Abstract

A new neural net is described that can easily and cost-effectively accommodate multiple objects in the field of view in parallel. The use of a correlator achieves shift invariance and accommodates multiple objects in parallel. Distortion-invariant filters provide aspect-invariant distortion. Symbolic encoding, the use of generic object parts, and a production system neural net allow large class problems to be addressed. Optical laboratory data on the production system inputs are provided and emphasized. Test data assume binary inputs, although analog (probability) input neurons are possible.

© 1992 Optical Society of America

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References

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  1. D. E. Rumelhart, G. E. Hinton, R. J. Williams, “Learning internal representations by error propagation,” in Parallel Distributed ProcessingD. E. Rumelhart, J. L. McClelland, eds. (MIT Press, Cambridge, Mass., 1986), Vol. 1, pp. 318–362; P. Werbos, Ph.D. dissertation (Harvard University, Cambridge, Mass., 1974).
  2. C. L. Giles, R. D. Griffen, T. Maxwell, “Encoding geometric invariances in higher-order neural networks,” Neural Information Processing Systems, D. Anderson, ed. (American Institute of Physics, New York, 1988), pp. 301–309.
  3. K. Fukushima, “Neocognitron: a self-organizing neural network model for a mechanism of pattern recognition unaffected by a shift in position,” Biol. Cybern. 36, 193–202 (1980).
    [CrossRef] [PubMed]
  4. E. Barnard, D. Casasent, “Shift invariance and the neocognitron,” Neural Networks 3, 403–410 (1990).
    [CrossRef]
  5. E. Barnard, D. Casasent, “Image processing for image understanding with neural nets,” in Proceedings of the International Joint Conference on Neural Networks, IEEE Catalog No. 89CH2765-6 (Institute of Electrical and Electronic Engineers, Washington, D.C., 1989), Vol. 1, pp. I-111–115.
  6. D. Casasent, A. Mahalanobis, “Rule-based symbolic processor for object recognition,” Appl. Opt. 26, 4795–4802 (1987).
    [CrossRef] [PubMed]
  7. E. Botha, D. Casasent, E. Barnard, “Optical production systems using neural networks and symbolic substitution,” Appl. Opt. 27, 5185–5193 (1988).
    [CrossRef] [PubMed]
  8. D. Casasent, “Unified synthetic discriminant function computational formulation,” Appl. Opt. 23, 1620–1627 (1984).
    [CrossRef] [PubMed]
  9. See special issue on optical pattern recognition, Opt. Eng. 29(9) (1990).
  10. D. Casasent, E. Barnard, “Adaptive clustering optical neural net,” Appl. Opt. 29, 2603–2615 (1990).
    [CrossRef] [PubMed]
  11. E. Barnard, P. Vermeulen, D. Casasent, “Optical correlation CGHs with modulated error diffusion,” Appl. Opt. 28, 5358–5362 (1989).
    [CrossRef] [PubMed]

1990 (3)

E. Barnard, D. Casasent, “Shift invariance and the neocognitron,” Neural Networks 3, 403–410 (1990).
[CrossRef]

See special issue on optical pattern recognition, Opt. Eng. 29(9) (1990).

D. Casasent, E. Barnard, “Adaptive clustering optical neural net,” Appl. Opt. 29, 2603–2615 (1990).
[CrossRef] [PubMed]

1989 (1)

1988 (1)

1987 (1)

1984 (1)

1980 (1)

K. Fukushima, “Neocognitron: a self-organizing neural network model for a mechanism of pattern recognition unaffected by a shift in position,” Biol. Cybern. 36, 193–202 (1980).
[CrossRef] [PubMed]

Barnard, E.

E. Barnard, D. Casasent, “Shift invariance and the neocognitron,” Neural Networks 3, 403–410 (1990).
[CrossRef]

D. Casasent, E. Barnard, “Adaptive clustering optical neural net,” Appl. Opt. 29, 2603–2615 (1990).
[CrossRef] [PubMed]

E. Barnard, P. Vermeulen, D. Casasent, “Optical correlation CGHs with modulated error diffusion,” Appl. Opt. 28, 5358–5362 (1989).
[CrossRef] [PubMed]

E. Botha, D. Casasent, E. Barnard, “Optical production systems using neural networks and symbolic substitution,” Appl. Opt. 27, 5185–5193 (1988).
[CrossRef] [PubMed]

E. Barnard, D. Casasent, “Image processing for image understanding with neural nets,” in Proceedings of the International Joint Conference on Neural Networks, IEEE Catalog No. 89CH2765-6 (Institute of Electrical and Electronic Engineers, Washington, D.C., 1989), Vol. 1, pp. I-111–115.

Botha, E.

Casasent, D.

Fukushima, K.

K. Fukushima, “Neocognitron: a self-organizing neural network model for a mechanism of pattern recognition unaffected by a shift in position,” Biol. Cybern. 36, 193–202 (1980).
[CrossRef] [PubMed]

Giles, C. L.

C. L. Giles, R. D. Griffen, T. Maxwell, “Encoding geometric invariances in higher-order neural networks,” Neural Information Processing Systems, D. Anderson, ed. (American Institute of Physics, New York, 1988), pp. 301–309.

Griffen, R. D.

C. L. Giles, R. D. Griffen, T. Maxwell, “Encoding geometric invariances in higher-order neural networks,” Neural Information Processing Systems, D. Anderson, ed. (American Institute of Physics, New York, 1988), pp. 301–309.

Hinton, G. E.

D. E. Rumelhart, G. E. Hinton, R. J. Williams, “Learning internal representations by error propagation,” in Parallel Distributed ProcessingD. E. Rumelhart, J. L. McClelland, eds. (MIT Press, Cambridge, Mass., 1986), Vol. 1, pp. 318–362; P. Werbos, Ph.D. dissertation (Harvard University, Cambridge, Mass., 1974).

Mahalanobis, A.

Maxwell, T.

C. L. Giles, R. D. Griffen, T. Maxwell, “Encoding geometric invariances in higher-order neural networks,” Neural Information Processing Systems, D. Anderson, ed. (American Institute of Physics, New York, 1988), pp. 301–309.

Rumelhart, D. E.

D. E. Rumelhart, G. E. Hinton, R. J. Williams, “Learning internal representations by error propagation,” in Parallel Distributed ProcessingD. E. Rumelhart, J. L. McClelland, eds. (MIT Press, Cambridge, Mass., 1986), Vol. 1, pp. 318–362; P. Werbos, Ph.D. dissertation (Harvard University, Cambridge, Mass., 1974).

Vermeulen, P.

Williams, R. J.

D. E. Rumelhart, G. E. Hinton, R. J. Williams, “Learning internal representations by error propagation,” in Parallel Distributed ProcessingD. E. Rumelhart, J. L. McClelland, eds. (MIT Press, Cambridge, Mass., 1986), Vol. 1, pp. 318–362; P. Werbos, Ph.D. dissertation (Harvard University, Cambridge, Mass., 1974).

Appl. Opt. (5)

Biol. Cybern. (1)

K. Fukushima, “Neocognitron: a self-organizing neural network model for a mechanism of pattern recognition unaffected by a shift in position,” Biol. Cybern. 36, 193–202 (1980).
[CrossRef] [PubMed]

Neural Networks (1)

E. Barnard, D. Casasent, “Shift invariance and the neocognitron,” Neural Networks 3, 403–410 (1990).
[CrossRef]

Opt. Eng. (1)

See special issue on optical pattern recognition, Opt. Eng. 29(9) (1990).

Other (3)

E. Barnard, D. Casasent, “Image processing for image understanding with neural nets,” in Proceedings of the International Joint Conference on Neural Networks, IEEE Catalog No. 89CH2765-6 (Institute of Electrical and Electronic Engineers, Washington, D.C., 1989), Vol. 1, pp. I-111–115.

D. E. Rumelhart, G. E. Hinton, R. J. Williams, “Learning internal representations by error propagation,” in Parallel Distributed ProcessingD. E. Rumelhart, J. L. McClelland, eds. (MIT Press, Cambridge, Mass., 1986), Vol. 1, pp. 318–362; P. Werbos, Ph.D. dissertation (Harvard University, Cambridge, Mass., 1974).

C. L. Giles, R. D. Griffen, T. Maxwell, “Encoding geometric invariances in higher-order neural networks,” Neural Information Processing Systems, D. Anderson, ed. (American Institute of Physics, New York, 1988), pp. 301–309.

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Figures (13)

Fig. 1
Fig. 1

Space- and frequency-multiplexed symbolic correlator NN.

Fig. 2
Fig. 2

Block diagram of the symbolic correlator production system NN.

Fig. 3
Fig. 3

Simple IF–THEN production rules.

Fig. 4
Fig. 4

Neural net for the rules in Fig. 3.

Fig. 5
Fig. 5

Optical production system NN net.

Fig. 6
Fig. 6

The 9 objects (and scaled versions of 2) in our initial production system.

Fig. 7
Fig. 7

The 12 parts that were used to describe as facts the multiple objects (Fig. 9) in our database.

Fig. 8
Fig. 8

Fence object at 0° and 30° aspect views (a) and (b) and the horizontal bar object part (c) and (d) at these orientations.

Fig. 9
Fig. 9

Truck object at 0° and 30° aspect views (a) and (b) and the big body object part (c) and (d) at these orientations.

Fig. 10
Fig. 10

Optical outputs of single filters: (a) correlation of the 0° tlight and post (121); (b) three correlation peaks for sfpost and 0° fence (96–111); (c) four correlation peaks for wheel and 0° truck (197–234).

Fig. 11
Fig. 11

Optical outputs of frequency-multiplexed filters of (left to right) the post, tbox, light, and name plate: (a) tlight input (contains post and tbox); (b) lamp input (contains post and light); (c) sign input (contains post and name plate).

Fig. 12
Fig. 12

(a) Rule base and (b) neural net for a parallel production system.

Fig. 13
Fig. 13

(a) Rule base and (b) neural net for an iterative production system.

Tables (10)

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Table I Database of 9 Objects

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Table II Multiple-Object Clusters Used for First Separation of Objects

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Table III Symbolic Parts for Each Object Cluster

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Table IV Cluster 1 Cross-Correlation Data

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Table V Cluster 2 Cross-Correlation Data

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Table VI Cluster 3 Cross-Correlation Data

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Table VII Single Filter Optical Laboratory Test Results

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Table VIII Optical Laboratory Results Using New CGH Encoded Binary Filters and 64 × 64 Images

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Table IX Effect of Spatial Resolution on the Object on True and False Class Correlation Peak Values for Two Cluster-2 Objects

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Table X Effect of Number of Amplitude Levels Required in the Filter Image on True and False Correlation Peak Values for the Cluster-2 Objects and Parts

Metrics