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Size and shape recognition using measurement statistics and random 3D reference structures

Arnab Sinha and David J. Brady

Open Access Open Access

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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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.

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Fig. 2.
Fig. 2. Schematic to determine the probability of visibility of a source cell to a sensor.

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Fig. 3.
Fig. 3. Experimental setup for verifying RST based size recognition.

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Fig. 4.
Fig. 4. Lens-less measurements obtained on CCD (a) without reference structure (b) with reference structure.

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Fig. 5.
Fig. 5. Histograms of different objects (a) without and (b) with reference structure.

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Fig. 6.
Fig. 6. Statistical moments plotted versus object area (a) 〈m〉, (b) 〈m 2〉, (c) 〈m 3〉, (d) 〈m 4〉.

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Fig. 7.
Fig. 7. The variance of the measurements of an RST system scales quadratically with the area of the 2D object.

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Fig. 8.
Fig. 8. Measurement statistics for three different object locations.

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Fig. 9.
Fig. 9. The statistical RST system measures the projected size of the object in different directions.

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Fig. 10.
Fig. 10. The measured projections can be used to reconstruct the convex hull of the object of interest.

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Fig. 11.
Fig. 11. Shapes used and their projections at θ=0°.

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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

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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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