Abstract

An optically based rigid-body six-degrees of freedom (DOF) measurement system optimized for prospective (real-time) motion correction in magnetic resonance imaging (MRI) applications is described. By optimizing system capabilities to the specific applications requirements, the six-DOF measurement is accomplished using a single camera and simple three-disc fiducial at rates of 50Hz. The algorithm utilizes successive approximation to solve the three point pose problem for angles close to the origin. Convergence to submicroradian levels occurs within 20 iterations for angles in an approximate half- radian (29°) arc centered on the origin. The overall absolute accuracy of the instrument is 10100μm for translational and <100μrad (0.005°) for rotational motions. Results for head nodding and speech tasks are presented for subjects in the MR scanner, and the instrument results are compared to standard prospective acquisition correction.

© 2011 Optical Society of America

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References

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  1. T. J. Silk, A. Vance, N. Rinehart, J. L. Bradshaw, and R. Cunnington, “Dysfunction in the fronto-parietal network in attention deficit hyperactivity disorder (ADHD): an fMRI study,” Brain Imaging and Behavior 2, 123–131 (2008).
    [CrossRef]
  2. M. Schulte-Ruther, E. Greimel, H. J. Markowitsch, I. Kamp-Becker, H. Remschmidt, G. R. Fink, and M. Piefke, “Dysfunctions in brain networks supporting empathy: an fMRI study in adults with autism spectrum disorders,” Soc. Neurosci. 6(1), 1–21 (2011).
    [CrossRef]
  3. C. Dold, M. Zaitsev, O. Speck, E. A. Firle, J. Hennig, and G. Sakas, “Advantages and limitations of prospective head motion compensation for MRI using an optical motion tracking device,” Acad. Radiol. 13, 1093–1103 (2006).
    [CrossRef] [PubMed]
  4. M. Tremblay, F. Tam, and S. J. Graham, “Retrospective coregistration of functional magnetic resonance imaging data using external monitoring,” Magn. Reson. Med. 53, 141–149 (2005).
    [CrossRef] [PubMed]
  5. T. Lerner, E. Rivlin, and M. Gur, “Vision based tracking system for head motion correction in fMRI images,” Commun. Comput. Inf. Sci. 4, 381–394 (2007).
    [CrossRef]
  6. L. Qin, P. van Gelderen, J. A. Derbyshire, F. Jin, J. Lee, J. A. de Zwart, Y. Tao, and J. H. Duyn, “Prospective head movement correction for high resolution MRI using an in-bore optical tracking system,” Magn. Reson. Med. 62, 924–934 (2009).
    [CrossRef] [PubMed]
  7. K. K. Gunnam, D. C. Hughes, J. L. Junkins, and N. Kehtarnavaz, “A vision-based DSP embedded navigation sensor,” IEEE Sens. J. 2, 428–442 (2002).
    [CrossRef]
  8. B. M. Haralick, C.-N. Lee, K. Ottenberg, and M. Nölle, “Analysis and solutions of the three point perspective pose estimation problem,” Proceedings CVPR ’91 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (1991), pp. 592–598.
  9. C. B. Bose and I. Amir, “Design of fiducials for accurate registration using machine vision,” IEEE Trans. Pattern Anal. Machine Intell. 12, 1196–1200 (1990).
    [CrossRef]
  10. A. Efrat and C. Gotsman, “Subpixel image registration using circular fiducials,” Int. J. Comput. Geom. Ap. 4, 403–422 (1994).
    [CrossRef]
  11. J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Machine Intell. 14, 965–980 (1992).
    [CrossRef]
  12. M. W. Spong, Robot Modeling and Control (Wiley, 2005).
  13. S. Thesen, O. Heid, E. Mueller, and L. R. Schad, “Prospective acquisition correction for head motion with image-based tracking for real-time fMRI,” Magn. Reson. Med. 44, 457–465 (2000).
    [CrossRef] [PubMed]

2011 (1)

M. Schulte-Ruther, E. Greimel, H. J. Markowitsch, I. Kamp-Becker, H. Remschmidt, G. R. Fink, and M. Piefke, “Dysfunctions in brain networks supporting empathy: an fMRI study in adults with autism spectrum disorders,” Soc. Neurosci. 6(1), 1–21 (2011).
[CrossRef]

2009 (1)

L. Qin, P. van Gelderen, J. A. Derbyshire, F. Jin, J. Lee, J. A. de Zwart, Y. Tao, and J. H. Duyn, “Prospective head movement correction for high resolution MRI using an in-bore optical tracking system,” Magn. Reson. Med. 62, 924–934 (2009).
[CrossRef] [PubMed]

2008 (1)

T. J. Silk, A. Vance, N. Rinehart, J. L. Bradshaw, and R. Cunnington, “Dysfunction in the fronto-parietal network in attention deficit hyperactivity disorder (ADHD): an fMRI study,” Brain Imaging and Behavior 2, 123–131 (2008).
[CrossRef]

2007 (1)

T. Lerner, E. Rivlin, and M. Gur, “Vision based tracking system for head motion correction in fMRI images,” Commun. Comput. Inf. Sci. 4, 381–394 (2007).
[CrossRef]

2006 (1)

C. Dold, M. Zaitsev, O. Speck, E. A. Firle, J. Hennig, and G. Sakas, “Advantages and limitations of prospective head motion compensation for MRI using an optical motion tracking device,” Acad. Radiol. 13, 1093–1103 (2006).
[CrossRef] [PubMed]

2005 (1)

M. Tremblay, F. Tam, and S. J. Graham, “Retrospective coregistration of functional magnetic resonance imaging data using external monitoring,” Magn. Reson. Med. 53, 141–149 (2005).
[CrossRef] [PubMed]

2002 (1)

K. K. Gunnam, D. C. Hughes, J. L. Junkins, and N. Kehtarnavaz, “A vision-based DSP embedded navigation sensor,” IEEE Sens. J. 2, 428–442 (2002).
[CrossRef]

2000 (1)

S. Thesen, O. Heid, E. Mueller, and L. R. Schad, “Prospective acquisition correction for head motion with image-based tracking for real-time fMRI,” Magn. Reson. Med. 44, 457–465 (2000).
[CrossRef] [PubMed]

1994 (1)

A. Efrat and C. Gotsman, “Subpixel image registration using circular fiducials,” Int. J. Comput. Geom. Ap. 4, 403–422 (1994).
[CrossRef]

1992 (1)

J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Machine Intell. 14, 965–980 (1992).
[CrossRef]

1990 (1)

C. B. Bose and I. Amir, “Design of fiducials for accurate registration using machine vision,” IEEE Trans. Pattern Anal. Machine Intell. 12, 1196–1200 (1990).
[CrossRef]

Amir, I.

C. B. Bose and I. Amir, “Design of fiducials for accurate registration using machine vision,” IEEE Trans. Pattern Anal. Machine Intell. 12, 1196–1200 (1990).
[CrossRef]

Bose, C. B.

C. B. Bose and I. Amir, “Design of fiducials for accurate registration using machine vision,” IEEE Trans. Pattern Anal. Machine Intell. 12, 1196–1200 (1990).
[CrossRef]

Bradshaw, J. L.

T. J. Silk, A. Vance, N. Rinehart, J. L. Bradshaw, and R. Cunnington, “Dysfunction in the fronto-parietal network in attention deficit hyperactivity disorder (ADHD): an fMRI study,” Brain Imaging and Behavior 2, 123–131 (2008).
[CrossRef]

Cohen, P.

J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Machine Intell. 14, 965–980 (1992).
[CrossRef]

Cunnington, R.

T. J. Silk, A. Vance, N. Rinehart, J. L. Bradshaw, and R. Cunnington, “Dysfunction in the fronto-parietal network in attention deficit hyperactivity disorder (ADHD): an fMRI study,” Brain Imaging and Behavior 2, 123–131 (2008).
[CrossRef]

de Zwart, J. A.

L. Qin, P. van Gelderen, J. A. Derbyshire, F. Jin, J. Lee, J. A. de Zwart, Y. Tao, and J. H. Duyn, “Prospective head movement correction for high resolution MRI using an in-bore optical tracking system,” Magn. Reson. Med. 62, 924–934 (2009).
[CrossRef] [PubMed]

Derbyshire, J. A.

L. Qin, P. van Gelderen, J. A. Derbyshire, F. Jin, J. Lee, J. A. de Zwart, Y. Tao, and J. H. Duyn, “Prospective head movement correction for high resolution MRI using an in-bore optical tracking system,” Magn. Reson. Med. 62, 924–934 (2009).
[CrossRef] [PubMed]

Dold, C.

C. Dold, M. Zaitsev, O. Speck, E. A. Firle, J. Hennig, and G. Sakas, “Advantages and limitations of prospective head motion compensation for MRI using an optical motion tracking device,” Acad. Radiol. 13, 1093–1103 (2006).
[CrossRef] [PubMed]

Duyn, J. H.

L. Qin, P. van Gelderen, J. A. Derbyshire, F. Jin, J. Lee, J. A. de Zwart, Y. Tao, and J. H. Duyn, “Prospective head movement correction for high resolution MRI using an in-bore optical tracking system,” Magn. Reson. Med. 62, 924–934 (2009).
[CrossRef] [PubMed]

Efrat, A.

A. Efrat and C. Gotsman, “Subpixel image registration using circular fiducials,” Int. J. Comput. Geom. Ap. 4, 403–422 (1994).
[CrossRef]

Fink, G. R.

M. Schulte-Ruther, E. Greimel, H. J. Markowitsch, I. Kamp-Becker, H. Remschmidt, G. R. Fink, and M. Piefke, “Dysfunctions in brain networks supporting empathy: an fMRI study in adults with autism spectrum disorders,” Soc. Neurosci. 6(1), 1–21 (2011).
[CrossRef]

Firle, E. A.

C. Dold, M. Zaitsev, O. Speck, E. A. Firle, J. Hennig, and G. Sakas, “Advantages and limitations of prospective head motion compensation for MRI using an optical motion tracking device,” Acad. Radiol. 13, 1093–1103 (2006).
[CrossRef] [PubMed]

Gotsman, C.

A. Efrat and C. Gotsman, “Subpixel image registration using circular fiducials,” Int. J. Comput. Geom. Ap. 4, 403–422 (1994).
[CrossRef]

Graham, S. J.

M. Tremblay, F. Tam, and S. J. Graham, “Retrospective coregistration of functional magnetic resonance imaging data using external monitoring,” Magn. Reson. Med. 53, 141–149 (2005).
[CrossRef] [PubMed]

Greimel, E.

M. Schulte-Ruther, E. Greimel, H. J. Markowitsch, I. Kamp-Becker, H. Remschmidt, G. R. Fink, and M. Piefke, “Dysfunctions in brain networks supporting empathy: an fMRI study in adults with autism spectrum disorders,” Soc. Neurosci. 6(1), 1–21 (2011).
[CrossRef]

Gunnam, K. K.

K. K. Gunnam, D. C. Hughes, J. L. Junkins, and N. Kehtarnavaz, “A vision-based DSP embedded navigation sensor,” IEEE Sens. J. 2, 428–442 (2002).
[CrossRef]

Gur, M.

T. Lerner, E. Rivlin, and M. Gur, “Vision based tracking system for head motion correction in fMRI images,” Commun. Comput. Inf. Sci. 4, 381–394 (2007).
[CrossRef]

Haralick, B. M.

B. M. Haralick, C.-N. Lee, K. Ottenberg, and M. Nölle, “Analysis and solutions of the three point perspective pose estimation problem,” Proceedings CVPR ’91 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (1991), pp. 592–598.

Heid, O.

S. Thesen, O. Heid, E. Mueller, and L. R. Schad, “Prospective acquisition correction for head motion with image-based tracking for real-time fMRI,” Magn. Reson. Med. 44, 457–465 (2000).
[CrossRef] [PubMed]

Hennig, J.

C. Dold, M. Zaitsev, O. Speck, E. A. Firle, J. Hennig, and G. Sakas, “Advantages and limitations of prospective head motion compensation for MRI using an optical motion tracking device,” Acad. Radiol. 13, 1093–1103 (2006).
[CrossRef] [PubMed]

Herniou, M.

J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Machine Intell. 14, 965–980 (1992).
[CrossRef]

Hughes, D. C.

K. K. Gunnam, D. C. Hughes, J. L. Junkins, and N. Kehtarnavaz, “A vision-based DSP embedded navigation sensor,” IEEE Sens. J. 2, 428–442 (2002).
[CrossRef]

Jin, F.

L. Qin, P. van Gelderen, J. A. Derbyshire, F. Jin, J. Lee, J. A. de Zwart, Y. Tao, and J. H. Duyn, “Prospective head movement correction for high resolution MRI using an in-bore optical tracking system,” Magn. Reson. Med. 62, 924–934 (2009).
[CrossRef] [PubMed]

Junkins, J. L.

K. K. Gunnam, D. C. Hughes, J. L. Junkins, and N. Kehtarnavaz, “A vision-based DSP embedded navigation sensor,” IEEE Sens. J. 2, 428–442 (2002).
[CrossRef]

Kamp-Becker, I.

M. Schulte-Ruther, E. Greimel, H. J. Markowitsch, I. Kamp-Becker, H. Remschmidt, G. R. Fink, and M. Piefke, “Dysfunctions in brain networks supporting empathy: an fMRI study in adults with autism spectrum disorders,” Soc. Neurosci. 6(1), 1–21 (2011).
[CrossRef]

Kehtarnavaz, N.

K. K. Gunnam, D. C. Hughes, J. L. Junkins, and N. Kehtarnavaz, “A vision-based DSP embedded navigation sensor,” IEEE Sens. J. 2, 428–442 (2002).
[CrossRef]

Lee, C.-N.

B. M. Haralick, C.-N. Lee, K. Ottenberg, and M. Nölle, “Analysis and solutions of the three point perspective pose estimation problem,” Proceedings CVPR ’91 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (1991), pp. 592–598.

Lee, J.

L. Qin, P. van Gelderen, J. A. Derbyshire, F. Jin, J. Lee, J. A. de Zwart, Y. Tao, and J. H. Duyn, “Prospective head movement correction for high resolution MRI using an in-bore optical tracking system,” Magn. Reson. Med. 62, 924–934 (2009).
[CrossRef] [PubMed]

Lerner, T.

T. Lerner, E. Rivlin, and M. Gur, “Vision based tracking system for head motion correction in fMRI images,” Commun. Comput. Inf. Sci. 4, 381–394 (2007).
[CrossRef]

Markowitsch, H. J.

M. Schulte-Ruther, E. Greimel, H. J. Markowitsch, I. Kamp-Becker, H. Remschmidt, G. R. Fink, and M. Piefke, “Dysfunctions in brain networks supporting empathy: an fMRI study in adults with autism spectrum disorders,” Soc. Neurosci. 6(1), 1–21 (2011).
[CrossRef]

Mueller, E.

S. Thesen, O. Heid, E. Mueller, and L. R. Schad, “Prospective acquisition correction for head motion with image-based tracking for real-time fMRI,” Magn. Reson. Med. 44, 457–465 (2000).
[CrossRef] [PubMed]

Nölle, M.

B. M. Haralick, C.-N. Lee, K. Ottenberg, and M. Nölle, “Analysis and solutions of the three point perspective pose estimation problem,” Proceedings CVPR ’91 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (1991), pp. 592–598.

Ottenberg, K.

B. M. Haralick, C.-N. Lee, K. Ottenberg, and M. Nölle, “Analysis and solutions of the three point perspective pose estimation problem,” Proceedings CVPR ’91 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (1991), pp. 592–598.

Piefke, M.

M. Schulte-Ruther, E. Greimel, H. J. Markowitsch, I. Kamp-Becker, H. Remschmidt, G. R. Fink, and M. Piefke, “Dysfunctions in brain networks supporting empathy: an fMRI study in adults with autism spectrum disorders,” Soc. Neurosci. 6(1), 1–21 (2011).
[CrossRef]

Qin, L.

L. Qin, P. van Gelderen, J. A. Derbyshire, F. Jin, J. Lee, J. A. de Zwart, Y. Tao, and J. H. Duyn, “Prospective head movement correction for high resolution MRI using an in-bore optical tracking system,” Magn. Reson. Med. 62, 924–934 (2009).
[CrossRef] [PubMed]

Remschmidt, H.

M. Schulte-Ruther, E. Greimel, H. J. Markowitsch, I. Kamp-Becker, H. Remschmidt, G. R. Fink, and M. Piefke, “Dysfunctions in brain networks supporting empathy: an fMRI study in adults with autism spectrum disorders,” Soc. Neurosci. 6(1), 1–21 (2011).
[CrossRef]

Rinehart, N.

T. J. Silk, A. Vance, N. Rinehart, J. L. Bradshaw, and R. Cunnington, “Dysfunction in the fronto-parietal network in attention deficit hyperactivity disorder (ADHD): an fMRI study,” Brain Imaging and Behavior 2, 123–131 (2008).
[CrossRef]

Rivlin, E.

T. Lerner, E. Rivlin, and M. Gur, “Vision based tracking system for head motion correction in fMRI images,” Commun. Comput. Inf. Sci. 4, 381–394 (2007).
[CrossRef]

Sakas, G.

C. Dold, M. Zaitsev, O. Speck, E. A. Firle, J. Hennig, and G. Sakas, “Advantages and limitations of prospective head motion compensation for MRI using an optical motion tracking device,” Acad. Radiol. 13, 1093–1103 (2006).
[CrossRef] [PubMed]

Schad, L. R.

S. Thesen, O. Heid, E. Mueller, and L. R. Schad, “Prospective acquisition correction for head motion with image-based tracking for real-time fMRI,” Magn. Reson. Med. 44, 457–465 (2000).
[CrossRef] [PubMed]

Schulte-Ruther, M.

M. Schulte-Ruther, E. Greimel, H. J. Markowitsch, I. Kamp-Becker, H. Remschmidt, G. R. Fink, and M. Piefke, “Dysfunctions in brain networks supporting empathy: an fMRI study in adults with autism spectrum disorders,” Soc. Neurosci. 6(1), 1–21 (2011).
[CrossRef]

Silk, T. J.

T. J. Silk, A. Vance, N. Rinehart, J. L. Bradshaw, and R. Cunnington, “Dysfunction in the fronto-parietal network in attention deficit hyperactivity disorder (ADHD): an fMRI study,” Brain Imaging and Behavior 2, 123–131 (2008).
[CrossRef]

Speck, O.

C. Dold, M. Zaitsev, O. Speck, E. A. Firle, J. Hennig, and G. Sakas, “Advantages and limitations of prospective head motion compensation for MRI using an optical motion tracking device,” Acad. Radiol. 13, 1093–1103 (2006).
[CrossRef] [PubMed]

Spong, M. W.

M. W. Spong, Robot Modeling and Control (Wiley, 2005).

Tam, F.

M. Tremblay, F. Tam, and S. J. Graham, “Retrospective coregistration of functional magnetic resonance imaging data using external monitoring,” Magn. Reson. Med. 53, 141–149 (2005).
[CrossRef] [PubMed]

Tao, Y.

L. Qin, P. van Gelderen, J. A. Derbyshire, F. Jin, J. Lee, J. A. de Zwart, Y. Tao, and J. H. Duyn, “Prospective head movement correction for high resolution MRI using an in-bore optical tracking system,” Magn. Reson. Med. 62, 924–934 (2009).
[CrossRef] [PubMed]

Thesen, S.

S. Thesen, O. Heid, E. Mueller, and L. R. Schad, “Prospective acquisition correction for head motion with image-based tracking for real-time fMRI,” Magn. Reson. Med. 44, 457–465 (2000).
[CrossRef] [PubMed]

Tremblay, M.

M. Tremblay, F. Tam, and S. J. Graham, “Retrospective coregistration of functional magnetic resonance imaging data using external monitoring,” Magn. Reson. Med. 53, 141–149 (2005).
[CrossRef] [PubMed]

van Gelderen, P.

L. Qin, P. van Gelderen, J. A. Derbyshire, F. Jin, J. Lee, J. A. de Zwart, Y. Tao, and J. H. Duyn, “Prospective head movement correction for high resolution MRI using an in-bore optical tracking system,” Magn. Reson. Med. 62, 924–934 (2009).
[CrossRef] [PubMed]

Vance, A.

T. J. Silk, A. Vance, N. Rinehart, J. L. Bradshaw, and R. Cunnington, “Dysfunction in the fronto-parietal network in attention deficit hyperactivity disorder (ADHD): an fMRI study,” Brain Imaging and Behavior 2, 123–131 (2008).
[CrossRef]

Weng, J.

J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Machine Intell. 14, 965–980 (1992).
[CrossRef]

Zaitsev, M.

C. Dold, M. Zaitsev, O. Speck, E. A. Firle, J. Hennig, and G. Sakas, “Advantages and limitations of prospective head motion compensation for MRI using an optical motion tracking device,” Acad. Radiol. 13, 1093–1103 (2006).
[CrossRef] [PubMed]

Acad. Radiol. (1)

C. Dold, M. Zaitsev, O. Speck, E. A. Firle, J. Hennig, and G. Sakas, “Advantages and limitations of prospective head motion compensation for MRI using an optical motion tracking device,” Acad. Radiol. 13, 1093–1103 (2006).
[CrossRef] [PubMed]

Brain Imaging and Behavior (1)

T. J. Silk, A. Vance, N. Rinehart, J. L. Bradshaw, and R. Cunnington, “Dysfunction in the fronto-parietal network in attention deficit hyperactivity disorder (ADHD): an fMRI study,” Brain Imaging and Behavior 2, 123–131 (2008).
[CrossRef]

Commun. Comput. Inf. Sci. (1)

T. Lerner, E. Rivlin, and M. Gur, “Vision based tracking system for head motion correction in fMRI images,” Commun. Comput. Inf. Sci. 4, 381–394 (2007).
[CrossRef]

IEEE Sens. J. (1)

K. K. Gunnam, D. C. Hughes, J. L. Junkins, and N. Kehtarnavaz, “A vision-based DSP embedded navigation sensor,” IEEE Sens. J. 2, 428–442 (2002).
[CrossRef]

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

C. B. Bose and I. Amir, “Design of fiducials for accurate registration using machine vision,” IEEE Trans. Pattern Anal. Machine Intell. 12, 1196–1200 (1990).
[CrossRef]

J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Machine Intell. 14, 965–980 (1992).
[CrossRef]

Int. J. Comput. Geom. Ap. (1)

A. Efrat and C. Gotsman, “Subpixel image registration using circular fiducials,” Int. J. Comput. Geom. Ap. 4, 403–422 (1994).
[CrossRef]

Magn. Reson. Med. (3)

S. Thesen, O. Heid, E. Mueller, and L. R. Schad, “Prospective acquisition correction for head motion with image-based tracking for real-time fMRI,” Magn. Reson. Med. 44, 457–465 (2000).
[CrossRef] [PubMed]

L. Qin, P. van Gelderen, J. A. Derbyshire, F. Jin, J. Lee, J. A. de Zwart, Y. Tao, and J. H. Duyn, “Prospective head movement correction for high resolution MRI using an in-bore optical tracking system,” Magn. Reson. Med. 62, 924–934 (2009).
[CrossRef] [PubMed]

M. Tremblay, F. Tam, and S. J. Graham, “Retrospective coregistration of functional magnetic resonance imaging data using external monitoring,” Magn. Reson. Med. 53, 141–149 (2005).
[CrossRef] [PubMed]

Soc. Neurosci. (1)

M. Schulte-Ruther, E. Greimel, H. J. Markowitsch, I. Kamp-Becker, H. Remschmidt, G. R. Fink, and M. Piefke, “Dysfunctions in brain networks supporting empathy: an fMRI study in adults with autism spectrum disorders,” Soc. Neurosci. 6(1), 1–21 (2011).
[CrossRef]

Other (2)

B. M. Haralick, C.-N. Lee, K. Ottenberg, and M. Nölle, “Analysis and solutions of the three point perspective pose estimation problem,” Proceedings CVPR ’91 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (1991), pp. 592–598.

M. W. Spong, Robot Modeling and Control (Wiley, 2005).

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Figures (10)

Fig. 1
Fig. 1

Graphical diagram of the motion tracking instrument in the context of an fMRI protocol that includes a projector display for visual cues. For clarity, the scanner and head coil are shown in cut-away view and the mirror allowing the patient to view the projector screen is deleted.

Fig. 2
Fig. 2

Three-dimensional, rotation/translation centroid invariant optical fiducial targets used to determine the six degrees of motional freedom.

Fig. 3
Fig. 3

Photographs of system components. A, mirror and target mounted on a mock patient in the scanner; B, the optical and MRI readable fiducial mounted onto eyeglasses.

Fig. 4
Fig. 4

Flow chart for angle estimation algorithm. A fixed number of 20 iterations was used due to the requirement of real-time measurement.

Fig. 5
Fig. 5

Stalk-mounted target T2 shows an excess of movement under x and y axis rotations as compared to target T3. Rotation about the z axis mixes the relation.

Fig. 6
Fig. 6

Convergence for angles x, y, and z = 0.27 rad versus iteration from one to 20 cycles. Horizontal axis is loop iteration number, vertical axis is log10 of error magnitude in radians. Ten iterations of Newton’s Method were used to locate zeros in each cycle.

Fig. 7
Fig. 7

Contours showing the convergence performance of the angle finding algorithm for three cases of angle z and across a range of angles x and y. The contour units are log10 norm of angle error in radians. The horizontal axis shows changes in angle x in radians. The vertical axis shows changes in angle y in radians. From top to bottom the plots show z angles of + 0.31 , 0, and 0.31 rad , respectively. The dotted box represents an arc of approximately 0.62 rad ( 36 ° ) in x and y centered on the origin.

Fig. 8
Fig. 8

Measured error in translation using a single translation stage with no mechanical coupling to other stages. RMS of residual error from linear fit is 1.8 um . The error trend is consistent with foreshortening due to a 1.6 mrad stage x y misalignment ( 0.090 ° ).

Fig. 9
Fig. 9

Measured six degrees of freedom differential motion versus time for head nod movement of a subject in a 3 T scanner. Superimposed on the time series measured by the camera is the differential motion calculated from the PACE algorithm of the scanner. Head nodding occurred between approximately 18 and 30 s and between 43 and 56 s.

Fig. 10
Fig. 10

Measured six degrees of freedom differential motion versus time for counting aloud for a subject in a 3 T scanner. Superimposed on the time series measured by the camera is the differential motion calculated from the PACE algorithm of the scanner. Counting aloud occurred between approximately 7 and 20 s.

Tables (1)

Tables Icon

Table 1 Comparison of System Performance for Static Bench Measurements (Column 1), Six Axis Dynamic Bench Test with Calibrated Motions (Column 2), and Static Measure of Scanner Structure (Column 3). a

Equations (11)

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

R x = [ 1 0 0 0 cos ( θ x ) sin ( θ x ) 0 sin ( θ x ) cos ( θ x ) ] ,
R y = [ cos ( θ y ) 0 sin ( θ y ) 0 1 0 sin ( θ y ) 0 cos ( θ y ) ] ,
R z = [ cos ( θ z ) sin ( θ z ) 0 sin ( θ z ) cos ( θ z ) 0 0 0 1 ] .
R z R y R x ( x n x 1 , y n y 1 , z n z 1 ) T = ( x n x 1 , y n y 1 , z n z 1 ) T .
R z R y R x ( x n x 1 , y n y 1 , z n z 1 ) T ( x n x 1 , y n y 1 , z n z 1 ) T = 0.
{ ( x 2 x 1 ) cos ( θ y ) [ ( y 2 y 1 ) sin ( θ x ) + ( z 2 z 1 ) cos ( θ x ) ] sin ( θ y ) } cos ( θ z ) + [ ( y 2 y 1 ) cos ( θ x ) + ( z 2 z 1 ) sin ( θ x ) ] sin ( θ z ) ( x 2 x 1 ) = 0 ,
{ ( x 2 x 1 ) cos ( θ y ) [ ( y 2 y 1 ) sin ( θ x ) + ( z 2 z 1 ) cos ( θ x ) ] sin ( θ y ) } sin ( θ z ) + [ ( y 2 y 1 ) cos ( θ x ) + ( z 2 z 1 ) sin ( θ x ) ] cos ( θ z ) ( y 2 y 1 ) = 0 ,
( x 2 x 1 ) sin ( θ y ) + [ ( y 2 y 1 ) sin ( θ x ) + ( z 2 z 1 ) cos ( θ x ) ] cos ( θ y ) ( z 2 z 1 ) = 0 ,
{ ( x 3 x 1 ) cos ( θ y ) [ ( y 3 y 1 ) sin ( θ x ) + ( z 3 z 1 ) cos ( θ x ) ] sin ( θ y ) } cos ( θ z ) + [ ( y 3 y 1 ) cos ( θ x ) + ( z 3 z 1 ) sin ( θ x ) ] sin ( θ z ) ( x 3 x 1 ) = 0 ,
{ ( x 3 x 1 ) cos ( θ y ) [ ( y 3 y 1 ) sin ( θ x ) + ( z 3 z 1 ) cos ( θ x ) ] sin ( θ y ) } sin ( θ z ) + [ ( y 3 y 1 ) cos ( θ x ) + ( z 3 z 1 ) sin ( θ x ) ] cos ( θ z ) ( y 3 y 1 ) = 0 ,
( x 3 x 1 ) sin ( θ y ) + [ ( y 3 y 1 ) sin ( θ x ) + ( z 3 z 1 ) cos ( θ x ) ] cos ( θ y ) ( z 3 z 1 ) = 0.

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