Abstract

An approach for sensing a three-dimensional (3D) object surface with an arbitrary geometric shape is presented. Combining two different 3D sensing mechanisms, point-array encoding based on affine transformation and fringe encoding based on phase mapping, we construct a mathematic model for 3D vision in which the point-array encoding is initially applied to determine the fringe orders to create a control-vertex mesh with absolute coordinate values in 3D space. Then phase evaluation and phase unwrapping for fringe decoding is performed under the guidance of control-vertex mesh, leading to an absolute phase map and the corresponding range image of the test object. The computer simulations and experimental results are presented to demonstrate the theoretical prediction.

© 2006 Optical Society of America

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References

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  1. R. Jain, R. Kasturi, and B. G. Schunck, Machine Vision (McGraw Hill, 1995).
  2. L. Salas, E. Luna, J. Salinas, V. Garcia, and M. Servin, "Profilometry by fringe projection," Opt. Eng. 42, 3307-3314 (2003).
    [CrossRef]
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  13. G. Sansoni, M. Carocci, and R. Rodella, "Three-dimensional vision based on a combination of gray-code and phase-shift light projection: analysis and compensation of the systematic errors," Appl. Opt. 38, 6565-6573 (1999).
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2005

2003

L. Salas, E. Luna, J. Salinas, V. Garcia, and M. Servin, "Profilometry by fringe projection," Opt. Eng. 42, 3307-3314 (2003).
[CrossRef]

2000

F. Chen, G. M. Brown, and M. Song, "Overview of three-dimensional shape measurement using optical methods," Opt. Eng. 39, 10-22 (2000) and references therein.
[CrossRef]

1999

1997

1983

1974

Brangaccio, D. J.

Brown, G. M.

F. Chen, G. M. Brown, and M. Song, "Overview of three-dimensional shape measurement using optical methods," Opt. Eng. 39, 10-22 (2000) and references therein.
[CrossRef]

Bruning, J. H.

Carocci, M.

Chen, F.

F. Chen, G. M. Brown, and M. Song, "Overview of three-dimensional shape measurement using optical methods," Opt. Eng. 39, 10-22 (2000) and references therein.
[CrossRef]

Cho, G.

Corini, S.

G. Sansoni, S. Corini, S. Lazzari, R. Rodella, and F. Docchio, "Three-dimensional imaging based on gray-code light projection: characterization of the measuring algorithm and development of a measuring system for industrial applications," App. Opt. 36, 4463-4472 (1997).
[CrossRef]

Docchio, F.

G. Sansoni, S. Corini, S. Lazzari, R. Rodella, and F. Docchio, "Three-dimensional imaging based on gray-code light projection: characterization of the measuring algorithm and development of a measuring system for industrial applications," App. Opt. 36, 4463-4472 (1997).
[CrossRef]

Gallagher, J. E.

Garcia, V.

L. Salas, E. Luna, J. Salinas, V. Garcia, and M. Servin, "Profilometry by fringe projection," Opt. Eng. 42, 3307-3314 (2003).
[CrossRef]

Ghiglia, D. C.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998), Chaps. 2-6 and references therein.

Gu, W.

Herriott, D. R.

Huntley, J. M.

Jain, R.

R. Jain, R. Kasturi, and B. G. Schunck, Machine Vision (McGraw Hill, 1995).

Kasturi, R.

R. Jain, R. Kasturi, and B. G. Schunck, Machine Vision (McGraw Hill, 1995).

Kinoshita, M.

Lazzari, S.

G. Sansoni, S. Corini, S. Lazzari, R. Rodella, and F. Docchio, "Three-dimensional imaging based on gray-code light projection: characterization of the measuring algorithm and development of a measuring system for industrial applications," App. Opt. 36, 4463-4472 (1997).
[CrossRef]

Lu, C.

Luna, E.

L. Salas, E. Luna, J. Salinas, V. Garcia, and M. Servin, "Profilometry by fringe projection," Opt. Eng. 42, 3307-3314 (2003).
[CrossRef]

Mutoh, K.

Peng, X.

Pritt, M. D.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998), Chaps. 2-6 and references therein.

Rodella, R.

G. Sansoni, M. Carocci, and R. Rodella, "Three-dimensional vision based on a combination of gray-code and phase-shift light projection: analysis and compensation of the systematic errors," Appl. Opt. 38, 6565-6573 (1999).
[CrossRef]

G. Sansoni, S. Corini, S. Lazzari, R. Rodella, and F. Docchio, "Three-dimensional imaging based on gray-code light projection: characterization of the measuring algorithm and development of a measuring system for industrial applications," App. Opt. 36, 4463-4472 (1997).
[CrossRef]

Rosenfeld, D. P.

Salas, L.

L. Salas, E. Luna, J. Salinas, V. Garcia, and M. Servin, "Profilometry by fringe projection," Opt. Eng. 42, 3307-3314 (2003).
[CrossRef]

Saldner, H. O.

Salinas, J.

L. Salas, E. Luna, J. Salinas, V. Garcia, and M. Servin, "Profilometry by fringe projection," Opt. Eng. 42, 3307-3314 (2003).
[CrossRef]

Sansoni, G.

G. Sansoni, M. Carocci, and R. Rodella, "Three-dimensional vision based on a combination of gray-code and phase-shift light projection: analysis and compensation of the systematic errors," Appl. Opt. 38, 6565-6573 (1999).
[CrossRef]

G. Sansoni, S. Corini, S. Lazzari, R. Rodella, and F. Docchio, "Three-dimensional imaging based on gray-code light projection: characterization of the measuring algorithm and development of a measuring system for industrial applications," App. Opt. 36, 4463-4472 (1997).
[CrossRef]

Schunck, B. G.

R. Jain, R. Kasturi, and B. G. Schunck, Machine Vision (McGraw Hill, 1995).

Servin, M.

L. Salas, E. Luna, J. Salinas, V. Garcia, and M. Servin, "Profilometry by fringe projection," Opt. Eng. 42, 3307-3314 (2003).
[CrossRef]

Song, M.

F. Chen, G. M. Brown, and M. Song, "Overview of three-dimensional shape measurement using optical methods," Opt. Eng. 39, 10-22 (2000) and references therein.
[CrossRef]

Song, Y.

Takahashi, Y.

Takai, H.

Takeda, M.

Tian, J.

Wang, Y.

White, A. D.

Zhang, X.

Zheng, R.

App. Opt.

G. Sansoni, S. Corini, S. Lazzari, R. Rodella, and F. Docchio, "Three-dimensional imaging based on gray-code light projection: characterization of the measuring algorithm and development of a measuring system for industrial applications," App. Opt. 36, 4463-4472 (1997).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Eng.

F. Chen, G. M. Brown, and M. Song, "Overview of three-dimensional shape measurement using optical methods," Opt. Eng. 39, 10-22 (2000) and references therein.
[CrossRef]

L. Salas, E. Luna, J. Salinas, V. Garcia, and M. Servin, "Profilometry by fringe projection," Opt. Eng. 42, 3307-3314 (2003).
[CrossRef]

Opt. Express

Other

R. Jain, R. Kasturi, and B. G. Schunck, Machine Vision (McGraw Hill, 1995).

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998), Chaps. 2-6 and references therein.

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of the 3D sensing configuration based on a multisensing mechanism.

Fig. 2
Fig. 2

Three-dimensional simulation results for (a) the object image, (b) the wrapped phase map, (c) the range image of (b) with conventional spatial phase unwrapping, (d) the phase map with absolute phase of control points, (e) the phase map with absolute phase of control lines, (f) the range image obtained by hybrid encoding.

Fig. 3
Fig. 3

Three-dimensional sensing results of (a) the object image, (b) the point-array image, (c) the range image of (b), (d) the encoded fringe image, (e) the range image of (d) with conventional spatial phase unwrapping, (f) the range image obtained by hybrid encoding.

Equations (20)

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z w =
L m l x cos α L C + C m l x sin α C ( m l x sin α + L cos α ) + m l x cos α L sin α ,
C = δ x f + x 0 cos α L x 0 sin α ,
I ( x , y ) = a ( x , y ) + b ( x , y ) cos [ 2 π f 0 x + ϕ ( x , y ) ] ,
h ( x , y ) = L ϕ ( x , y ) ϕ ( x , y ) 2 π f 0 D ,
ϕ h ( m l x , n l y ) = 2 π f 0 D h ( m l x , n l y ) h ( m l x , n l y ) L .
ϕ u ( x , y ) = ϕ w ( x , y ) + 2 k π ,
x = 1 , 2 , , K ; y = 1 , 2 , , L ,
ϕ u p ( m l x , n l y ) = ϕ w ( m l x , n l y ) + 2 k h ( m l x , n l y ) π ,
k h ( m l x , n l y ) = NINT [ ϕ h ( m l x , n l y ) ϕ w ( m l x , n l y ) 2 π ] ,
k c = NINT { ϕ u p [ m l x ( n + 1 ) l y ] ϕ u p ( m l x , n l y ) 2 π } .
ϕ u l ( m l x , j ) = ϕ w ( m l x , j ) + 2 k h ( m l x , n l y ) π ,
j [ n l y , ( n + 1 ) l y ] .
ϕ u l ( m l x , j ) = ϕ w ( m l x , j ) + 2 k h ( m l x , n l y ) π .
ϕ u l ( m l x , j ) = ϕ w ( m l x , j ) + 2 k h [ m l x , ( n + 1 ) l y ] π .
k c 1 = NINT { ϕ u l ( m l x , j ) ϕ w ( m l x , j ) 2 π } ,
k c 2 = NINT { ϕ u l [ ( m + 1 ) l x , j ] ϕ w [ ( m + 1 ) l x , j ] 2 π } ,
ϕ u r ( i , j ) = ϕ w ( i , j ) + 2 k c 1 ( m l x , j ) π ,
ϕ u r ( i , j ) = ϕ w ( i , j ) + 2 k c 1 ( m l x , j ) π .
ϕ u r ( i , j ) = ϕ w ( i , j ) + 2 k c 2 [ ( m + 1 ) l x , j ] π .

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