Abstract

Three dimensional (3D) reference structures segment source spaces based on whether particular source locations are visible or invisible to the sensor. A lensless 3D reference structure based imaging system measures projections of this source space on a sensor array. We derive and experimentally verify a model to predict the statistics of the measured projections for a simple 2D object. We show that the statistics of the measurement can yield an accurate estimate of the size of the object without ever forming a physical image. Further, we conjecture that the measured statistics can be used to determine the shape of 3D objects and present preliminary experimental measurements for 3D shape recognition.

© 2003 Optical Society of America

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References

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Appl Opt (2)

M.R. Descour, C.E. Volin, E.L. Derenaiak, T.M. Gleeson, M.F. Hopkins, D.W.Wilson and P.D. Maker, �??Demonstration of a computed tomography imager spectrometer using a computer-generated hologram dispenser,�?? Appl. Opt. 36, 3694-3698, (1997).
[CrossRef] [PubMed]

D.J. Brady and Z.U. Rahman, �??Integrated analysis and design of analog and digital processing in imaging systems: introduction to feature issue,�?? Appl. Opt. 41, 6049-6049, (2002).
[CrossRef] [PubMed]

Appl. Opt (1)

E.R. Dowski and W.T. Cathey, �??Extended depth of field through wave-front coding,�?? Appl. Opt. 34, 1859-1866 (1995).
[CrossRef] [PubMed]

Appl. Opt. (6)

Jrnl. of Appl. Optics (1)

Y. Frauel and B. Javidi,�??Digital Three-dimensional image correlation using computer-reconstructed integral imaging,�?? Jrnl. of Appl. Optics 41, 5488-5496 (2002).
[CrossRef]

Opt Lett (1)

A. Sinha and G. Barbastathis, �??Volume holographic telescope,�?? Opt. Lett. 27, 1690-1692 (2002).
[CrossRef]

Opt. Express (4)

Opt. Lett (1)

J. Rosen,�??Three-dimensional optical Fourier transform and correlation,�?? Opt. Lett. 22, 964-966 (1993).
[CrossRef]

Opt. Lett. (2)

B. Javidi and E. Tajahuerce,�??B. Javidi and E. Tajahuerce,�??Three-dimensional object recognition by use of digital holography,�?? Opt. Lett. 22, 610-612 (2000).,�?? Opt. Lett. 22, 610-612 (2000).
[CrossRef]

G. Barbastathis, M. Balberg and D. J. Brady, �??Confocal microscopy with a volume holographic filter,�?? Opt. Lett. 24, 811-813 (1999).
[CrossRef]

Optical Engineering (1)

T. Cannon and E. Fenimore, �??Coded aperture imaging - many holes make light work,�?? Optical Engineering 19, 283-289, (1980).

Patten Recognition (1)

N. Saito et al.,�??Discriminant feature extraction using empirical probability density estimation and a local basis library,�?? Patten Recognition 35, 2841-2852 (2002).

Proceedings of the IEEE (1)

G. Barbastathis and D.J. Brady, �??Multidimensional tomographic imaging using volume holography,�?? Proceedings of the IEEE 87, 2098-2120, (1999).
[CrossRef]

Science (1)

D.L. Marks, R.A. Stack, D.J. Brady, D.C. Munson and R.B. Brady, �??Visible Cone beam tomography with a lensless interferometric camera,�?? Science 284, 1561-1564, (1999).
[CrossRef]

Other (1)

J. W. Goodman, �??Statistical Optics,�?? John Wiley & sons Ch.6, 237 (2000).

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Figures (12)

Fig. 1.
Fig. 1.

Obscurants distributed within the reference structure volume segments the source space based on whether a region is visible to a sensor.

Fig. 2.
Fig. 2.

Schematic to determine the probability of visibility of a source cell to a sensor.

Fig. 3.
Fig. 3.

Experimental setup for verifying RST based size recognition.

Fig. 4.
Fig. 4.

Lens-less measurements obtained on CCD (a) without reference structure (b) with reference structure.

Fig. 5.
Fig. 5.

Histograms of different objects (a) without and (b) with reference structure.

Fig. 6.
Fig. 6.

Statistical moments plotted versus object area (a) 〈m〉, (b) 〈m 2〉, (c) 〈m 3〉, (d) 〈m 4〉.

Fig. 7.
Fig. 7.

The variance of the measurements of an RST system scales quadratically with the area of the 2D object.

Fig. 8.
Fig. 8.

Measurement statistics for three different object locations.

Fig. 9.
Fig. 9.

The statistical RST system measures the projected size of the object in different directions.

Fig. 10.
Fig. 10.

The measured projections can be used to reconstruct the convex hull of the object of interest.

Fig. 11.
Fig. 11.

Shapes used and their projections at θ=0°.

Fig. 12.
Fig. 12.

(a) Shapes used and their projections (b) Statistical “images” (A(θ)) of the shapes. These statistical images are a representation of the object shape

Equations (17)

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

m = v ( r m , r ) s ( r ) d r .
m = i v m , i s i .
m j = i v j , i s i .
m = i ( 1 × p m , i s i + 0 × ( 1 p m , i ) s i ) .
v m , i = 1 × p m , i + 0 × ( 1 p m , i ) .
m = i v m , i s i = i p m , i s i .
N = V v .
K = σ v .
m = p m i s i .
m n = p m n ( i s i ) n .
m n = c n × A n .
x 0 ,
x l ( π 2 ) ,
y 0 ,
y l ( 0 ) .
y x tan θ l ( θ ) sec θ + l ( π 2 ) tan θ 0 ,
y x tan θ l ( θ ) sec θ l ( 0 ) 0 .

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