Abstract

A modified binary synthetic discriminant function filter designed to recognize objects over a range of rotated views has been verified on a laboratory optical correlator. A binary synthetic discriminant function filter has been previously described that will produce a specified correlation response for a set of training images. [See D. A. Jared and D. J. Ennis, “ Inclusion of Filter Modulation in Synthetic-Discriminant-Function Construction,” Appl. Opt. 28, 232– 239 ( 1989).] In the filter design, the modulation characteristics of the device onto which the filter is mapped are included in the synthesis equations. The system of nonlinear equations is then solved using an iteration procedure based on the Newton–Raphson algorithm. The development of the filter–SDF (fSDF) method was driven by the practical concern to make currently available spatial light modulators with limited modulation capabilities functional for distortion invariant pattern recognition. This technique is used to synthesize filters for a binary magnetooptic spatial light modulator (MOSLM), the Sight-MOD produced by Semetex. Two MOSLMs are used in the laboratory correlator, one in the filter plane and one in the input plane. We demonstrate that a single filter produces equal correlation peaks for a sample object (a Shuttle Orbiter in these tests) over in-plane and out-of-plane rotation ranges up to 75°. The correlator is able to track dynamically the shuttle as it moves along a curved path across the input field. Views of the object in between those in the training set are also recognized when training images are sufficiently close in angle (~5° apart).

© 1990 Optical Society of America

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References

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  1. D. A. Jared, D. J. Ennis, “Inclusion of Filter Modulation in Synthetic-Discriminant-Function Construction,” Appl. Opt. 28, 232–239 (1989).
    [CrossRef] [PubMed]
  2. D. A. Jared, “Distortion Range of Filter Synthetic Discriminant Function Binary Phase-Only Filters,” Appl. Opt. 28, 4835–4839 (1989).
    [CrossRef] [PubMed]
  3. D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984).
    [CrossRef]
  4. D. F. Flannery, A. M. Biernacki, J. J. Loomis, S. L. Cartwright, “Real-Time Coherent Correlator Using Binary Magnetooptic Spatial Light Modulators at Input and Fourier Planes,” Appl. Opt. 25, 466–466 (1986).
    [CrossRef] [PubMed]
  5. M. A. Flavin, J. L. Horner, “Amplitude Encoded Phase-Only Filters,” Appl. Opt. 28, 1692–1696 (1989).
    [CrossRef] [PubMed]

1989

1986

1984

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984).
[CrossRef]

Biernacki, A. M.

Cartwright, S. L.

Ennis, D. J.

Flannery, D. F.

Flavin, M. A.

Horner, J. L.

Jared, D. A.

Loomis, J. J.

Paek, E. G.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984).
[CrossRef]

Psaltis, D.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984).
[CrossRef]

Venkatesh, S. S.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Three lens correlator using magnetooptic spatial light modulators (MSLMs) in the input and filter planes. Lens 3 performs both phase correction and the inverse transform. The phase errors need not be known with precision ahead of time. If the errors present in practice require a lens of focal length f″ for correction, then the detector in the correlation plane is simply moved to a point f′ = 1/(1/f3 − 1/f″) from the filter plane. As f″ ≈ f in practice, letting f3f/2 produces f′ ≈ f, which is a convenient operational point.

Fig. 2
Fig. 2

(a) Input images (showing range of rotational views). (b) Output illustrating equal intensity peaks obtained using one fSDF filter. Peak (closed squares) and clutter (open squares) data are given normalized to the peak response of a BPOF matched filter for the shuttle at 0°.

Fig. 3
Fig. 3

Average fSDF peak and clutter vs in-plane rotation distortion range. Data points are the average peak (closed squares) and (open squares) responses for each image within the distortion range, measured at every 1°. For example, the data points for peak and clutter at 60° are the average of all sixty-one peak and clutter data points shown in Fig. 2(b). The data are normalized to the peak of a BPOF matched to the shuttle oriented at 0°.

Fig. 4
Fig. 4

Minimum peak and maximum clutter response vs in-plane distortion range. Peak data (closed squares) are the lowest responses measured at any 1° angle over the distortion range. Clutter data (open squares) are the highest responses over the distortion range.

Fig. 5
Fig. 5

Out-of-plane views of shuttle orbiter: (a) 0°, (b) 45°, and (c) 90°.

Fig. 6
Fig. 6

(a) Average fSDF peak and clutter vs out-of-plane rotation distortion range. One end of the distortion range is the 0° (nose-on) view of Fig. 5(a). Data points are the average peak (closed squares) and clutter (open squares) responses for each image within the distortion range, measured at every 1°. The data are normalized to the peak response of a BPOF matched to the out-of-plane shuttle oriented at 0°. (b) Minimum peak (closed squares) and maximum clutter (open squares) response vs out-of-plane distortion range.

Fig. 7
Fig. 7

Normalized peak (open circles for images in the training set, closed squares for images inbetween the training angles) and clutter (open squares) vs out-of-plane image angle for an fSDF designed for invariance to out-of-plane rotations from 0–20°. While peaks for the training images are nearly constant, the distortion range is not sampled finely enough to provide a constant response for angles inbetween the training angles.

Fig. 8
Fig. 8

(a) Average fSDF peak and clutter vs out-of-plane rotation distortion range. One end of the distortion range is the 90° (side-on) view of Fig. 5(b). Data points are the average peak (closed squares) and clutter (open squares) responses for each image within the distortion range, measured at every 1°. The data are normalized to the peak response of a BPOF matched to the out-of-plane shuttle oriented at 90°. (b) Minimum peak (closed squares) and maximum clutter (open squares) response vs out-of-plane distortion range.

Fig. 9
Fig. 9

Correlation response of two images with an fSDF designed for invariance to in-plane rotation of the shuttle orbiter over a range of 60°. (a) shuttle orbiter, (b) correlator output using shuttle input, (c) F/18, and (d) correlator output using F/18 input.

Fig. 10
Fig. 10

Correlation peak of F–18 and lowest correlation peak of shuttle with fSDFs designed to recognize the shuttle over the given distortion ranges. Shuttle peak correlation data (closed squares) are the lowest responses measured at any 1° angle over the distortion range. The dashed line is a threshold for shuttle recognition. The peak correlation responses of an F/18 image with the given filters is given by the closed circles.

Equations (8)

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t n ( x , y ) s * ( x , y ) d x d y = t n ( x , y ) s ( x , y ) = c n ,
s ( x , y ) = F - 1 M F [ s ( x , y ) ] * ,
s ( x , y ) = n = 0 k a n t n ( x , y ) .
t n ( x , y ) F - 1 M F m = 0 k a m * t m ( x , y ) = c n .
a n i + 1 = a n i + β [ c n - c 0 ( m n i m 0 i ) ] ,
P = c ( 0 , 0 ) 2 .
C = max c ( x , y ) 2 , such that x , y > 3 , and c x = c y = 0.
PSR c = P min C max ,

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