Abstract

A multichannel, multilayer feed forward neural network model is proposed for rotation invariant recognition of objects. In the M channel network, each channel consists of a one dimensional slice of the two dimensional (2D) Fourier transform (FT) of the input pattern that connects fully to the weight matrix. Each slice is taken at different angles from the 2D FT of the object. From each channel, only one neuron can fire in the presence of the training object. The output layer sums up the response of the hidden layer neuron and confirms the presence of the object. Rotation invariant recognition from 0° to 360° is obtained even in the case of degraded images.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Arsenault and Y. Sheng, “Properties of the circular harmonic expansion for rotation-invariant pattern recognition,” Appl. Opt. 25, 3225–3229 (1986).
    [CrossRef] [PubMed]
  2. P. Bone, R. Young, and C. Chatwin, “Position-, rotation-, scale-, and orientation-invariant multiple object recognition from cluttered scenes,” Opt. Eng. 45, 077203 (2006).
    [CrossRef]
  3. C. Hester and D. Casasent, “Multivariant technique for multiclass pattern recognition,” Appl. Opt. 19, 1758–1761 (1980).
    [CrossRef] [PubMed]
  4. B. V. K. Vijaya Kumar, L. Hassebrook, and L. Hostetler, “Linear phase coefficient composite filter banks for distortion-invariant optical pattern recognition,” Opt. Eng. 29, 1033–1043 (1990).
    [CrossRef]
  5. B. V. K. Vijaya Kumar, A. Mahalanobis, and A. Takessian, “Optimal tradeoff circular harmonic function correlation filter methods providing controlled in-plane rotation response,” IEEE Trans. Image Process. 9, 1025–1034 (2000).
    [CrossRef]
  6. V. R. Riasati and M. A. G. Abushagur, “Projection-slice synthetic discriminant functions for optical pattern recognition,” Appl. Opt. 36, 3022–3034 (1997).
    [CrossRef] [PubMed]
  7. S. Goyal, N. K. Nischal, V. K. Beri, and A. K. Gupta, “Wavelet modified maximum average correlation height filter for rotation invariance that uses chirp encoding in a hybrid digital optical correlator,” Appl. Opt. 45, 4850–4857 (2006).
    [CrossRef] [PubMed]
  8. N. Wu, R. D. Alcock, N. A. Halliwell, and J. Coupland, “Rotationally invariant pattern recognition by use of linear and nonlinear cascaded filters,” Appl. Opt. 44, 4315–4322(2005).
    [CrossRef] [PubMed]
  9. M. Wang and A. Knoesen, “Rotation- and scale-invariant texture features based on spectral moment invariants,” J. Opt. Soc. Am. A 24, 2550–2557 (2007).
    [CrossRef]
  10. A. Mahalanobis, B. V. K. Vijaya Kumar, and D. Casasent, “Minimum average correlation filters,” Appl. Opt. 26, 3633–3640 (1987).
    [CrossRef] [PubMed]
  11. A. Mahalanobis, B. V. K. Vijaya Kumar, S. Song, and J. F. Epperson, “Unconstrained correlation filters,” Appl. Opt. 33, 3751–3759 (1994).
    [CrossRef] [PubMed]
  12. D. Casasent and Y. Wang, “A hierarchical classifier using new support vector machines for automatic target recognition,” Neural Netw. 18, 541–548 (2005).
    [CrossRef] [PubMed]
  13. G. L. Giles and T. Maxwell, “Learning, invariances and generalizations in higher order neural networks,” Appl. Opt. 26, 4972–4978 (1987).
    [CrossRef] [PubMed]
  14. Z. Yanxin, “Artificial neural networks and their optical implementation,” J. Optoelectron. Laser 1, 1–11 (1990).
  15. R. N. Bracewell, The Fourier Transform and Its Application, 3rd ed. (McGraw-Hill, 1999).
  16. M. Pohit, “A neural network model for object recognition under rotational distortion,” International Conference of Optics and Photonics (2009).
  17. R. Duda, P. Hart, and D. G. Stork, Pattern Classification, 2nd ed. (Wiley-Interscience, 2000).
  18. S. Haykin, Neural Networks, A Comprehensive Foundation, 2nd ed. (Prentice-Hall, 1999).
  19. MPEG7 shape image database downloaded from http://www.imageprocessingplace.com/root_files_V3/image_databases.htm.
  20. Caltech image database downloaded from www.vision.caltech.edu/Image_Datasets/

2007

2006

2005

N. Wu, R. D. Alcock, N. A. Halliwell, and J. Coupland, “Rotationally invariant pattern recognition by use of linear and nonlinear cascaded filters,” Appl. Opt. 44, 4315–4322(2005).
[CrossRef] [PubMed]

D. Casasent and Y. Wang, “A hierarchical classifier using new support vector machines for automatic target recognition,” Neural Netw. 18, 541–548 (2005).
[CrossRef] [PubMed]

2000

B. V. K. Vijaya Kumar, A. Mahalanobis, and A. Takessian, “Optimal tradeoff circular harmonic function correlation filter methods providing controlled in-plane rotation response,” IEEE Trans. Image Process. 9, 1025–1034 (2000).
[CrossRef]

1997

1994

1990

Z. Yanxin, “Artificial neural networks and their optical implementation,” J. Optoelectron. Laser 1, 1–11 (1990).

B. V. K. Vijaya Kumar, L. Hassebrook, and L. Hostetler, “Linear phase coefficient composite filter banks for distortion-invariant optical pattern recognition,” Opt. Eng. 29, 1033–1043 (1990).
[CrossRef]

1987

1986

1980

Abushagur, M. A. G.

Alcock, R. D.

Arsenault, H.

Beri, V. K.

Bone, P.

P. Bone, R. Young, and C. Chatwin, “Position-, rotation-, scale-, and orientation-invariant multiple object recognition from cluttered scenes,” Opt. Eng. 45, 077203 (2006).
[CrossRef]

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and Its Application, 3rd ed. (McGraw-Hill, 1999).

Casasent, D.

Chatwin, C.

P. Bone, R. Young, and C. Chatwin, “Position-, rotation-, scale-, and orientation-invariant multiple object recognition from cluttered scenes,” Opt. Eng. 45, 077203 (2006).
[CrossRef]

Coupland, J.

Duda, R.

R. Duda, P. Hart, and D. G. Stork, Pattern Classification, 2nd ed. (Wiley-Interscience, 2000).

Epperson, J. F.

Giles, G. L.

Goyal, S.

Gupta, A. K.

Halliwell, N. A.

Hart, P.

R. Duda, P. Hart, and D. G. Stork, Pattern Classification, 2nd ed. (Wiley-Interscience, 2000).

Hassebrook, L.

B. V. K. Vijaya Kumar, L. Hassebrook, and L. Hostetler, “Linear phase coefficient composite filter banks for distortion-invariant optical pattern recognition,” Opt. Eng. 29, 1033–1043 (1990).
[CrossRef]

Haykin, S.

S. Haykin, Neural Networks, A Comprehensive Foundation, 2nd ed. (Prentice-Hall, 1999).

Hester, C.

Hostetler, L.

B. V. K. Vijaya Kumar, L. Hassebrook, and L. Hostetler, “Linear phase coefficient composite filter banks for distortion-invariant optical pattern recognition,” Opt. Eng. 29, 1033–1043 (1990).
[CrossRef]

Knoesen, A.

Kumar, B. V. K. Vijaya

B. V. K. Vijaya Kumar, A. Mahalanobis, and A. Takessian, “Optimal tradeoff circular harmonic function correlation filter methods providing controlled in-plane rotation response,” IEEE Trans. Image Process. 9, 1025–1034 (2000).
[CrossRef]

A. Mahalanobis, B. V. K. Vijaya Kumar, S. Song, and J. F. Epperson, “Unconstrained correlation filters,” Appl. Opt. 33, 3751–3759 (1994).
[CrossRef] [PubMed]

B. V. K. Vijaya Kumar, L. Hassebrook, and L. Hostetler, “Linear phase coefficient composite filter banks for distortion-invariant optical pattern recognition,” Opt. Eng. 29, 1033–1043 (1990).
[CrossRef]

A. Mahalanobis, B. V. K. Vijaya Kumar, and D. Casasent, “Minimum average correlation filters,” Appl. Opt. 26, 3633–3640 (1987).
[CrossRef] [PubMed]

Mahalanobis, A.

B. V. K. Vijaya Kumar, A. Mahalanobis, and A. Takessian, “Optimal tradeoff circular harmonic function correlation filter methods providing controlled in-plane rotation response,” IEEE Trans. Image Process. 9, 1025–1034 (2000).
[CrossRef]

A. Mahalanobis, B. V. K. Vijaya Kumar, S. Song, and J. F. Epperson, “Unconstrained correlation filters,” Appl. Opt. 33, 3751–3759 (1994).
[CrossRef] [PubMed]

A. Mahalanobis, B. V. K. Vijaya Kumar, and D. Casasent, “Minimum average correlation filters,” Appl. Opt. 26, 3633–3640 (1987).
[CrossRef] [PubMed]

Maxwell, T.

Nischal, N. K.

Pohit, M.

M. Pohit, “A neural network model for object recognition under rotational distortion,” International Conference of Optics and Photonics (2009).

Riasati, V. R.

Sheng, Y.

Song, S.

Stork, D. G.

R. Duda, P. Hart, and D. G. Stork, Pattern Classification, 2nd ed. (Wiley-Interscience, 2000).

Takessian, A.

B. V. K. Vijaya Kumar, A. Mahalanobis, and A. Takessian, “Optimal tradeoff circular harmonic function correlation filter methods providing controlled in-plane rotation response,” IEEE Trans. Image Process. 9, 1025–1034 (2000).
[CrossRef]

Wang, M.

Wang, Y.

D. Casasent and Y. Wang, “A hierarchical classifier using new support vector machines for automatic target recognition,” Neural Netw. 18, 541–548 (2005).
[CrossRef] [PubMed]

Wu, N.

Yanxin, Z.

Z. Yanxin, “Artificial neural networks and their optical implementation,” J. Optoelectron. Laser 1, 1–11 (1990).

Young, R.

P. Bone, R. Young, and C. Chatwin, “Position-, rotation-, scale-, and orientation-invariant multiple object recognition from cluttered scenes,” Opt. Eng. 45, 077203 (2006).
[CrossRef]

Appl. Opt.

IEEE Trans. Image Process.

B. V. K. Vijaya Kumar, A. Mahalanobis, and A. Takessian, “Optimal tradeoff circular harmonic function correlation filter methods providing controlled in-plane rotation response,” IEEE Trans. Image Process. 9, 1025–1034 (2000).
[CrossRef]

J. Opt. Soc. Am. A

J. Optoelectron. Laser

Z. Yanxin, “Artificial neural networks and their optical implementation,” J. Optoelectron. Laser 1, 1–11 (1990).

Neural Netw.

D. Casasent and Y. Wang, “A hierarchical classifier using new support vector machines for automatic target recognition,” Neural Netw. 18, 541–548 (2005).
[CrossRef] [PubMed]

Opt. Eng.

B. V. K. Vijaya Kumar, L. Hassebrook, and L. Hostetler, “Linear phase coefficient composite filter banks for distortion-invariant optical pattern recognition,” Opt. Eng. 29, 1033–1043 (1990).
[CrossRef]

P. Bone, R. Young, and C. Chatwin, “Position-, rotation-, scale-, and orientation-invariant multiple object recognition from cluttered scenes,” Opt. Eng. 45, 077203 (2006).
[CrossRef]

Other

R. N. Bracewell, The Fourier Transform and Its Application, 3rd ed. (McGraw-Hill, 1999).

M. Pohit, “A neural network model for object recognition under rotational distortion,” International Conference of Optics and Photonics (2009).

R. Duda, P. Hart, and D. G. Stork, Pattern Classification, 2nd ed. (Wiley-Interscience, 2000).

S. Haykin, Neural Networks, A Comprehensive Foundation, 2nd ed. (Prentice-Hall, 1999).

MPEG7 shape image database downloaded from http://www.imageprocessingplace.com/root_files_V3/image_databases.htm.

Caltech image database downloaded from www.vision.caltech.edu/Image_Datasets/

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (15)

Fig. 1
Fig. 1

ith channel network with the 1D FT slice.

Fig. 2
Fig. 2

Neural network model for rotation invariant recognition.

Fig. 3
Fig. 3

(a) to (g) Images used for verification.

Fig. 4
Fig. 4

(a) Square modulus of the complex matched filter for image in Fig. 3a. (b) Square modulus of the weight matrix formed from Fig. 4a.

Fig. 5
Fig. 5

Average normalized output for the object in Fig. 3a for full 360 ° rotation.

Fig. 6
Fig. 6

Comparison of the output from all channels for the Figs. 3a, 3b. The horizontal axis represents the channel number, and the vertical axis represents the corresponding outputs.

Fig. 7
Fig. 7

Comparison of outputs from all channels for all the images in the database.

Fig. 8
Fig. 8

Degraded version of Fig. 3a at 110 ° : (a) noisy image, (b) blurred image, and (c) both noise and blur present.

Fig. 9
Fig. 9

Degraded version of Fig. 3a at 110 ° : (a) noisy image, (b) blurred image, and (c) both noise and blur present.

Fig. 10
Fig. 10

Output for all channels for the images in (a) Figs. 8a, 9a, (b) Figs. 8b, 9b, and (c) Figs. 8c, 9c.

Fig. 11
Fig. 11

(a) and (b) Gray level images.

Fig. 12
Fig. 12

(a) Square modulus of the complex matched filter for image in Fig. 11a. (b) Square modulus of the weight matrix formed from Fig. 11a.

Fig. 13
Fig. 13

Average normalized output for the object in Fig. 11 for full 360 ° rotation.

Fig. 14
Fig. 14

(a) and (b) Images in Figs. 11a, 11b with cluttered background.

Fig. 15
Fig. 15

Average normalized output for the object in Fig. 11 for full 360 ° rotation.

Equations (11)

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

net j = i = 0 m x i w j i ,
y j = f ( net j ) ,
net k = j = 0 n y j w k j ,
z k = f ( net k ) .
X i = [ x i 1 , x i 2 , x i 3 , , x i j , x i N ] ,
W k = [ w k 1 w k 2 w k j w k N ] ,
W [ w k j ] ,
h k = max ( IFT { W k X i } ) ,
H i = [ h k i ] T .
O i = 1 if max ( h k i ) d esired correlation peak value = 0 if max ( h k i ) < d esired correlation peak value ,
O = f ( k = 1 M u i O i + u 0 ) ,

Metrics