherence tomography,” J. Biomed. Opt 4, 95–105 (1999).
    [Crossref]
  32. W. Luo, D. L. Marks, T. S. Ralston, and S. A. Boppart, ”Three-dimensional optical coherence tomography of the embryonic murine cardiovascular system,” J. Biomed. Opt 11, 021014–021018 (2006).
    [Crossref] [PubMed]
  33. A. M. Zysk and S. A. Boppart, ”Computational methods for analysis of human breast tumor tissue in optical coherence tomography images,” J. Biomed. Opt 11, 054015 (2006).
    [Crossref] [PubMed]
  34. M. Wojtkowski, V. J. Srinivasan, T. H. Ko, J. G. Fujimoto, A. Kowalczyk, and J. S. Duker, ”Ultrahigh-resolution, high-speed, fourier domain optical coherence tomography and methods for dispersion compensation,” Opt. Express 12, 2404–2422 (2004).
    [Crossref] [PubMed]
  35. R. J. Housden, A. H. Gee, R. W. Prager, and G. M. Treece, ”Rotational motion in sensorless freehand three-dimensional ultrasound,” Ultrasonics 48, 412–422 (2008).
    [Crossref] [PubMed]
  36. R. J. Housden, A. H. Gee, G. M. Treece, and R. W. Prager, ”Subsample interpolation strategies for sensorless freehand 3D ultrasound,” Ultrasound Med. Biol 32, 1897–1904 (2006).
    [Crossref] [PubMed]

2008 (3)

A. L. Oldenburg, V. Crecea, S. A. Rinne, and S. A. Boppart, “Phase-resolved magnetomotive OCT for imaging nanomolar concentrations of magnetic nanoparticles in tissues,” Opt. Express 16, 11525–11539 (2008).
[PubMed]

S. Han, M. V. Sarunic, J. Wu, M. Humayun, and C. Yang, “Handheld forward-imaging needle endoscope for ophthalmic optical coherence tomography inspection,” J. Biomed. Opt 13, 020505 (2008).
[Crossref] [PubMed]

R. J. Housden, A. H. Gee, R. W. Prager, and G. M. Treece, ”Rotational motion in sensorless freehand three-dimensional ultrasound,” Ultrasonics 48, 412–422 (2008).
[Crossref] [PubMed]

2007 (2)

R. J. Zawadzki, S. S. Choi, S. M. Jones, S. S. Oliver, and J. S. Werner, ”Adaptive optics-optical coherence tomography: optimizing visualization of microscopic retinal structures in three dimensions,” J. Opt. Soc. Am. A 24, 1373–1383 (2007).
[Crossref]

A. M. Zysk, F. T. Nguyen, A. L. Oldenburg, D. L. Marks, and S. A. Boppart, “Optical coherence tomography: a review of clinical development from bench to bedside,” J. Biomed. Opt 12, 051403–051421 (2007).
[Crossref] [PubMed]

2006 (8)

R. Huber, M. Wojtkowski, and J. G. Fujimoto, “Fourier domain mode locking (FDML): A new laser operating regime and applications for optical coherence tomography,” Opt. Express 14, 3225–3237 (2006).
[Crossref] [PubMed]

J. J. Pasquesi, S. C. Schlachter, M. D. Boppart, E. J. Chaney, S. J. Kaufman, and S. A. Boppart, “In vivo detection of exercise-induced ultrastructural changes in genetically-altered murine skeletal muscle using polarization-sensitive optical coherence tomography,” Opt. Express 14, 1547–1556 (2006).
[Crossref] [PubMed]

A. H. Gee, R. James Housden, P. Hassenpflug, G. M. Treece, and R. W. Prager, “Sensorless freehand 3D ultrasound in real tissue: Speckle decorrelation without fully developed speckle,” Med. Image Anal 10, 137–149 (2006).
[Crossref]

W. Luo, D. L. Marks, T. S. Ralston, and S. A. Boppart, ”Three-dimensional optical coherence tomography of the embryonic murine cardiovascular system,” J. Biomed. Opt 11, 021014–021018 (2006).
[Crossref] [PubMed]

A. M. Zysk and S. A. Boppart, ”Computational methods for analysis of human breast tumor tissue in optical coherence tomography images,” J. Biomed. Opt 11, 054015 (2006).
[Crossref] [PubMed]

R. J. Housden, A. H. Gee, G. M. Treece, and R. W. Prager, ”Subsample interpolation strategies for sensorless freehand 3D ultrasound,” Ultrasound Med. Biol 32, 1897–1904 (2006).
[Crossref] [PubMed]

S. J. Kirkpatrick, R. K. Wang, and D. D. Duncan, “OCT-based elastography for large and small deformations,” Opt. Express 14, 11585–11597 (2006).
[Crossref] [PubMed]

H.-J. Ko, W. Tan, R. Stack, and S. A. Boppart, ”Optical coherence elastography of engineered and developing tissue,” Tissue Eng 12, 63–73 (2006).
[Crossref] [PubMed]

2005 (2)

L. Mercier, T. Langø, F. Lindseth, and D. L. Collins, “A review of calibration techniques for freehand 3-D ultrasound systems,” Ultrasound Med. Biol 31, 449–471 (2005).
[Crossref] [PubMed]

P. Hassenpflug, R. W. Prager, G. M. Treece, and A. H. Gee, “Speckle classification for sensorless freehand 3-D ultrasound,” Ultrasound Med. Biol 31, 1499–1508 (2005).
[Crossref] [PubMed]

2004 (3)

2003 (2)

K. W. Gossage, T. S. Tkaczyk, J. J. Rodriguez, and J. K. Barton, “Texture analysis of optical coherence tomography images: feasibility for tissue classification,” J. Biomed. Opt 8, 570–575 (2003).
[Crossref] [PubMed]

R. W. Prager, A. H. Gee, G. M. Treece, C. J. C. Cash, and L. H. Berman, “Sensorless freehand 3-D ultrasound using regression of the echo intensity,” Ultrasound Med. Biol 29, 437–446 (2003).
[Crossref] [PubMed]

2002 (2)

P. C. Li, C. Y. Li, and W. C. Yeh, “Tissue motion and elevational speckle decorrelation in freehand 3D ultrasound,” Ultrason. Imaging 24, 1–12 (2002).
[PubMed]

D. D. Duncan and S. J. Kirkpatrick, ”Performance analysis of a maximum-likelihood speckle motion estimator,” Opt. Express 10, 927–941 (2002).
[PubMed]

2001 (4)

D. D. Duncan and S. J. Kirkpatrick, ”Processing algorithms for tracking speckle shifts in optical elastography of biological tissues,” J. Biomed. Opt 6, 418–426 (2001).
[Crossref] [PubMed]

S. Radhakrishnan, A. M. Rollins, J. E. Roth, S. Yazdanfar, V. Westphal, D. S. Bardenstein, and J. A. Izatt, “Real-time optical coherence tomography of the anterior segment at 1310 nm,” Arch. Ophthalmol. 119, 1179–1185 (2001).
[PubMed]

R. L. Galloway, “The process and development of image guided procedures,” Annu. Rev. Biomed. Eng 3, 83–108 (2001).
[Crossref] [PubMed]

L. Pai-Chi, C. Chong-Jing, and Y. Chih-Kuang, “On velocity estimation using speckle decorrelation” IEEE. Trans. Ultrason. Ferroelectr. Freq. Control 48, 1084–1091 (2001).
[Crossref]

2000 (1)

1999 (2)

Z. Chen, Z. Yonghua, S. M. Srinivas, J. S. Nelson, N. Prakash, and R. D. Frostig, “Optical Doppler tomography,” IEEE J. Sel. Top. Quantum Electron. 5, 1134–1142 (1999).
[Crossref]

J. M. Schmitt, S. H. Xiang, and K. M. Yung, ”Speckle in optical coherence tomography,” J. Biomed. Opt 4, 95–105 (1999).
[Crossref]

1998 (1)

T. A Tuthill, J. F. Krucker, J. B. Fowlkes, and P. L. Carson, “Automated three-dimensional US frame positioning computed from elevational speckle decorrelation,” Radiology 209, 575–582 (1998).
[PubMed]

1997 (1)

1995 (1)

P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
[Crossref]

1991 (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Bainville, E.

P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
[Crossref]

Barbe, C.

P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
[Crossref]

Bardenstein, D. S.

S. Radhakrishnan, A. M. Rollins, J. E. Roth, S. Yazdanfar, V. Westphal, D. S. Bardenstein, and J. A. Izatt, “Real-time optical coherence tomography of the anterior segment at 1310 nm,” Arch. Ophthalmol. 119, 1179–1185 (2001).
[PubMed]

Barton, J. K.

K. W. Gossage, T. S. Tkaczyk, J. J. Rodriguez, and J. K. Barton, “Texture analysis of optical coherence tomography images: feasibility for tissue classification,” J. Biomed. Opt 8, 570–575 (2003).
[Crossref] [PubMed]

Berman, L. H.

R. W. Prager, A. H. Gee, G. M. Treece, C. J. C. Cash, and L. H. Berman, “Sensorless freehand 3-D ultrasound using regression of the echo intensity,” Ultrasound Med. Biol 29, 437–446 (2003).
[Crossref] [PubMed]

Bittar, E.

P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
[Crossref]

Boppart, M. D.

Boppart, S. A.

A. L. Oldenburg, V. Crecea, S. A. Rinne, and S. A. Boppart, “Phase-resolved magnetomotive OCT for imaging nanomolar concentrations of magnetic nanoparticles in tissues,” Opt. Express 16, 11525–11539 (2008).
[PubMed]

A. M. Zysk, F. T. Nguyen, A. L. Oldenburg, D. L. Marks, and S. A. Boppart, “Optical coherence tomography: a review of clinical development from bench to bedside,” J. Biomed. Opt 12, 051403–051421 (2007).
[Crossref] [PubMed]

J. J. Pasquesi, S. C. Schlachter, M. D. Boppart, E. J. Chaney, S. J. Kaufman, and S. A. Boppart, “In vivo detection of exercise-induced ultrastructural changes in genetically-altered murine skeletal muscle using polarization-sensitive optical coherence tomography,” Opt. Express 14, 1547–1556 (2006).
[Crossref] [PubMed]

H.-J. Ko, W. Tan, R. Stack, and S. A. Boppart, ”Optical coherence elastography of engineered and developing tissue,” Tissue Eng 12, 63–73 (2006).
[Crossref] [PubMed]

W. Luo, D. L. Marks, T. S. Ralston, and S. A. Boppart, ”Three-dimensional optical coherence tomography of the embryonic murine cardiovascular system,” J. Biomed. Opt 11, 021014–021018 (2006).
[Crossref] [PubMed]

A. M. Zysk and S. A. Boppart, ”Computational methods for analysis of human breast tumor tissue in optical coherence tomography images,” J. Biomed. Opt 11, 054015 (2006).
[Crossref] [PubMed]

S. A. Boppart, W. Luo, D. L. Marks, and K. W. Singletary, “Optical coherence tomography: feasibility for basic research and image-guided surgery of breast cancer,” Breast Cancer Res. Treatment 84, 85–97 (2004).
[Crossref]

S. A. Boppart, B. E. Bouma, C. Pitris, G. J. Tearney, J. G. Fujimoto, and M. E. Brezinski, “Forward-imaging instruments for optical coherence tomography,” Opt. Lett. 22, 1618–1620 (1997).
[Crossref]

Bouchard, V.

P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
[Crossref]

Bouma, B. E.

Brezinski, M. E.

Bricault, I.

P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
[Crossref]

Carson, P. L.

T. A Tuthill, J. F. Krucker, J. B. Fowlkes, and P. L. Carson, “Automated three-dimensional US frame positioning computed from elevational speckle decorrelation,” Radiology 209, 575–582 (1998).
[PubMed]

Cash, C. J. C.

R. W. Prager, A. H. Gee, G. M. Treece, C. J. C. Cash, and L. H. Berman, “Sensorless freehand 3-D ultrasound using regression of the echo intensity,” Ultrasound Med. Biol 29, 437–446 (2003).
[Crossref] [PubMed]

Champleboux, G.

P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
[Crossref]

Chaney, E. J.

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Chen, Z.

Z. Chen, Z. Yonghua, S. M. Srinivas, J. S. Nelson, N. Prakash, and R. D. Frostig, “Optical Doppler tomography,” IEEE J. Sel. Top. Quantum Electron. 5, 1134–1142 (1999).
[Crossref]

Chenin, M.

P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
[Crossref]

Chevalier, L.

P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
[Crossref]

Chih-Kuang, Y.

L. Pai-Chi, C. Chong-Jing, and Y. Chih-Kuang, “On velocity estimation using speckle decorrelation” IEEE. Trans. Ultrason. Ferroelectr. Freq. Control 48, 1084–1091 (2001).
[Crossref]

Choi, S. S.

Chong-Jing, C.

L. Pai-Chi, C. Chong-Jing, and Y. Chih-Kuang, “On velocity estimation using speckle decorrelation” IEEE. Trans. Ultrason. Ferroelectr. Freq. Control 48, 1084–1091 (2001).
[Crossref]

Chudoba, C.

Cinquin, P.

P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
[Crossref]

Collins, D. L.

L. Mercier, T. Langø, F. Lindseth, and D. L. Collins, “A review of calibration techniques for freehand 3-D ultrasound systems,” Ultrasound Med. Biol 31, 449–471 (2005).
[Crossref] [PubMed]

Crecea, V.

de Boer, J. F.

Delnondedieu, Y.

P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
[Crossref]

Desbat, L.

P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
[Crossref]

Dessenne, V.

P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
[Crossref]

Drexler, W.

W. Drexler and J. G. Fujimoto, Optical coherence tomography: technology and applications (Springer, New York2008).
[Crossref]

Duker, J. S.

Duncan, D. D.

Feldchtein, F. I.

F. I. Feldchtein, V. M. Gelikonov, and G. V. Gelikonov, “Design of OCT scanners” in Handbook of optical coherence tomography (Marcel Dekker, Inc, 2002).

Fichtinger, G.

A. Krupa, G. Fichtinger, and G. D. Hager, “Full Motion Tracking in Ultrasound Using Image Speckle Information and Visual Servoing,” in Proceedings of IEEE International Conference on Robotics and Automation (2007), pp. 2458–2464.
[Crossref]

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Fowlkes, J. B.

T. A Tuthill, J. F. Krucker, J. B. Fowlkes, and P. L. Carson, “Automated three-dimensional US frame positioning computed from elevational speckle decorrelation,” Radiology 209, 575–582 (1998).
[PubMed]

Frostig, R. D.

Z. Chen, Z. Yonghua, S. M. Srinivas, J. S. Nelson, N. Prakash, and R. D. Frostig, “Optical Doppler tomography,” IEEE J. Sel. Top. Quantum Electron. 5, 1134–1142 (1999).
[Crossref]

Fujimoto, J. G.

Galloway, R. L.

R. L. Galloway, “The process and development of image guided procedures,” Annu. Rev. Biomed. Eng 3, 83–108 (2001).
[Crossref] [PubMed]

Gee, A. H.

R. J. Housden, A. H. Gee, R. W. Prager, and G. M. Treece, ”Rotational motion in sensorless freehand three-dimensional ultrasound,” Ultrasonics 48, 412–422 (2008).
[Crossref] [PubMed]

R. J. Housden, A. H. Gee, G. M. Treece, and R. W. Prager, ”Subsample interpolation strategies for sensorless freehand 3D ultrasound,” Ultrasound Med. Biol 32, 1897–1904 (2006).
[Crossref] [PubMed]

A. H. Gee, R. James Housden, P. Hassenpflug, G. M. Treece, and R. W. Prager, “Sensorless freehand 3D ultrasound in real tissue: Speckle decorrelation without fully developed speckle,” Med. Image Anal 10, 137–149 (2006).
[Crossref]

P. Hassenpflug, R. W. Prager, G. M. Treece, and A. H. Gee, “Speckle classification for sensorless freehand 3-D ultrasound,” Ultrasound Med. Biol 31, 1499–1508 (2005).
[Crossref] [PubMed]

R. W. Prager, A. H. Gee, G. M. Treece, C. J. C. Cash, and L. H. Berman, “Sensorless freehand 3-D ultrasound using regression of the echo intensity,” Ultrasound Med. Biol 29, 437–446 (2003).
[Crossref] [PubMed]

Gelikonov, G. V.

F. I. Feldchtein, V. M. Gelikonov, and G. V. Gelikonov, “Design of OCT scanners” in Handbook of optical coherence tomography (Marcel Dekker, Inc, 2002).

Gelikonov, V. M.

F. I. Feldchtein, V. M. Gelikonov, and G. V. Gelikonov, “Design of OCT scanners” in Handbook of optical coherence tomography (Marcel Dekker, Inc, 2002).

Gossage, K. W.

K. W. Gossage, T. S. Tkaczyk, J. J. Rodriguez, and J. K. Barton, “Texture analysis of optical coherence tomography images: feasibility for tissue classification,” J. Biomed. Opt 8, 570–575 (2003).
[Crossref] [PubMed]

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Hager, G. D.

A. Krupa, G. Fichtinger, and G. D. Hager, “Full Motion Tracking in Ultrasound Using Image Speckle Information and Visual Servoing,” in Proceedings of IEEE International Conference on Robotics and Automation (2007), pp. 2458–2464.
[Crossref]

Hamadeh, A.

P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
[Crossref]

Han, S.

S. Han, M. V. Sarunic, J. Wu, M. Humayun, and C. Yang, “Handheld forward-imaging needle endoscope for ophthalmic optical coherence tomography inspection,” J. Biomed. Opt 13, 020505 (2008).
[Crossref] [PubMed]

Hassenpflug, P.

A. H. Gee, R. James Housden, P. Hassenpflug, G. M. Treece, and R. W. Prager, “Sensorless freehand 3D ultrasound in real tissue: Speckle decorrelation without fully developed speckle,” Med. Image Anal 10, 137–149 (2006).
[Crossref]

P. Hassenpflug, R. W. Prager, G. M. Treece, and A. H. Gee, “Speckle classification for sensorless freehand 3-D ultrasound,” Ultrasound Med. Biol 31, 1499–1508 (2005).
[Crossref] [PubMed]

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Henry, D.

P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
[Crossref]

Housden, R. J.

R. J. Housden, A. H. Gee, R. W. Prager, and G. M. Treece, ”Rotational motion in sensorless freehand three-dimensional ultrasound,” Ultrasonics 48, 412–422 (2008).
[Crossref] [PubMed]

R. J. Housden, A. H. Gee, G. M. Treece, and R. W. Prager, ”Subsample interpolation strategies for sensorless freehand 3D ultrasound,” Ultrasound Med. Biol 32, 1897–1904 (2006).
[Crossref] [PubMed]

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Huber, R.

Humayun, M.

S. Han, M. V. Sarunic, J. Wu, M. Humayun, and C. Yang, “Handheld forward-imaging needle endoscope for ophthalmic optical coherence tomography inspection,” J. Biomed. Opt 13, 020505 (2008).
[Crossref] [PubMed]

Izatt, J. A.

S. Radhakrishnan, A. M. Rollins, J. E. Roth, S. Yazdanfar, V. Westphal, D. S. Bardenstein, and J. A. Izatt, “Real-time optical coherence tomography of the anterior segment at 1310 nm,” Arch. Ophthalmol. 119, 1179–1185 (2001).
[PubMed]

James Housden, R.

A. H. Gee, R. James Housden, P. Hassenpflug, G. M. Treece, and R. W. Prager, “Sensorless freehand 3D ultrasound in real tissue: Speckle decorrelation without fully developed speckle,” Med. Image Anal 10, 137–149 (2006).
[Crossref]

Jones, S. M.

Kaufman, S. J.

Kirkpatrick, S. J.

Ko, H.-J.

H.-J. Ko, W. Tan, R. Stack, and S. A. Boppart, ”Optical coherence elastography of engineered and developing tissue,” Tissue Eng 12, 63–73 (2006).
[Crossref] [PubMed]

Ko, T.

Ko, T. H.

Kowalczyk, A.

Krucker, J. F.

T. A Tuthill, J. F. Krucker, J. B. Fowlkes, and P. L. Carson, “Automated three-dimensional US frame positioning computed from elevational speckle decorrelation,” Radiology 209, 575–582 (1998).
[PubMed]

Krupa, A.

A. Krupa, G. Fichtinger, and G. D. Hager, “Full Motion Tracking in Ultrasound Using Image Speckle Information and Visual Servoing,” in Proceedings of IEEE International Conference on Robotics and Automation (2007), pp. 2458–2464.
[Crossref]

Laieb, N.

P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
[Crossref]

Langø, T.

L. Mercier, T. Langø, F. Lindseth, and D. L. Collins, “A review of calibration techniques for freehand 3-D ultrasound systems,” Ultrasound Med. Biol 31, 449–471 (2005).
[Crossref] [PubMed]

Lavallee, S.

P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
[Crossref]

Lefebvre, J. M.

P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
[Crossref]

Leitner, F.

P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
[Crossref]

Li, C. Y.

P. C. Li, C. Y. Li, and W. C. Yeh, “Tissue motion and elevational speckle decorrelation in freehand 3D ultrasound,” Ultrason. Imaging 24, 1–12 (2002).
[PubMed]

Li, P. C.

P. C. Li, C. Y. Li, and W. C. Yeh, “Tissue motion and elevational speckle decorrelation in freehand 3D ultrasound,” Ultrason. Imaging 24, 1–12 (2002).
[PubMed]

Li, X.

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Lindseth, F.

L. Mercier, T. Langø, F. Lindseth, and D. L. Collins, “A review of calibration techniques for freehand 3-D ultrasound systems,” Ultrasound Med. Biol 31, 449–471 (2005).
[Crossref] [PubMed]

Luo, W.

W. Luo, D. L. Marks, T. S. Ralston, and S. A. Boppart, ”Three-dimensional optical coherence tomography of the embryonic murine cardiovascular system,” J. Biomed. Opt 11, 021014–021018 (2006).
[Crossref] [PubMed]

S. A. Boppart, W. Luo, D. L. Marks, and K. W. Singletary, “Optical coherence tomography: feasibility for basic research and image-guided surgery of breast cancer,” Breast Cancer Res. Treatment 84, 85–97 (2004).
[Crossref]

Marks, D. L.

A. M. Zysk, F. T. Nguyen, A. L. Oldenburg, D. L. Marks, and S. A. Boppart, “Optical coherence tomography: a review of clinical development from bench to bedside,” J. Biomed. Opt 12, 051403–051421 (2007).
[Crossref] [PubMed]

W. Luo, D. L. Marks, T. S. Ralston, and S. A. Boppart, ”Three-dimensional optical coherence tomography of the embryonic murine cardiovascular system,” J. Biomed. Opt 11, 021014–021018 (2006).
[Crossref] [PubMed]

S. A. Boppart, W. Luo, D. L. Marks, and K. W. Singletary, “Optical coherence tomography: feasibility for basic research and image-guided surgery of breast cancer,” Breast Cancer Res. Treatment 84, 85–97 (2004).
[Crossref]

Menguy, Y.

P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
[Crossref]

Mercier, L.

L. Mercier, T. Langø, F. Lindseth, and D. L. Collins, “A review of calibration techniques for freehand 3-D ultrasound systems,” Ultrasound Med. Biol 31, 449–471 (2005).
[Crossref] [PubMed]

Nelson, J. S.

Z. Chen, Z. Yonghua, S. M. Srinivas, J. S. Nelson, N. Prakash, and R. D. Frostig, “Optical Doppler tomography,” IEEE J. Sel. Top. Quantum Electron. 5, 1134–1142 (1999).
[Crossref]

Nguyen, F. T.

A. M. Zysk, F. T. Nguyen, A. L. Oldenburg, D. L. Marks, and S. A. Boppart, “Optical coherence tomography: a review of clinical development from bench to bedside,” J. Biomed. Opt 12, 051403–051421 (2007).
[Crossref] [PubMed]

Oldenburg, A. L.

A. L. Oldenburg, V. Crecea, S. A. Rinne, and S. A. Boppart, “Phase-resolved magnetomotive OCT for imaging nanomolar concentrations of magnetic nanoparticles in tissues,” Opt. Express 16, 11525–11539 (2008).
[PubMed]

A. M. Zysk, F. T. Nguyen, A. L. Oldenburg, D. L. Marks, and S. A. Boppart, “Optical coherence tomography: a review of clinical development from bench to bedside,” J. Biomed. Opt 12, 051403–051421 (2007).
[Crossref] [PubMed]

Oliver, S. S.

Padieu, F.

P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
[Crossref]

Pai-Chi, L.

L. Pai-Chi, C. Chong-Jing, and Y. Chih-Kuang, “On velocity estimation using speckle decorrelation” IEEE. Trans. Ultrason. Ferroelectr. Freq. Control 48, 1084–1091 (2001).
[Crossref]

Pasquesi, J. J.

Peria, O.

P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
[Crossref]

Pitris, C.

Poyet, A.

P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
[Crossref]

Prager, R. W.

R. J. Housden, A. H. Gee, R. W. Prager, and G. M. Treece, ”Rotational motion in sensorless freehand three-dimensional ultrasound,” Ultrasonics 48, 412–422 (2008).
[Crossref] [PubMed]

R. J. Housden, A. H. Gee, G. M. Treece, and R. W. Prager, ”Subsample interpolation strategies for sensorless freehand 3D ultrasound,” Ultrasound Med. Biol 32, 1897–1904 (2006).
[Crossref] [PubMed]

A. H. Gee, R. James Housden, P. Hassenpflug, G. M. Treece, and R. W. Prager, “Sensorless freehand 3D ultrasound in real tissue: Speckle decorrelation without fully developed speckle,” Med. Image Anal 10, 137–149 (2006).
[Crossref]

P. Hassenpflug, R. W. Prager, G. M. Treece, and A. H. Gee, “Speckle classification for sensorless freehand 3-D ultrasound,” Ultrasound Med. Biol 31, 1499–1508 (2005).
[Crossref] [PubMed]

R. W. Prager, A. H. Gee, G. M. Treece, C. J. C. Cash, and L. H. Berman, “Sensorless freehand 3-D ultrasound using regression of the echo intensity,” Ultrasound Med. Biol 29, 437–446 (2003).
[Crossref] [PubMed]

Prakash, N.

Z. Chen, Z. Yonghua, S. M. Srinivas, J. S. Nelson, N. Prakash, and R. D. Frostig, “Optical Doppler tomography,” IEEE J. Sel. Top. Quantum Electron. 5, 1134–1142 (1999).
[Crossref]

Promayon, M.

P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
[Crossref]

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Radhakrishnan, S.

S. Radhakrishnan, A. M. Rollins, J. E. Roth, S. Yazdanfar, V. Westphal, D. S. Bardenstein, and J. A. Izatt, “Real-time optical coherence tomography of the anterior segment at 1310 nm,” Arch. Ophthalmol. 119, 1179–1185 (2001).
[PubMed]

Ralston, T. S.

W. Luo, D. L. Marks, T. S. Ralston, and S. A. Boppart, ”Three-dimensional optical coherence tomography of the embryonic murine cardiovascular system,” J. Biomed. Opt 11, 021014–021018 (2006).
[Crossref] [PubMed]

Rinne, S. A.

Rodriguez, J. J.

K. W. Gossage, T. S. Tkaczyk, J. J. Rodriguez, and J. K. Barton, “Texture analysis of optical coherence tomography images: feasibility for tissue classification,” J. Biomed. Opt 8, 570–575 (2003).
[Crossref] [PubMed]

Rollins, A. M.

S. Radhakrishnan, A. M. Rollins, J. E. Roth, S. Yazdanfar, V. Westphal, D. S. Bardenstein, and J. A. Izatt, “Real-time optical coherence tomography of the anterior segment at 1310 nm,” Arch. Ophthalmol. 119, 1179–1185 (2001).
[PubMed]

Roth, J. E.

S. Radhakrishnan, A. M. Rollins, J. E. Roth, S. Yazdanfar, V. Westphal, D. S. Bardenstein, and J. A. Izatt, “Real-time optical coherence tomography of the anterior segment at 1310 nm,” Arch. Ophthalmol. 119, 1179–1185 (2001).
[PubMed]

Rouault, S.

P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
[Crossref]

Sarunic, M. V.

S. Han, M. V. Sarunic, J. Wu, M. Humayun, and C. Yang, “Handheld forward-imaging needle endoscope for ophthalmic optical coherence tomography inspection,” J. Biomed. Opt 13, 020505 (2008).
[Crossref] [PubMed]

Sautot, P.

P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
[Crossref]

Schlachter, S. C.

Schmitt, J. M.

J. M. Schmitt, S. H. Xiang, and K. M. Yung, ”Speckle in optical coherence tomography,” J. Biomed. Opt 4, 95–105 (1999).
[Crossref]

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Singletary, K. W.

S. A. Boppart, W. Luo, D. L. Marks, and K. W. Singletary, “Optical coherence tomography: feasibility for basic research and image-guided surgery of breast cancer,” Breast Cancer Res. Treatment 84, 85–97 (2004).
[Crossref]

Srinivas, S. M.

Z. Chen, Z. Yonghua, S. M. Srinivas, J. S. Nelson, N. Prakash, and R. D. Frostig, “Optical Doppler tomography,” IEEE J. Sel. Top. Quantum Electron. 5, 1134–1142 (1999).
[Crossref]

Srinivasan, V. J.

Stack, R.

H.-J. Ko, W. Tan, R. Stack, and S. A. Boppart, ”Optical coherence elastography of engineered and developing tissue,” Tissue Eng 12, 63–73 (2006).
[Crossref] [PubMed]

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Tan, W.

H.-J. Ko, W. Tan, R. Stack, and S. A. Boppart, ”Optical coherence elastography of engineered and developing tissue,” Tissue Eng 12, 63–73 (2006).
[Crossref] [PubMed]

Tearney, G. J.

Tkaczyk, T. S.

K. W. Gossage, T. S. Tkaczyk, J. J. Rodriguez, and J. K. Barton, “Texture analysis of optical coherence tomography images: feasibility for tissue classification,” J. Biomed. Opt 8, 570–575 (2003).
[Crossref] [PubMed]

Treece, G. M.

R. J. Housden, A. H. Gee, R. W. Prager, and G. M. Treece, ”Rotational motion in sensorless freehand three-dimensional ultrasound,” Ultrasonics 48, 412–422 (2008).
[Crossref] [PubMed]

R. J. Housden, A. H. Gee, G. M. Treece, and R. W. Prager, ”Subsample interpolation strategies for sensorless freehand 3D ultrasound,” Ultrasound Med. Biol 32, 1897–1904 (2006).
[Crossref] [PubMed]

A. H. Gee, R. James Housden, P. Hassenpflug, G. M. Treece, and R. W. Prager, “Sensorless freehand 3D ultrasound in real tissue: Speckle decorrelation without fully developed speckle,” Med. Image Anal 10, 137–149 (2006).
[Crossref]

P. Hassenpflug, R. W. Prager, G. M. Treece, and A. H. Gee, “Speckle classification for sensorless freehand 3-D ultrasound,” Ultrasound Med. Biol 31, 1499–1508 (2005).
[Crossref] [PubMed]

R. W. Prager, A. H. Gee, G. M. Treece, C. J. C. Cash, and L. H. Berman, “Sensorless freehand 3-D ultrasound using regression of the echo intensity,” Ultrasound Med. Biol 29, 437–446 (2003).
[Crossref] [PubMed]

Troccaz, J.

P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
[Crossref]

Tuthill, T. A

T. A Tuthill, J. F. Krucker, J. B. Fowlkes, and P. L. Carson, “Automated three-dimensional US frame positioning computed from elevational speckle decorrelation,” Radiology 209, 575–582 (1998).
[PubMed]

Vassal, P.

P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
[Crossref]

Wang, R. K.

Werner, J. S.

Westphal, V.

S. Radhakrishnan, A. M. Rollins, J. E. Roth, S. Yazdanfar, V. Westphal, D. S. Bardenstein, and J. A. Izatt, “Real-time optical coherence tomography of the anterior segment at 1310 nm,” Arch. Ophthalmol. 119, 1179–1185 (2001).
[PubMed]

Wojtkowski, M.

Wu, J.

S. Han, M. V. Sarunic, J. Wu, M. Humayun, and C. Yang, “Handheld forward-imaging needle endoscope for ophthalmic optical coherence tomography inspection,” J. Biomed. Opt 13, 020505 (2008).
[Crossref] [PubMed]

Xiang, S. H.

J. M. Schmitt, S. H. Xiang, and K. M. Yung, ”Speckle in optical coherence tomography,” J. Biomed. Opt 4, 95–105 (1999).
[Crossref]

Yang, C.

S. Han, M. V. Sarunic, J. Wu, M. Humayun, and C. Yang, “Handheld forward-imaging needle endoscope for ophthalmic optical coherence tomography inspection,” J. Biomed. Opt 13, 020505 (2008).
[Crossref] [PubMed]

Yazdanfar, S.

S. Radhakrishnan, A. M. Rollins, J. E. Roth, S. Yazdanfar, V. Westphal, D. S. Bardenstein, and J. A. Izatt, “Real-time optical coherence tomography of the anterior segment at 1310 nm,” Arch. Ophthalmol. 119, 1179–1185 (2001).
[PubMed]

Yeh, W. C.

P. C. Li, C. Y. Li, and W. C. Yeh, “Tissue motion and elevational speckle decorrelation in freehand 3D ultrasound,” Ultrason. Imaging 24, 1–12 (2002).
[PubMed]

Yonghua, Z.

Z. Chen, Z. Yonghua, S. M. Srinivas, J. S. Nelson, N. Prakash, and R. D. Frostig, “Optical Doppler tomography,” IEEE J. Sel. Top. Quantum Electron. 5, 1134–1142 (1999).
[Crossref]

Yun, S. H.

Yung, K. M.

J. M. Schmitt, S. H. Xiang, and K. M. Yung, ”Speckle in optical coherence tomography,” J. Biomed. Opt 4, 95–105 (1999).
[Crossref]

Zawadzki, R. J.

Zysk, A. M.

A. M. Zysk, F. T. Nguyen, A. L. Oldenburg, D. L. Marks, and S. A. Boppart, “Optical coherence tomography: a review of clinical development from bench to bedside,” J. Biomed. Opt 12, 051403–051421 (2007).
[Crossref] [PubMed]

A. M. Zysk and S. A. Boppart, ”Computational methods for analysis of human breast tumor tissue in optical coherence tomography images,” J. Biomed. Opt 11, 054015 (2006).
[Crossref] [PubMed]

Annu. Rev. Biomed. Eng (1)

R. L. Galloway, “The process and development of image guided procedures,” Annu. Rev. Biomed. Eng 3, 83–108 (2001).
[Crossref] [PubMed]

Arch. Ophthalmol. (1)

S. Radhakrishnan, A. M. Rollins, J. E. Roth, S. Yazdanfar, V. Westphal, D. S. Bardenstein, and J. A. Izatt, “Real-time optical coherence tomography of the anterior segment at 1310 nm,” Arch. Ophthalmol. 119, 1179–1185 (2001).
[PubMed]

Breast Cancer Res. Treatment (1)

S. A. Boppart, W. Luo, D. L. Marks, and K. W. Singletary, “Optical coherence tomography: feasibility for basic research and image-guided surgery of breast cancer,” Breast Cancer Res. Treatment 84, 85–97 (2004).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

Z. Chen, Z. Yonghua, S. M. Srinivas, J. S. Nelson, N. Prakash, and R. D. Frostig, “Optical Doppler tomography,” IEEE J. Sel. Top. Quantum Electron. 5, 1134–1142 (1999).
[Crossref]

IEEE. Eng. Med. Biol. Mag (1)

P. Cinquin, E. Bainville, C. Barbe, E. Bittar, V. Bouchard, I. Bricault, G. Champleboux, M. Chenin, L. Chevalier, Y. Delnondedieu, L. Desbat, V. Dessenne, A. Hamadeh, D. Henry, N. Laieb, S. Lavallee, J. M. Lefebvre, F. Leitner, Y. Menguy, F. Padieu, O. Peria, A. Poyet, M. Promayon, S. Rouault, P. Sautot, J. Troccaz, and P. Vassal, “Computer assisted medical interventions,” IEEE. Eng. Med. Biol. Mag 14, 254–263 (1995).
[Crossref]

IEEE. Trans. Ultrason. Ferroelectr. Freq. Control (1)

L. Pai-Chi, C. Chong-Jing, and Y. Chih-Kuang, “On velocity estimation using speckle decorrelation” IEEE. Trans. Ultrason. Ferroelectr. Freq. Control 48, 1084–1091 (2001).
[Crossref]

J. Biomed. Opt (7)

K. W. Gossage, T. S. Tkaczyk, J. J. Rodriguez, and J. K. Barton, “Texture analysis of optical coherence tomography images: feasibility for tissue classification,” J. Biomed. Opt 8, 570–575 (2003).
[Crossref] [PubMed]

D. D. Duncan and S. J. Kirkpatrick, ”Processing algorithms for tracking speckle shifts in optical elastography of biological tissues,” J. Biomed. Opt 6, 418–426 (2001).
[Crossref] [PubMed]

J. M. Schmitt, S. H. Xiang, and K. M. Yung, ”Speckle in optical coherence tomography,” J. Biomed. Opt 4, 95–105 (1999).
[Crossref]

W. Luo, D. L. Marks, T. S. Ralston, and S. A. Boppart, ”Three-dimensional optical coherence tomography of the embryonic murine cardiovascular system,” J. Biomed. Opt 11, 021014–021018 (2006).
[Crossref] [PubMed]

A. M. Zysk and S. A. Boppart, ”Computational methods for analysis of human breast tumor tissue in optical coherence tomography images,” J. Biomed. Opt 11, 054015 (2006).
[Crossref] [PubMed]

A. M. Zysk, F. T. Nguyen, A. L. Oldenburg, D. L. Marks, and S. A. Boppart, “Optical coherence tomography: a review of clinical development from bench to bedside,” J. Biomed. Opt 12, 051403–051421 (2007).
[Crossref] [PubMed]

S. Han, M. V. Sarunic, J. Wu, M. Humayun, and C. Yang, “Handheld forward-imaging needle endoscope for ophthalmic optical coherence tomography inspection,” J. Biomed. Opt 13, 020505 (2008).
[Crossref] [PubMed]

J. Opt. Soc. Am. A (1)

Med. Image Anal (1)

A. H. Gee, R. James Housden, P. Hassenpflug, G. M. Treece, and R. W. Prager, “Sensorless freehand 3D ultrasound in real tissue: Speckle decorrelation without fully developed speckle,” Med. Image Anal 10, 137–149 (2006).
[Crossref]

Opt. Express (7)

R. Huber, M. Wojtkowski, and J. G. Fujimoto, “Fourier domain mode locking (FDML): A new laser operating regime and applications for optical coherence tomography,” Opt. Express 14, 3225–3237 (2006).
[Crossref] [PubMed]

J. J. Pasquesi, S. C. Schlachter, M. D. Boppart, E. J. Chaney, S. J. Kaufman, and S. A. Boppart, “In vivo detection of exercise-induced ultrastructural changes in genetically-altered murine skeletal muscle using polarization-sensitive optical coherence tomography,” Opt. Express 14, 1547–1556 (2006).
[Crossref] [PubMed]

A. L. Oldenburg, V. Crecea, S. A. Rinne, and S. A. Boppart, “Phase-resolved magnetomotive OCT for imaging nanomolar concentrations of magnetic nanoparticles in tissues,” Opt. Express 16, 11525–11539 (2008).
[PubMed]

S. H. Yun, G. J. Tearney, J. F. de Boer, and B. E. Bouma, ”Motion artifacts in optical coherence tomography with frequency-domain ranging,” Opt. Express 12, 2977–2998 (2004).
[Crossref] [PubMed]

M. Wojtkowski, V. J. Srinivasan, T. H. Ko, J. G. Fujimoto, A. Kowalczyk, and J. S. Duker, ”Ultrahigh-resolution, high-speed, fourier domain optical coherence tomography and methods for dispersion compensation,” Opt. Express 12, 2404–2422 (2004).
[Crossref] [PubMed]

D. D. Duncan and S. J. Kirkpatrick, ”Performance analysis of a maximum-likelihood speckle motion estimator,” Opt. Express 10, 927–941 (2002).
[PubMed]

S. J. Kirkpatrick, R. K. Wang, and D. D. Duncan, “OCT-based elastography for large and small deformations,” Opt. Express 14, 11585–11597 (2006).
[Crossref] [PubMed]

Opt. Lett. (2)

Radiology (1)

T. A Tuthill, J. F. Krucker, J. B. Fowlkes, and P. L. Carson, “Automated three-dimensional US frame positioning computed from elevational speckle decorrelation,” Radiology 209, 575–582 (1998).
[PubMed]

Science (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Tissue Eng (1)

H.-J. Ko, W. Tan, R. Stack, and S. A. Boppart, ”Optical coherence elastography of engineered and developing tissue,” Tissue Eng 12, 63–73 (2006).
[Crossref] [PubMed]

Ultrason. Imaging (1)

P. C. Li, C. Y. Li, and W. C. Yeh, “Tissue motion and elevational speckle decorrelation in freehand 3D ultrasound,” Ultrason. Imaging 24, 1–12 (2002).
[PubMed]

Ultrasonics (1)

R. J. Housden, A. H. Gee, R. W. Prager, and G. M. Treece, ”Rotational motion in sensorless freehand three-dimensional ultrasound,” Ultrasonics 48, 412–422 (2008).
[Crossref] [PubMed]

Ultrasound Med. Biol (4)

R. J. Housden, A. H. Gee, G. M. Treece, and R. W. Prager, ”Subsample interpolation strategies for sensorless freehand 3D ultrasound,” Ultrasound Med. Biol 32, 1897–1904 (2006).
[Crossref] [PubMed]

R. W. Prager, A. H. Gee, G. M. Treece, C. J. C. Cash, and L. H. Berman, “Sensorless freehand 3-D ultrasound using regression of the echo intensity,” Ultrasound Med. Biol 29, 437–446 (2003).
[Crossref] [PubMed]

L. Mercier, T. Langø, F. Lindseth, and D. L. Collins, “A review of calibration techniques for freehand 3-D ultrasound systems,” Ultrasound Med. Biol 31, 449–471 (2005).
[Crossref] [PubMed]

P. Hassenpflug, R. W. Prager, G. M. Treece, and A. H. Gee, “Speckle classification for sensorless freehand 3-D ultrasound,” Ultrasound Med. Biol 31, 1499–1508 (2005).
[Crossref] [PubMed]

Other (3)

W. Drexler and J. G. Fujimoto, Optical coherence tomography: technology and applications (Springer, New York2008).
[Crossref]

F. I. Feldchtein, V. M. Gelikonov, and G. V. Gelikonov, “Design of OCT scanners” in Handbook of optical coherence tomography (Marcel Dekker, Inc, 2002).

A. Krupa, G. Fichtinger, and G. D. Hager, “Full Motion Tracking in Ultrasound Using Image Speckle Information and Visual Servoing,” in Proceedings of IEEE International Conference on Robotics and Automation (2007), pp. 2458–2464.
[Crossref]

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Figures (7)

Fig. 1.
Fig. 1.

(a) Flow chart representation of the algorithm. (b) The cross-correlation between A-scans decreases with the lateral displacement of the beam. The raw dataset contains A-scans uniformly placed in time, but due to non-uniform manual scanning, the successive A-scans have non-uniform displacement. The assembled image consists of A-scans selected by the algorithm which are uniformly spaced in distance.

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Fig. 2.
Fig. 2.

Decorrelation curves obtained from galvanometer-scanned images of several tissue phantom samples and biological tissues (negative distance corresponds to the cross-correlation between the current A-scan and previously acquired A-scans). The tissue phantom was a silicone-based sample with titanium dioxide (TiO2) scattering particles.

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Fig. 3.
Fig. 3.

Results with a silicone-based tissue phantom with titanium dioxide (TiO2) scattering particles. (a) Decorrelation curve as a function of lateral distance. The solid curve is the mean and the dotted curves are the standard deviations of the correlation coefficients. (b) A-scan Redundancy Ratio (ARR) as computed by the algorithm for various sample scan velocities. The error bars show one standard deviation above and below the mean.

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Fig. 4.
Fig. 4.

Image assembly for a silicone-based tissue phantom with titanium dioxide (TiO2) scattering particles. (a) Motorized stage scanned image (uniformly sampled in distance and time). (b) Non-uniformly scanned image (sampled non-uniformly in distance but uniformly in time). (c) Assembled image using A-scan selection algorithm (compensated for non-uniform sampling in distance). (d) Cross-correlation matrix with red points showing the A-scans selected for image assembly by the algorithm.

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Fig. 5.
Fig. 5.

Image assembly for a plasticine sample over a sample length of 1 cm. (a) Uniformly scanned image using a motorized stage. (b) Non-uniform hand-scanned image. (c) Assembled image. (d) Cross-correlation matrix with red points showing the A-scans selected for image assembly.

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Fig. 6.
Fig. 6.

Image assembly for human adipose tissue over a sample length of 1.5 mm. (a) Galvanometer-scanned image. (b) Non-uniform hand-scanned image. (c) Assembled image. (d) Cross-correlation matrix with red points showing the A-scans selected for image assembly.

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Fig. 7.
Fig. 7.

Image assembly for a human breast tissue over a sample length of 1 cm. (a) Uniformly scanned image using a motorized stage. (b) Non-uniform hand-scanned image. (c) Assembled image. (d) Cross-correlation matrix with red points showing the A-scans selected for image assembly.

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Equations (2)

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ζ=fsΔxv
ρ(i,j)=<(Ii−μi)(Ij−μj)>σiσj

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