Abstract

We introduce a new and efficient distortion-invariant super image tracker and pose estimator based on a linear phase coefficient composite filter. The super image consists of a weighted sum of training images chosen to span the distortion range under analysis. Unlike correlation-based composite filter design, the super image is implemented by means of a complex vector inner product operation. A super image vector inner product is implemented by elementwise multiplication of a super image template by a window of interest in the input scene and summation of the elementwise operations. The resulting amplitude indicates target detection, and the resulting phase indicates the value of scale, orientation, or movement of the target object. The mathematical characteristics of the super image vector inner product are presented, and its application is demonstrated.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  8. W. Su, L. G. Hassebrook, and V. G. Yalla, "Active mulitspot projection for object tracking and recongnition," in Optical Information Systems II, B. Javidi and D. Psaltis, eds., Proc. SPIE 5557,223-232 (2004).
  9. M. E. Lhamon, L. G. Hassebrook, and R. Daley, "Distortion-invariant optical pattern recognition without correlation," in Optical Pattern Recognition VI, D.P. Casasent and T.-H. Chao, eds., Proc. SPIE 2490,278-290 (1995).
  10. M. E. Lhamon and L. G. Hassebrook, "Translation-invariant optical pattern recognition without correlation," Opt. Eng. 35, 2700-2709 (1996).
    [CrossRef]
  11. L. G. Hassebrook, M. E. Lhamon, M. Wang, and J. P. Chatterjee, "Distortion parameter estimation using complex distortion-invariant correlation filter bank responses," in Optical Pattern Recognition VI, D.P. Casasent and T.-H. Chao, eds., Proc. SPIE 2490,64-76 (1995).
  12. L. G. Hassebrook, M. E. Lhamon, M. Wang, and J. Chatterjee, "Postprocessing of correlation for orientation estimation," Opt. Eng. 36, 2710-2718 (1997).
    [CrossRef]
  13. W. J. Chimitt and L. G. Hassebrook, "Scene reconstruction from partially overlapping images with use of composite filters," J. Opt. Soc. Am. A 16, 2124-2135 (1999).
    [CrossRef]
  14. M. E. Lhamon, L. G. Hassebrook, and J. P. Chatterjee, "Complex spatial images for multi-parameter distortion-invariant optical pattern recognition and high level morphological transformations," in Optical Pattern Recognition VII, D. Casasent, ed., Proc. SPIE 2752,23-30 (1996).
  15. R. W. Cohn and L. G. Hassebrook, "Representation of fully complex functions on real-time spatial light modulators," in Optical Information Processing, F.T.S. Yu and S. Jutamulia, eds. (Cambridge U. Press, 1998), pp. 396-432.
  16. M. E. Lhamon, L. G. Hassebrook, and J. P. Chatterjee, "Complex spatial images for rotation-invariant pattern recognition and gray level morphological transforms," Asian J. Phys. 8, 347-354 (1999).
  17. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: the Art of Scientific Computing (Cambridge U. Press, 1992).
  18. A. Alsamman and M. S. Alam, "Face recognition through pose estimation and fringe-adjusted joint transform correlation," Opt. Eng. 42, 560-567 (2003).
    [CrossRef]

2003

A. Alsamman and M. S. Alam, "Face recognition through pose estimation and fringe-adjusted joint transform correlation," Opt. Eng. 42, 560-567 (2003).
[CrossRef]

1999

W. J. Chimitt and L. G. Hassebrook, "Scene reconstruction from partially overlapping images with use of composite filters," J. Opt. Soc. Am. A 16, 2124-2135 (1999).
[CrossRef]

M. E. Lhamon, L. G. Hassebrook, and J. P. Chatterjee, "Complex spatial images for rotation-invariant pattern recognition and gray level morphological transforms," Asian J. Phys. 8, 347-354 (1999).

1997

L. G. Hassebrook, M. E. Lhamon, M. Wang, and J. Chatterjee, "Postprocessing of correlation for orientation estimation," Opt. Eng. 36, 2710-2718 (1997).
[CrossRef]

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]

1996

M. E. Lhamon and L. G. Hassebrook, "Translation-invariant optical pattern recognition without correlation," Opt. Eng. 35, 2700-2709 (1996).
[CrossRef]

1994

1992

1990

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

1980

1964

A. Vander Lugt, "Signal detection by complex spatial filtering," IEEE Trans. Inf. Theory 10, 139-145 (1964).
[CrossRef]

Abushagur, M. A. G.

Alam, M. S.

A. Alsamman and M. S. Alam, "Face recognition through pose estimation and fringe-adjusted joint transform correlation," Opt. Eng. 42, 560-567 (2003).
[CrossRef]

Alsamman, A.

A. Alsamman and M. S. Alam, "Face recognition through pose estimation and fringe-adjusted joint transform correlation," Opt. Eng. 42, 560-567 (2003).
[CrossRef]

Casasent, D.

Chatterjee, J.

L. G. Hassebrook, M. E. Lhamon, M. Wang, and J. Chatterjee, "Postprocessing of correlation for orientation estimation," Opt. Eng. 36, 2710-2718 (1997).
[CrossRef]

Chatterjee, J. P.

M. E. Lhamon, L. G. Hassebrook, and J. P. Chatterjee, "Complex spatial images for rotation-invariant pattern recognition and gray level morphological transforms," Asian J. Phys. 8, 347-354 (1999).

M. E. Lhamon, L. G. Hassebrook, and J. P. Chatterjee, "Complex spatial images for multi-parameter distortion-invariant optical pattern recognition and high level morphological transformations," in Optical Pattern Recognition VII, D. Casasent, ed., Proc. SPIE 2752,23-30 (1996).

L. G. Hassebrook, M. E. Lhamon, M. Wang, and J. P. Chatterjee, "Distortion parameter estimation using complex distortion-invariant correlation filter bank responses," in Optical Pattern Recognition VI, D.P. Casasent and T.-H. Chao, eds., Proc. SPIE 2490,64-76 (1995).

Chimitt, W. J.

Cohn, R. W.

R. W. Cohn and L. G. Hassebrook, "Representation of fully complex functions on real-time spatial light modulators," in Optical Information Processing, F.T.S. Yu and S. Jutamulia, eds. (Cambridge U. Press, 1998), pp. 396-432.

Daley, R.

M. E. Lhamon, L. G. Hassebrook, and R. Daley, "Distortion-invariant optical pattern recognition without correlation," in Optical Pattern Recognition VI, D.P. Casasent and T.-H. Chao, eds., Proc. SPIE 2490,278-290 (1995).

Epperson, J. F.

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: the Art of Scientific Computing (Cambridge U. Press, 1992).

Hassebrook, L. G.

M. E. Lhamon, L. G. Hassebrook, and J. P. Chatterjee, "Complex spatial images for rotation-invariant pattern recognition and gray level morphological transforms," Asian J. Phys. 8, 347-354 (1999).

W. J. Chimitt and L. G. Hassebrook, "Scene reconstruction from partially overlapping images with use of composite filters," J. Opt. Soc. Am. A 16, 2124-2135 (1999).
[CrossRef]

L. G. Hassebrook, M. E. Lhamon, M. Wang, and J. Chatterjee, "Postprocessing of correlation for orientation estimation," Opt. Eng. 36, 2710-2718 (1997).
[CrossRef]

M. E. Lhamon and L. G. Hassebrook, "Translation-invariant optical pattern recognition without correlation," Opt. Eng. 35, 2700-2709 (1996).
[CrossRef]

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

L. G. Hassebrook, M. E. Lhamon, M. Wang, and J. P. Chatterjee, "Distortion parameter estimation using complex distortion-invariant correlation filter bank responses," in Optical Pattern Recognition VI, D.P. Casasent and T.-H. Chao, eds., Proc. SPIE 2490,64-76 (1995).

W. Su, L. G. Hassebrook, and V. G. Yalla, "Active mulitspot projection for object tracking and recongnition," in Optical Information Systems II, B. Javidi and D. Psaltis, eds., Proc. SPIE 5557,223-232 (2004).

M. E. Lhamon, L. G. Hassebrook, and R. Daley, "Distortion-invariant optical pattern recognition without correlation," in Optical Pattern Recognition VI, D.P. Casasent and T.-H. Chao, eds., Proc. SPIE 2490,278-290 (1995).

M. E. Lhamon, L. G. Hassebrook, and J. P. Chatterjee, "Complex spatial images for multi-parameter distortion-invariant optical pattern recognition and high level morphological transformations," in Optical Pattern Recognition VII, D. Casasent, ed., Proc. SPIE 2752,23-30 (1996).

R. W. Cohn and L. G. Hassebrook, "Representation of fully complex functions on real-time spatial light modulators," in Optical Information Processing, F.T.S. Yu and S. Jutamulia, eds. (Cambridge U. Press, 1998), pp. 396-432.

Hester, C. F.

Hostetler, L.

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

Kumar, B. V. K. Vijaya

Lhamon, M. E.

M. E. Lhamon, L. G. Hassebrook, and J. P. Chatterjee, "Complex spatial images for rotation-invariant pattern recognition and gray level morphological transforms," Asian J. Phys. 8, 347-354 (1999).

L. G. Hassebrook, M. E. Lhamon, M. Wang, and J. Chatterjee, "Postprocessing of correlation for orientation estimation," Opt. Eng. 36, 2710-2718 (1997).
[CrossRef]

M. E. Lhamon and L. G. Hassebrook, "Translation-invariant optical pattern recognition without correlation," Opt. Eng. 35, 2700-2709 (1996).
[CrossRef]

M. E. Lhamon, L. G. Hassebrook, and J. P. Chatterjee, "Complex spatial images for multi-parameter distortion-invariant optical pattern recognition and high level morphological transformations," in Optical Pattern Recognition VII, D. Casasent, ed., Proc. SPIE 2752,23-30 (1996).

M. E. Lhamon, L. G. Hassebrook, and R. Daley, "Distortion-invariant optical pattern recognition without correlation," in Optical Pattern Recognition VI, D.P. Casasent and T.-H. Chao, eds., Proc. SPIE 2490,278-290 (1995).

L. G. Hassebrook, M. E. Lhamon, M. Wang, and J. P. Chatterjee, "Distortion parameter estimation using complex distortion-invariant correlation filter bank responses," in Optical Pattern Recognition VI, D.P. Casasent and T.-H. Chao, eds., Proc. SPIE 2490,64-76 (1995).

Mahalanobis, A.

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: the Art of Scientific Computing (Cambridge U. Press, 1992).

Ravichandran, G.

Riasati, V. R.

Sims, S. R. F.

Song, S.

Su, W.

W. Su, L. G. Hassebrook, and V. G. Yalla, "Active mulitspot projection for object tracking and recongnition," in Optical Information Systems II, B. Javidi and D. Psaltis, eds., Proc. SPIE 5557,223-232 (2004).

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: the Art of Scientific Computing (Cambridge U. Press, 1992).

Vander Lugt, A.

A. Vander Lugt, "Signal detection by complex spatial filtering," IEEE Trans. Inf. Theory 10, 139-145 (1964).
[CrossRef]

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: the Art of Scientific Computing (Cambridge U. Press, 1992).

Wang, M.

L. G. Hassebrook, M. E. Lhamon, M. Wang, and J. Chatterjee, "Postprocessing of correlation for orientation estimation," Opt. Eng. 36, 2710-2718 (1997).
[CrossRef]

L. G. Hassebrook, M. E. Lhamon, M. Wang, and J. P. Chatterjee, "Distortion parameter estimation using complex distortion-invariant correlation filter bank responses," in Optical Pattern Recognition VI, D.P. Casasent and T.-H. Chao, eds., Proc. SPIE 2490,64-76 (1995).

Yalla, V. G.

W. Su, L. G. Hassebrook, and V. G. Yalla, "Active mulitspot projection for object tracking and recongnition," in Optical Information Systems II, B. Javidi and D. Psaltis, eds., Proc. SPIE 5557,223-232 (2004).

Appl. Opt.

Asian J. Phys.

M. E. Lhamon, L. G. Hassebrook, and J. P. Chatterjee, "Complex spatial images for rotation-invariant pattern recognition and gray level morphological transforms," Asian J. Phys. 8, 347-354 (1999).

IEEE Trans. Inf. Theory

A. Vander Lugt, "Signal detection by complex spatial filtering," IEEE Trans. Inf. Theory 10, 139-145 (1964).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

L. G. Hassebrook, M. E. Lhamon, M. Wang, and J. Chatterjee, "Postprocessing of correlation for orientation estimation," Opt. Eng. 36, 2710-2718 (1997).
[CrossRef]

M. E. Lhamon and L. G. Hassebrook, "Translation-invariant optical pattern recognition without correlation," Opt. Eng. 35, 2700-2709 (1996).
[CrossRef]

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

A. Alsamman and M. S. Alam, "Face recognition through pose estimation and fringe-adjusted joint transform correlation," Opt. Eng. 42, 560-567 (2003).
[CrossRef]

Other

W. Su, L. G. Hassebrook, and V. G. Yalla, "Active mulitspot projection for object tracking and recongnition," in Optical Information Systems II, B. Javidi and D. Psaltis, eds., Proc. SPIE 5557,223-232 (2004).

M. E. Lhamon, L. G. Hassebrook, and R. Daley, "Distortion-invariant optical pattern recognition without correlation," in Optical Pattern Recognition VI, D.P. Casasent and T.-H. Chao, eds., Proc. SPIE 2490,278-290 (1995).

L. G. Hassebrook, M. E. Lhamon, M. Wang, and J. P. Chatterjee, "Distortion parameter estimation using complex distortion-invariant correlation filter bank responses," in Optical Pattern Recognition VI, D.P. Casasent and T.-H. Chao, eds., Proc. SPIE 2490,64-76 (1995).

M. E. Lhamon, L. G. Hassebrook, and J. P. Chatterjee, "Complex spatial images for multi-parameter distortion-invariant optical pattern recognition and high level morphological transformations," in Optical Pattern Recognition VII, D. Casasent, ed., Proc. SPIE 2752,23-30 (1996).

R. W. Cohn and L. G. Hassebrook, "Representation of fully complex functions on real-time spatial light modulators," in Optical Information Processing, F.T.S. Yu and S. Jutamulia, eds. (Cambridge U. Press, 1998), pp. 396-432.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: the Art of Scientific Computing (Cambridge U. Press, 1992).

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Figures (11)

Fig. 1
Fig. 1

(Color online) (a) Original nanobeads scene with 320 × 240 pixels. (b) Three nanobead matched filters at different depth z planes; the size of the first filter is 12 × 12 .

Fig. 2
Fig. 2

(Color online) Using the matched filter to detect and track the nanobeads.

Fig. 3
Fig. 3

Layout of a position-tracking SIVIP.

Fig. 4
Fig. 4

Decision tree.

Fig. 5
Fig. 5

(Color online) Target tracking trajectory.

Fig. 6
Fig. 6

(a) Direction and (b) distance SIVIP magnitude and phase.

Fig. 7
Fig. 7

(Color online) Tracking results with various shift steps.

Fig. 8
Fig. 8

Five face pose images used to create a rotational SIVIP.

Fig. 9
Fig. 9

(Color online) Magnitude and phase of face pose and scale-detection SIVIP.

Fig. 10
Fig. 10

(a) Rotation, (b) scale, (c) direction, and (d) distance SIVIP magnitude and phase.

Fig. 11
Fig. 11

(a) Superimposed image sequence of 11 original faces from a 100 frame video sequence. (b) Superimposed 3D face model with orientation and position estimated from an input sequence.

Tables (2)

Tables Icon

Table 1 MSEs for Various Shift Steps

Tables Icon

Table 2 Numerical Performance of SIVIP Versus Correlation

Equations (15)

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

R ( x , y ) = x , y I ( x + x , y + y ) h M F ( x , y ) x , y I ( x + x ,   y + y ) 2 x , y h M F ( x , y ) 2 ,
g ( x + Δ x n , y + Δ y n ) = t ( x , y ) ,
h s ( x , y ) = n = 0 N 1 g ( x + Δ x n , y + Δ y n ) e j θ n ,
θ n = 2 π r n r max ,
θ n = arctan ( Δ y n Δ x n ) .
z = x P ¯ y P ¯ h s ( x , y ) g ( x + Δ x m , y + Δ y m ) ,
h s ( x , y ) = n = 0 N 1 g ( x + Δ x n , y + Δ y n ) α n ,
G ¯ = [ g ¯ 0 g ¯ 1 g ¯ N 1 ] ,
g ¯ n = [ g ( x + Δ x n , y + Δ y n ) ] T .
h ¯ s , k = G ¯ α ¯ ,
c n = g ¯ n T h ¯ s , k .
c ¯ = G ¯ T h ¯ k = G ¯ T G ¯ α
α ¯ = ( G ¯ T G ¯ ) 1 c ¯ .
c n = exp ( j 2 π p n / N ) ,
c n = exp ( j 2 π s n / M ) ,

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