Abstract

Passive three-dimensional (3D) imaging is an enabling technology for a number of applications. We present a technique for profilometry and optical slicing of objects using 3D multiperspective imaging. We use the spectral radiation pattern (SRP) in object space and establish its relationship to different perspective images. A method is proposed to infer the depth of Lambertian surfaces from the statistics of the SRP. Experimental results are presented to show the feasibility of this method. To the best of our knowledge, this is the first time that statistics of the ray intensity-angle is used for 3D depth mapping.

© 2009 Optical Society of America

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2008 (2)

2007 (1)

2006 (2)

A. Stern and B. Javidi, Proc. IEEE 94, 591 (2006).
[CrossRef]

M. Levoy, IEEE Computer 39, 46 (2006).

2005 (1)

A. Stern and B. Javidi, J. Disp. Technol. 1, 141 (2005).
[CrossRef]

2004 (2)

A. N. Rajagopalan, S. Chaudhuri, and U. Mudenagudi, IEEE Trans. Pattern Anal. Mach. Intell. 26, 1521 (2004).
[CrossRef] [PubMed]

S.-H. Hong, J.-S. Jang, and B. Javidi, Opt. Express 12, 483 (2004).
[CrossRef] [PubMed]

2000 (1)

M. Pollefeys, R. Koch, M. Vergauwen, B. Deknuydt, and L. Van Gool, Proc. SPIE 3958, 215 (2000).
[CrossRef]

1993 (1)

M. Okutomi and T. Kanade, IEEE Trans. Pattern Anal. Mach. Intell. 15, 353 (1993).
[CrossRef]

1986 (1)

1953 (1)

Castro, A.

Chaudhuri, S.

A. N. Rajagopalan, S. Chaudhuri, and U. Mudenagudi, IEEE Trans. Pattern Anal. Mach. Intell. 26, 1521 (2004).
[CrossRef] [PubMed]

Daneshpanah, M.

Deknuydt, B.

M. Pollefeys, R. Koch, M. Vergauwen, B. Deknuydt, and L. Van Gool, Proc. SPIE 3958, 215 (2000).
[CrossRef]

Frauel, Y.

Hong, S.-H.

Jang, J.-S.

Javidi, B.

Kanade, T.

M. Okutomi and T. Kanade, IEEE Trans. Pattern Anal. Mach. Intell. 15, 353 (1993).
[CrossRef]

Koch, R.

M. Pollefeys, R. Koch, M. Vergauwen, B. Deknuydt, and L. Van Gool, Proc. SPIE 3958, 215 (2000).
[CrossRef]

Levoy, M.

M. Levoy, IEEE Computer 39, 46 (2006).

Martinez, M.

Martinez, R.

Mudenagudi, U.

A. N. Rajagopalan, S. Chaudhuri, and U. Mudenagudi, IEEE Trans. Pattern Anal. Mach. Intell. 26, 1521 (2004).
[CrossRef] [PubMed]

Navarro, H.

Ogle, K. N.

Okano, F.

B. Javidi, F. Okano, and J.-Y. Son, Three-Dimensional Imaging, Visualization, and Display (Springer, 2009).
[CrossRef]

Okutomi, M.

M. Okutomi and T. Kanade, IEEE Trans. Pattern Anal. Mach. Intell. 15, 353 (1993).
[CrossRef]

Pollefeys, M.

M. Pollefeys, R. Koch, M. Vergauwen, B. Deknuydt, and L. Van Gool, Proc. SPIE 3958, 215 (2000).
[CrossRef]

Rajagopalan, A. N.

A. N. Rajagopalan, S. Chaudhuri, and U. Mudenagudi, IEEE Trans. Pattern Anal. Mach. Intell. 26, 1521 (2004).
[CrossRef] [PubMed]

Saavedra, G.

Son, J.-Y.

B. Javidi, F. Okano, and J.-Y. Son, Three-Dimensional Imaging, Visualization, and Display (Springer, 2009).
[CrossRef]

Stern, A.

A. Stern and B. Javidi, Proc. IEEE 94, 591 (2006).
[CrossRef]

A. Stern and B. Javidi, J. Disp. Technol. 1, 141 (2005).
[CrossRef]

Torre, V.

Van Gool, L.

M. Pollefeys, R. Koch, M. Vergauwen, B. Deknuydt, and L. Van Gool, Proc. SPIE 3958, 215 (2000).
[CrossRef]

Vergauwen, M.

M. Pollefeys, R. Koch, M. Vergauwen, B. Deknuydt, and L. Van Gool, Proc. SPIE 3958, 215 (2000).
[CrossRef]

Verri, A.

Watson, E. A.

IEEE Computer (1)

M. Levoy, IEEE Computer 39, 46 (2006).

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

M. Okutomi and T. Kanade, IEEE Trans. Pattern Anal. Mach. Intell. 15, 353 (1993).
[CrossRef]

A. N. Rajagopalan, S. Chaudhuri, and U. Mudenagudi, IEEE Trans. Pattern Anal. Mach. Intell. 26, 1521 (2004).
[CrossRef] [PubMed]

J. Disp. Technol. (1)

A. Stern and B. Javidi, J. Disp. Technol. 1, 141 (2005).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Express (4)

Proc. IEEE (1)

A. Stern and B. Javidi, Proc. IEEE 94, 591 (2006).
[CrossRef]

Proc. SPIE (1)

M. Pollefeys, R. Koch, M. Vergauwen, B. Deknuydt, and L. Van Gool, Proc. SPIE 3958, 215 (2000).
[CrossRef]

Other (1)

B. Javidi, F. Okano, and J.-Y. Son, Three-Dimensional Imaging, Visualization, and Display (Springer, 2009).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

(a) Ray diagram showing distinct SRPs at surface and free-space voxels, (b) parameter definition for SRP.

Fig. 2
Fig. 2

Extracted depth with contours of equal depth. Inset, original scene.

Fig. 3
Fig. 3

Optical sections: (a) 28 33 cm , (b) 36 42 cm , (c) 45 52 cm , (d) conventional reconstruction.

Equations (13)

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L ( θ , ϕ , λ ) ( a.u. of intensity ) ,
V = { L : [ π 2 : π 2 , 0 : 2 π , λ min : λ max ] R } ,
θ i = arctan ( x p i x ) 2 + ( y p i y ) 2 z p i z ,
ϕ i = ( arctan y p i y x p i x ) + { 0 x p i x π x p i < x } .
L ( θ i , ϕ i , λ ) = γ i × I i ( ξ , η , λ ) ,
( ξ , η ) = g i tan θ i × ( cos ϕ i , sin θ i )
I ( λ ) = 1 2 π L ( θ , ϕ , λ ) d θ d ϕ continuous ,
= 1 N i = 1 N L ( θ i , ϕ i , λ ) discrete .
D ( x , y , z ) = [ L ( θ , ϕ , λ ) I ( λ ) ] ( x , y , z ) 2 d θ d ϕ d λ .
z ̂ ( x , y ) = arg min z Z D ( x , y , z ) .
z ̂ ( x , y ) = arg min z Z j = 1 3 i = 1 N [ L ( θ i , ϕ i , λ j ) I ( λ j ) ] ( x , y , z ) 2 .
z ̂ ( x , y ) void z Z : D ( x , y , z ) D 0 ,
Δ z min = μ z 2 P g μ z .

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