Abstract

A general transformation equation is derived and applied to dynamic and static image differences. It uses translation, rotation, scale, and velocity changes as fundamental object features for image segmentation. A linear minimization algorithm is derived based on a spatial smoothness constraint. The transformation and algorithm constitute an automatic target recognition preprocessor architecture.

© 1990 Optical Society of America

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References

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  1. W. M. Crowe, J. C. Kirsch, “Optical Correlator Guidance Technology Demonstration,” Proc. Soc. Photo-Opt. Instrum. Eng.29–35 (1988).
  2. J. G. Duthie, J. Upatnieks, “Compact Real-Time Coherent Optical Correlators,” Opt. Eng. 23, 007–011 (Jan./Feb.1984).
  3. D. A. Gregory, H.-K. Liu, “Large-Memory Real-Time Multichannel Multiplexed Pattern Recognition,” Appl. Opt. 23, 4560–4570 (1984).
    [CrossRef] [PubMed]
  4. A. Verri, F. Girosi, V. Torre, “Mathematical Properties of the Two-Dimensional Motion Field: from Singular Points to Motion Parameters,” J. Opt. Soc. Am. A 6, 698–712 (1989).
    [CrossRef]
  5. H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, MA (1950), Chap. 8, Sec. 8-6.
  6. R. B. Leighton, Principles of Modern Physics (McGraw-Hill, New York, 1959), Chap. 1, Sec. 1-11.
  7. D. E. Rumelhart, J. C. McClelland, Parallel Distributed Processing (MIT Press, Cambridge, 1986), Vols. 1 and 2.
  8. B. Widrow, M. E. Hoff, “Adaptive Switching Circuits,” IRE WESCON Conv. Rec. Part 4, 96 (1980).
  9. S. Grossberg, “Nonlinear Neural Networks: Principles, Mechanisms, and Architectures,” Neural Networks 1, No. 1, 17–62 (1988).
    [CrossRef]
  10. R. Hecht-Nielsen, “Theory of the Backpropagation Neural Network,” INNS/IEEE Proc. 1 JCNN 1, 593–606 (1989).
  11. B. K. P. Horn, Robot Vision (McGraw-Hill, New York, 1986), Chap. 12, p. 284.
  12. B. K. P. Horn, Robot Vision (McGraw-Hill, New York, 1986), Chap. 13, p. 318.

1989 (2)

1988 (2)

S. Grossberg, “Nonlinear Neural Networks: Principles, Mechanisms, and Architectures,” Neural Networks 1, No. 1, 17–62 (1988).
[CrossRef]

W. M. Crowe, J. C. Kirsch, “Optical Correlator Guidance Technology Demonstration,” Proc. Soc. Photo-Opt. Instrum. Eng.29–35 (1988).

1984 (2)

J. G. Duthie, J. Upatnieks, “Compact Real-Time Coherent Optical Correlators,” Opt. Eng. 23, 007–011 (Jan./Feb.1984).

D. A. Gregory, H.-K. Liu, “Large-Memory Real-Time Multichannel Multiplexed Pattern Recognition,” Appl. Opt. 23, 4560–4570 (1984).
[CrossRef] [PubMed]

1980 (1)

B. Widrow, M. E. Hoff, “Adaptive Switching Circuits,” IRE WESCON Conv. Rec. Part 4, 96 (1980).

Crowe, W. M.

W. M. Crowe, J. C. Kirsch, “Optical Correlator Guidance Technology Demonstration,” Proc. Soc. Photo-Opt. Instrum. Eng.29–35 (1988).

Duthie, J. G.

J. G. Duthie, J. Upatnieks, “Compact Real-Time Coherent Optical Correlators,” Opt. Eng. 23, 007–011 (Jan./Feb.1984).

Girosi, F.

Goldstein, H.

H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, MA (1950), Chap. 8, Sec. 8-6.

Gregory, D. A.

D. A. Gregory, H.-K. Liu, “Large-Memory Real-Time Multichannel Multiplexed Pattern Recognition,” Appl. Opt. 23, 4560–4570 (1984).
[CrossRef] [PubMed]

Grossberg, S.

S. Grossberg, “Nonlinear Neural Networks: Principles, Mechanisms, and Architectures,” Neural Networks 1, No. 1, 17–62 (1988).
[CrossRef]

Hecht-Nielsen, R.

R. Hecht-Nielsen, “Theory of the Backpropagation Neural Network,” INNS/IEEE Proc. 1 JCNN 1, 593–606 (1989).

Hoff, M. E.

B. Widrow, M. E. Hoff, “Adaptive Switching Circuits,” IRE WESCON Conv. Rec. Part 4, 96 (1980).

Horn, B. K. P.

B. K. P. Horn, Robot Vision (McGraw-Hill, New York, 1986), Chap. 12, p. 284.

B. K. P. Horn, Robot Vision (McGraw-Hill, New York, 1986), Chap. 13, p. 318.

Kirsch, J. C.

W. M. Crowe, J. C. Kirsch, “Optical Correlator Guidance Technology Demonstration,” Proc. Soc. Photo-Opt. Instrum. Eng.29–35 (1988).

Leighton, R. B.

R. B. Leighton, Principles of Modern Physics (McGraw-Hill, New York, 1959), Chap. 1, Sec. 1-11.

Liu, H.-K.

D. A. Gregory, H.-K. Liu, “Large-Memory Real-Time Multichannel Multiplexed Pattern Recognition,” Appl. Opt. 23, 4560–4570 (1984).
[CrossRef] [PubMed]

McClelland, J. C.

D. E. Rumelhart, J. C. McClelland, Parallel Distributed Processing (MIT Press, Cambridge, 1986), Vols. 1 and 2.

Rumelhart, D. E.

D. E. Rumelhart, J. C. McClelland, Parallel Distributed Processing (MIT Press, Cambridge, 1986), Vols. 1 and 2.

Torre, V.

Upatnieks, J.

J. G. Duthie, J. Upatnieks, “Compact Real-Time Coherent Optical Correlators,” Opt. Eng. 23, 007–011 (Jan./Feb.1984).

Verri, A.

Widrow, B.

B. Widrow, M. E. Hoff, “Adaptive Switching Circuits,” IRE WESCON Conv. Rec. Part 4, 96 (1980).

Appl. Opt. (1)

D. A. Gregory, H.-K. Liu, “Large-Memory Real-Time Multichannel Multiplexed Pattern Recognition,” Appl. Opt. 23, 4560–4570 (1984).
[CrossRef] [PubMed]

INNS/IEEE Proc. 1 JCNN (1)

R. Hecht-Nielsen, “Theory of the Backpropagation Neural Network,” INNS/IEEE Proc. 1 JCNN 1, 593–606 (1989).

IRE WESCON Conv. Rec. Part (1)

B. Widrow, M. E. Hoff, “Adaptive Switching Circuits,” IRE WESCON Conv. Rec. Part 4, 96 (1980).

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

Neural Networks (1)

S. Grossberg, “Nonlinear Neural Networks: Principles, Mechanisms, and Architectures,” Neural Networks 1, No. 1, 17–62 (1988).
[CrossRef]

Opt. Eng. (1)

J. G. Duthie, J. Upatnieks, “Compact Real-Time Coherent Optical Correlators,” Opt. Eng. 23, 007–011 (Jan./Feb.1984).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

W. M. Crowe, J. C. Kirsch, “Optical Correlator Guidance Technology Demonstration,” Proc. Soc. Photo-Opt. Instrum. Eng.29–35 (1988).

Other (5)

B. K. P. Horn, Robot Vision (McGraw-Hill, New York, 1986), Chap. 12, p. 284.

B. K. P. Horn, Robot Vision (McGraw-Hill, New York, 1986), Chap. 13, p. 318.

H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, MA (1950), Chap. 8, Sec. 8-6.

R. B. Leighton, Principles of Modern Physics (McGraw-Hill, New York, 1959), Chap. 1, Sec. 1-11.

D. E. Rumelhart, J. C. McClelland, Parallel Distributed Processing (MIT Press, Cambridge, 1986), Vols. 1 and 2.

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Figures (5)

Fig. 1
Fig. 1

Geometry for a missile mounted camera. The optical axis of the camera is fixed parallel to the forward velocity, and the focal plane defines the local 2-D image coordinates.

Fig. 2
Fig. 2

Binocular system. The right image is obtained in terms of the left imaging by a translation l ¯ along the baseline and a rotation α ¯ through the stereo angle. Both |l| and |α| are assumed small.

Fig. 3
Fig. 3

Rotating surveillance camera. The camera rotates at a uniform angular velocity about the vertical axis. Its purpose is to detect targets moving with respect to the background.

Fig. 4
Fig. 4

Linear relaxation network. At each pixel the frame differenc is used to train the single weight by means of the LMS technique.

Fig. 5
Fig. 5

Linear architecture for the adaptive smoothness algorithm of Eq. (22). The weights are interpreted as signals while the fixed derivative images are used as weights, thus resolving the issue of weight transport from one node to the next.

Equations (57)

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δ f = f - f .
T R S L = ( 1 + δ T ) ( 1 + δ R ) ( 1 + δ S ) ( 1 + δ L ) 1 + δ T + δ R + δ S + δ L .
x = ( T ) x = ( 1 + δ T ) x = x + ( δ T ) x .
x = x + d x ,
( δ T ) x = d x .
( δ T ) y = d y ;
( δ T ) z = d z ;
( δ T ) t = d t .
r = d θ × r , t = t , or ( δ R ) x = z d θ y - y d θ z ,
( δ R ) y = x d θ z - z d θ x ,
( δ R ) z = y d θ x - x d θ y ,
( δ R ) t = 0.
( δ S ) x = ( d k ) x ,
( δ S ) y = ( d k ) y ,
( δ S ) z = ( d k ) z ,
( δ S ) t = ( d k ) t .
r = r - ( d V ) t , t = t - 1 c 2 ( d V · r ) ,
( δ L ) x = - d V x t ,
( δ L ) y = - d V y t ,
( δ L ) z = - d V z t ,
( δ L ) t = - 1 c 2 ( d V x x + d V y y + d V z z ) .
x = x + x , y = y + y , z = z + z , t = t + t ,
x = d x + d k x - d V x t + z d θ y - y d θ z , y = d y + d k y - d V y t + x d θ z - z d θ x , z = d z + d k z - d V z t + y d θ x - x d θ y , t = d t + d k t - 1 c 2 ( x d V x + y d V y + z d V z ) .
ν = d x ν + μ d α μ ν x μ
f = f + μ μ f x μ .
f ( x , y , z , t ) = f ( x , y , z , t ) + d t f t + d r · f + d θ · ( r × f ) + d k ( t f t + r · f ) - d V · ( r c 2 f t + t f ) .
r × f ( r - R c ) × f
r · f ( r - r 0 ) · f ,
f = f - f 0 τ z k V K · f + τ J ω J · [ ( r + f 0 z R J ) × f ] + Δ z z r · f + τ ω M · ( r × f ) ,
T = f - f = - f 0 τ z ( V x - ω R Y ) f x - f 0 τ z ( V y + ω R x ) f y + ω τ ( x f y - y f x ) + Δ z z ( x f x + y f y ) .
T ( x , y ) = j = 1 4 α j ( x , y ) I j ( x , y ) ,
I 1 = f x , I 2 = f y , I 3 = x f y - y f x , I 4 = x f x + y f y ,
f R = f L - l f L x + α ( z f L x - x f L z ) .
f R - f L = ( α z - l ) δ f L x .
f L - f R = - ( α z - l ) f R x .
f R - f L = - f 0 ( l z - α ) x ( f R + f L 2 ) .
Δ f = ( f 0 z V x - f 0 ω ) τ f x + f 0 z V y τ f y .
Δ f + f 0 w τ f x = f 0 z V · f .
Δ f = i exp [ i ( k z - ω t ) ] [ - ω d t + k d z - ω t ( d ω ω ) + k z d k k - d V ω z c 2 + d V ( k t ) ] ,
Δ f = ( c t - z ) ( k d V c - d k ) .
d k = k d V c .
d k = k c g d t = k g c d z c
d k k = g d z c 2 ,
T n = j α n j I n j ,
S n = j m n j I n j .
n n 2 .
E = a n n 2 + b n j σ n j 2 ,
n j σ n j 2 = ( 1 2 K ) n j k = n - K n + K ( m k j - m ¯ n j ) 2 ,
m ¯ n j = ( 1 2 K + 1 ) l = n - k n + K m l j ,
E m p q = - m ˙ p q .
- 2 a ( T p - S p ) I p q .
1 2 K n j k 2 ( m k j - m ¯ n j ) [ δ p k - ( 1 2 K + 1 ) l δ p l ] δ q j ,
1 K n k = n - K n + K m k δ p k , - 1 K ( 2 K + 1 ) n k = n - K n + K l = n - K n + K m l δ p k , - 1 K ( 2 K + 1 ) n k = n - K n + K l = n - K n + K m k δ p l , + 1 K ( 2 K + 1 ) 2 n k = n - K n + K l = n - K n + K h = n - K n + K m h δ p l ,
1 K n k m k δ p k = 1 K n = p - K p + K m p = 2 K + 1 K m p , = 1 K ( 2 K + 1 ) n k , l m l δ p k = - 1 K ( 2 K + 1 ) n = p - K p + K l = n - K n + K m l = - ( 2 K + 1 K ) ( m ¯ ¯ p ) ,
m ˙ p q = 2 a ( T p - S p ) I p q + [ ( 2 K + 1 ) / K ] b ( m ¯ ¯ p - m p ) .
m ¯ ¯ p = 1 9 ( m p - 2 + 2 m p - 1 + 3 m p + 2 m p + 1 + m p + 2 ) ,
m ¯ ¯ p = 1 25 ( m p - 4 + 2 m p - 3 + 3 m p - 2 + 4 m p - 1 + 5 m p + 4 m p + 1 + 3 m p + 2 + 2 m p + 3 + m p + 4 ) .

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