Abstract

A common approach to structured light-illumination measurement is to encode a surface topology successively with binary light-stripe patterns of variable spatial frequency. Each surface location is thereby encoded with a binary sequence associated with its height. By analyzing the lateral displacements of the reflected encoded pattern, one can reconstruct the surface topology without ambiguity. We present a model for multistripe analysis in terms of an information channel for which the maximum spatial stripe frequency is related to channel capacity and maximized accordingly by use of Shannon’s theorems. The objective is to improve lateral resolution through optimized spatial frequency while maintaining a fixed range resolution. Given an optimized spatial frequency, a technique is presented to enhance lateral resolution further by multiplexing the light structure. Theoretical and numerical results are compared with experimental data.

© 1998 Optical Society of America

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References

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  1. G. Schmaltz, “A method for presenting the profile curves of rough surfaces,” Naturwissenschaften 18, 315–316 (1932).
    [CrossRef]
  2. A. Jarvis, “A perspective on range finding techniques for computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. 5, 122–139 (1983).
    [CrossRef] [PubMed]
  3. D. Poussart and D. Laurendeau, “3-D sensing for industrial computer vision,” in Advances in Machine Vision, J. L. C. Sanz, ed. (Springer-Verlag, New York, 1989).
    [CrossRef]
  4. J. K. Aggarwal and Y. F. Wang, “Inference of object surface structure from structured lighting—an overview,” in Machine Vision, Herbert Freeman, ed. (Academic, Boston, 1988), pp. 193–220.
  5. D. Ashley, D. Goodman, L. G. Hassebrook, and R. Solomon, “Printed circuit line height measuring techniques,” IBM Tech. Discl. Bull. 27, 2870–2873 (1984).
  6. P. M. Will and K. S. Pennington, “Grid coding: a preprocessing technique for robot and machine vision,” Artif. Intell. 2, 319–329 (1971).
    [CrossRef]
  7. K. Biderman, “Image encoding in modulated gratings from 1899–1970,” Opt. Acta 17, 631–635 (1970).
  8. L. G. Hassebrook, “Sine sectioning illumination method,” IBM Tech. Discl. Bull. 27, 3553–3554 (1984).
  9. P. Wu, F. Yu, Z. Li, Z. Yan, and Y. Shun, “Analysis technique for the measurement of a three-dimensional object shape,” Appl. Opt. 32, 737–742 (1993).
    [CrossRef] [PubMed]
  10. D. S. Goodman and L. G. Hassebrook, “Surface contour measuring instrument,” IBM Tech. Discl. Bull. 27, 2671–2673 (1984).
  11. K. L. Boyer and A. C. Kak, “Colored-encoded structured light for rapid active ranging,” IEEE Trans. Pattern Anal. Mach. Intell. 9, 14–28 (1987).
    [CrossRef] [PubMed]
  12. R. C. Daley, L. G. Hassebrook, and M. E. Lhamon, “Topographical analysis with time modulated structured light,” in Visual Information Processing IV, F. O. Huck and R. D. Juday, eds. Proc. SPIE 2488, 396–407 (1995).
    [CrossRef]
  13. P. F. Jones and G. J. M. Aitken, “Comparison of three three-dimensional imaging systems,” J. Opt. Soc. Am. A 11, 2613–2621 (1994).
    [CrossRef]
  14. E. Müller, “Fast three-dimensional form measurement system,” Opt. Eng. 34, 2754–2756 (1995).
    [CrossRef]
  15. S. Haykin, Digital Communications (Wiley, New York, 1988).
  16. L. D. Dickson, “Characteristics of a propagating Gaussian beam,” Appl. Opt. 9, 1854–1861 (1970).
    [CrossRef] [PubMed]
  17. R. C. Daley and L. G. Hassebrook, “Improved light sectioning resolution by optimized thresholding,” in Three-Dimensional and Laser-Based Systems for Metrology and Inspection II, K. G. Harding and D. J. Svetkoff, eds., Proc. SPIE 2909, 151–161 (1996).
    [CrossRef]

1995

E. Müller, “Fast three-dimensional form measurement system,” Opt. Eng. 34, 2754–2756 (1995).
[CrossRef]

1994

1993

1987

K. L. Boyer and A. C. Kak, “Colored-encoded structured light for rapid active ranging,” IEEE Trans. Pattern Anal. Mach. Intell. 9, 14–28 (1987).
[CrossRef] [PubMed]

1984

L. G. Hassebrook, “Sine sectioning illumination method,” IBM Tech. Discl. Bull. 27, 3553–3554 (1984).

D. S. Goodman and L. G. Hassebrook, “Surface contour measuring instrument,” IBM Tech. Discl. Bull. 27, 2671–2673 (1984).

D. Ashley, D. Goodman, L. G. Hassebrook, and R. Solomon, “Printed circuit line height measuring techniques,” IBM Tech. Discl. Bull. 27, 2870–2873 (1984).

1983

A. Jarvis, “A perspective on range finding techniques for computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. 5, 122–139 (1983).
[CrossRef] [PubMed]

1971

P. M. Will and K. S. Pennington, “Grid coding: a preprocessing technique for robot and machine vision,” Artif. Intell. 2, 319–329 (1971).
[CrossRef]

1970

K. Biderman, “Image encoding in modulated gratings from 1899–1970,” Opt. Acta 17, 631–635 (1970).

L. D. Dickson, “Characteristics of a propagating Gaussian beam,” Appl. Opt. 9, 1854–1861 (1970).
[CrossRef] [PubMed]

1932

G. Schmaltz, “A method for presenting the profile curves of rough surfaces,” Naturwissenschaften 18, 315–316 (1932).
[CrossRef]

Aggarwal, J. K.

J. K. Aggarwal and Y. F. Wang, “Inference of object surface structure from structured lighting—an overview,” in Machine Vision, Herbert Freeman, ed. (Academic, Boston, 1988), pp. 193–220.

Aitken, G. J. M.

Ashley, D.

D. Ashley, D. Goodman, L. G. Hassebrook, and R. Solomon, “Printed circuit line height measuring techniques,” IBM Tech. Discl. Bull. 27, 2870–2873 (1984).

Biderman, K.

K. Biderman, “Image encoding in modulated gratings from 1899–1970,” Opt. Acta 17, 631–635 (1970).

Boyer, K. L.

K. L. Boyer and A. C. Kak, “Colored-encoded structured light for rapid active ranging,” IEEE Trans. Pattern Anal. Mach. Intell. 9, 14–28 (1987).
[CrossRef] [PubMed]

Daley, R. C.

R. C. Daley, L. G. Hassebrook, and M. E. Lhamon, “Topographical analysis with time modulated structured light,” in Visual Information Processing IV, F. O. Huck and R. D. Juday, eds. Proc. SPIE 2488, 396–407 (1995).
[CrossRef]

R. C. Daley and L. G. Hassebrook, “Improved light sectioning resolution by optimized thresholding,” in Three-Dimensional and Laser-Based Systems for Metrology and Inspection II, K. G. Harding and D. J. Svetkoff, eds., Proc. SPIE 2909, 151–161 (1996).
[CrossRef]

Dickson, L. D.

Goodman, D.

D. Ashley, D. Goodman, L. G. Hassebrook, and R. Solomon, “Printed circuit line height measuring techniques,” IBM Tech. Discl. Bull. 27, 2870–2873 (1984).

Goodman, D. S.

D. S. Goodman and L. G. Hassebrook, “Surface contour measuring instrument,” IBM Tech. Discl. Bull. 27, 2671–2673 (1984).

Hassebrook, L. G.

D. S. Goodman and L. G. Hassebrook, “Surface contour measuring instrument,” IBM Tech. Discl. Bull. 27, 2671–2673 (1984).

L. G. Hassebrook, “Sine sectioning illumination method,” IBM Tech. Discl. Bull. 27, 3553–3554 (1984).

D. Ashley, D. Goodman, L. G. Hassebrook, and R. Solomon, “Printed circuit line height measuring techniques,” IBM Tech. Discl. Bull. 27, 2870–2873 (1984).

R. C. Daley and L. G. Hassebrook, “Improved light sectioning resolution by optimized thresholding,” in Three-Dimensional and Laser-Based Systems for Metrology and Inspection II, K. G. Harding and D. J. Svetkoff, eds., Proc. SPIE 2909, 151–161 (1996).
[CrossRef]

R. C. Daley, L. G. Hassebrook, and M. E. Lhamon, “Topographical analysis with time modulated structured light,” in Visual Information Processing IV, F. O. Huck and R. D. Juday, eds. Proc. SPIE 2488, 396–407 (1995).
[CrossRef]

Haykin, S.

S. Haykin, Digital Communications (Wiley, New York, 1988).

Jarvis, A.

A. Jarvis, “A perspective on range finding techniques for computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. 5, 122–139 (1983).
[CrossRef] [PubMed]

Jones, P. F.

Kak, A. C.

K. L. Boyer and A. C. Kak, “Colored-encoded structured light for rapid active ranging,” IEEE Trans. Pattern Anal. Mach. Intell. 9, 14–28 (1987).
[CrossRef] [PubMed]

Laurendeau, D.

D. Poussart and D. Laurendeau, “3-D sensing for industrial computer vision,” in Advances in Machine Vision, J. L. C. Sanz, ed. (Springer-Verlag, New York, 1989).
[CrossRef]

Lhamon, M. E.

R. C. Daley, L. G. Hassebrook, and M. E. Lhamon, “Topographical analysis with time modulated structured light,” in Visual Information Processing IV, F. O. Huck and R. D. Juday, eds. Proc. SPIE 2488, 396–407 (1995).
[CrossRef]

Li, Z.

Müller, E.

E. Müller, “Fast three-dimensional form measurement system,” Opt. Eng. 34, 2754–2756 (1995).
[CrossRef]

Pennington, K. S.

P. M. Will and K. S. Pennington, “Grid coding: a preprocessing technique for robot and machine vision,” Artif. Intell. 2, 319–329 (1971).
[CrossRef]

Poussart, D.

D. Poussart and D. Laurendeau, “3-D sensing for industrial computer vision,” in Advances in Machine Vision, J. L. C. Sanz, ed. (Springer-Verlag, New York, 1989).
[CrossRef]

Schmaltz, G.

G. Schmaltz, “A method for presenting the profile curves of rough surfaces,” Naturwissenschaften 18, 315–316 (1932).
[CrossRef]

Shun, Y.

Solomon, R.

D. Ashley, D. Goodman, L. G. Hassebrook, and R. Solomon, “Printed circuit line height measuring techniques,” IBM Tech. Discl. Bull. 27, 2870–2873 (1984).

Wang, Y. F.

J. K. Aggarwal and Y. F. Wang, “Inference of object surface structure from structured lighting—an overview,” in Machine Vision, Herbert Freeman, ed. (Academic, Boston, 1988), pp. 193–220.

Will, P. M.

P. M. Will and K. S. Pennington, “Grid coding: a preprocessing technique for robot and machine vision,” Artif. Intell. 2, 319–329 (1971).
[CrossRef]

Wu, P.

Yan, Z.

Yu, F.

Appl. Opt.

Artif. Intell.

P. M. Will and K. S. Pennington, “Grid coding: a preprocessing technique for robot and machine vision,” Artif. Intell. 2, 319–329 (1971).
[CrossRef]

IBM Tech. Discl. Bull.

D. Ashley, D. Goodman, L. G. Hassebrook, and R. Solomon, “Printed circuit line height measuring techniques,” IBM Tech. Discl. Bull. 27, 2870–2873 (1984).

L. G. Hassebrook, “Sine sectioning illumination method,” IBM Tech. Discl. Bull. 27, 3553–3554 (1984).

D. S. Goodman and L. G. Hassebrook, “Surface contour measuring instrument,” IBM Tech. Discl. Bull. 27, 2671–2673 (1984).

IEEE Trans. Pattern Anal. Mach. Intell.

K. L. Boyer and A. C. Kak, “Colored-encoded structured light for rapid active ranging,” IEEE Trans. Pattern Anal. Mach. Intell. 9, 14–28 (1987).
[CrossRef] [PubMed]

A. Jarvis, “A perspective on range finding techniques for computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. 5, 122–139 (1983).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

Naturwissenschaften

G. Schmaltz, “A method for presenting the profile curves of rough surfaces,” Naturwissenschaften 18, 315–316 (1932).
[CrossRef]

Opt. Acta

K. Biderman, “Image encoding in modulated gratings from 1899–1970,” Opt. Acta 17, 631–635 (1970).

Opt. Eng.

E. Müller, “Fast three-dimensional form measurement system,” Opt. Eng. 34, 2754–2756 (1995).
[CrossRef]

Other

S. Haykin, Digital Communications (Wiley, New York, 1988).

R. C. Daley and L. G. Hassebrook, “Improved light sectioning resolution by optimized thresholding,” in Three-Dimensional and Laser-Based Systems for Metrology and Inspection II, K. G. Harding and D. J. Svetkoff, eds., Proc. SPIE 2909, 151–161 (1996).
[CrossRef]

D. Poussart and D. Laurendeau, “3-D sensing for industrial computer vision,” in Advances in Machine Vision, J. L. C. Sanz, ed. (Springer-Verlag, New York, 1989).
[CrossRef]

J. K. Aggarwal and Y. F. Wang, “Inference of object surface structure from structured lighting—an overview,” in Machine Vision, Herbert Freeman, ed. (Academic, Boston, 1988), pp. 193–220.

R. C. Daley, L. G. Hassebrook, and M. E. Lhamon, “Topographical analysis with time modulated structured light,” in Visual Information Processing IV, F. O. Huck and R. D. Juday, eds. Proc. SPIE 2488, 396–407 (1995).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Multiple spatial frequencies, demonstrating increased ISI.

Fig. 2
Fig. 2

Light-stripe patterns: (a) experimental low frequency, (b) numerical model, (c) experimental high frequency, (d) numerical model.

Fig. 3
Fig. 3

Two-dimensional PDF’s for the images in Fig. 2.

Fig. 4
Fig. 4

Probability of error as a function of threshold.

Fig. 5
Fig. 5

Binary stripe images with center locations.

Fig. 6
Fig. 6

Entropy regions for stripe images.

Fig. 7
Fig. 7

Polyhedron object.

Fig. 8
Fig. 8

Received light-stripe projections.

Fig. 9
Fig. 9

Combined encoding for determining interlace boundaries.

Fig. 10
Fig. 10

Noninterlaced (top) and interlaced (bottom) range images.

Equations (16)

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s x = q x   *   h ISI x ,
h ISI x = exp - x 2 2 σ x 2 ,
g ˜ x = s x + w ˜ x ,
f g ˜ , x ˜ g ,   x = f g ˜ | x g | x f x ˜ x = f g ˜ , | q x g | q x f x ˜ x ,
f g ˜ , x ˜ g ,   x = 1 T x 2 π σ w exp - g - s x 2 2 σ w 2
MSE σ x 2 = 1 MN i = 1 N j = 1 M g j i - s x i 2 ,
P e = x 0 η   f g ˜ , x ˜ g ,   x d g d x + x 1 - η   f g ˜ , x ˜ g ,   x d g d x ,
r x = 1 q x η 0 q x < η ,
C x = I x Q ;   R | p 1 = p 0 = 0.5 .
I x Q ;   R = j = 0 1 k = 0 1   P r x = k | q x = j p j × log 2 P r x = k | q x = j P r x = k ,
P r x = k = j = 0 1   P r x = k | q x = j p j .
p c x = P r x = 0 | q x = 1 = P r x = 1 | q x = 0 ,
q c x = 1 - p c x = P r x = 0 | q x = 0 = P r x = 1 | q x = 1 .
p c x = η   f g ˜ | x g | q x = 0 d g for   x 0 - η   f g ˜ | x g | q x = 1 d g for   x 1 .
C x = 1 - H p ,
H p = - p c x log 2 p c x - q c x log 2 q c x .

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