Abstract

We propose a filtering technique that uses laser radar (ladar) data to detect a target’s three-dimensional (3D) coordinates and shape within an input scene. A two-dimensional ladar range image is converted into 3D space, and then the 3D optimum nonlinear filtering technique is used to detect the 3D coordinates of targets (including the target’s distance from the sensor). The 3D optimum nonlinear filter is designed to detect distorted targets (i.e., out-of-plane and in-plane rotations and scale changes) and to be noise robust. The nonlinear filter is derived to minimize the mean of the output energy in response to the input scene in the presence of disjoint background noise and additive noise and to maintain a fixed output peak for the members of the true-class target training set. The system is tested with real ladar imagery in the presence of background clutter. The background clutter used in the system evaluation includes false objects that are similar to the true targets. The correlation output of ladar images shows a dominant peak at the target’s 3D coordinates.

© 2004 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2002 (1)

1997 (1)

S. Chang, M. Rioux, J. Domey, “Face recognition with range images and intensity images,” Opt. Eng. 35(4), 1106–1112 (1997).
[CrossRef]

1996 (1)

1995 (1)

1994 (1)

1989 (1)

1976 (1)

1960 (1)

J. L. Turin, “An introduction to matched filters,” IRE Trans. Inf. Theor. IT-6, 311–329 (1960).
[CrossRef]

Casasent, D.

Chang, S.

S. Chang, M. Rioux, J. Domey, “Face recognition with range images and intensity images,” Opt. Eng. 35(4), 1106–1112 (1997).
[CrossRef]

Domey, J.

S. Chang, M. Rioux, J. Domey, “Face recognition with range images and intensity images,” Opt. Eng. 35(4), 1106–1112 (1997).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Hong, S.

Javidi, B.

Laude, V.

Mahalanobis, A.

M. T. Prona, A. Mahalanobis, K. N. Zachery, “LADAR automatic target recognition using correlation filters,” in Automatic Target Recognition IX, F. A. Sadjadi, ed., Proc. SPIE3718, 388–396 (1999).
[CrossRef]

M. T. Prona, A. Mahalanobis, K. N. Zachery, “System level evaluations of LADAR ATR using correlation filters,” in Automatic Target Recognition X, F. A. Sadjadi, ed., Proc. SPIE4050, 69–75 (2000).
[CrossRef]

A. Mahalanobis, A. J. Van Nevel, “Performance of multi-dimensional algorithms for target detection in LADAR imagery,” in Algorithms and Systems for Optical Information Processing VI, B. Javidi, D. Psaltis, eds., Proc. SPIE4789, 134–147 (2002).
[CrossRef]

A. Mahalanobis, “Review of correlation filters and their application for scene matching,” in Optoelectronic Devices and Systems for Processing, Critical Reviews of Optical Science Technology, B. Javidi, K. M. Johnson, eds., Proc. SPIE CR65, 240–260 (1996).

Painchaud, D.

Prona, M. T.

M. T. Prona, A. Mahalanobis, K. N. Zachery, “LADAR automatic target recognition using correlation filters,” in Automatic Target Recognition IX, F. A. Sadjadi, ed., Proc. SPIE3718, 388–396 (1999).
[CrossRef]

M. T. Prona, A. Mahalanobis, K. N. Zachery, “System level evaluations of LADAR ATR using correlation filters,” in Automatic Target Recognition X, F. A. Sadjadi, ed., Proc. SPIE4050, 69–75 (2000).
[CrossRef]

Psaltis, D.

Refreigher, P.

Rioux, M.

S. Chang, M. Rioux, J. Domey, “Face recognition with range images and intensity images,” Opt. Eng. 35(4), 1106–1112 (1997).
[CrossRef]

Turin, J. L.

J. L. Turin, “An introduction to matched filters,” IRE Trans. Inf. Theor. IT-6, 311–329 (1960).
[CrossRef]

Van Nevel, A. J.

A. Mahalanobis, A. J. Van Nevel, “Performance of multi-dimensional algorithms for target detection in LADAR imagery,” in Algorithms and Systems for Optical Information Processing VI, B. Javidi, D. Psaltis, eds., Proc. SPIE4789, 134–147 (2002).
[CrossRef]

VanderLugt, A.

A. VanderLugt, Optical Signal Processing (Wiley, New York, 1992).

Wang, J.

Zachery, K. N.

M. T. Prona, A. Mahalanobis, K. N. Zachery, “System level evaluations of LADAR ATR using correlation filters,” in Automatic Target Recognition X, F. A. Sadjadi, ed., Proc. SPIE4050, 69–75 (2000).
[CrossRef]

M. T. Prona, A. Mahalanobis, K. N. Zachery, “LADAR automatic target recognition using correlation filters,” in Automatic Target Recognition IX, F. A. Sadjadi, ed., Proc. SPIE3718, 388–396 (1999).
[CrossRef]

Appl. Opt. (4)

IRE Trans. Inf. Theor. (1)

J. L. Turin, “An introduction to matched filters,” IRE Trans. Inf. Theor. IT-6, 311–329 (1960).
[CrossRef]

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

Opt. Eng. (1)

S. Chang, M. Rioux, J. Domey, “Face recognition with range images and intensity images,” Opt. Eng. 35(4), 1106–1112 (1997).
[CrossRef]

Opt. Lett. (1)

Other (8)

A. Mahalanobis, “Review of correlation filters and their application for scene matching,” in Optoelectronic Devices and Systems for Processing, Critical Reviews of Optical Science Technology, B. Javidi, K. M. Johnson, eds., Proc. SPIE CR65, 240–260 (1996).

B. Javidi, Image Recognition and Classification, Algorithms, Systems, and Applications (Marcel Dekker, New York, 2002).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

A. VanderLugt, Optical Signal Processing (Wiley, New York, 1992).

B. Javidi, J. L. Horner, eds., Real Time Optical Information Processing (Academic, New York, 1994).

M. T. Prona, A. Mahalanobis, K. N. Zachery, “LADAR automatic target recognition using correlation filters,” in Automatic Target Recognition IX, F. A. Sadjadi, ed., Proc. SPIE3718, 388–396 (1999).
[CrossRef]

M. T. Prona, A. Mahalanobis, K. N. Zachery, “System level evaluations of LADAR ATR using correlation filters,” in Automatic Target Recognition X, F. A. Sadjadi, ed., Proc. SPIE4050, 69–75 (2000).
[CrossRef]

A. Mahalanobis, A. J. Van Nevel, “Performance of multi-dimensional algorithms for target detection in LADAR imagery,” in Algorithms and Systems for Optical Information Processing VI, B. Javidi, D. Psaltis, eds., Proc. SPIE4789, 134–147 (2002).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Illustration of the conversion of a 2D-encoded ladar image to 3D binary space.

Fig. 2
Fig. 2

Two-dimensionally-encoded ladar range image used as a training target.

Fig. 3
Fig. 3

Two-dimensionally-encoded input ladar range image with the training target in the bottom right-hand corner.

Fig. 4
Fig. 4

Optimum nonlinear filter outputs without the background noise model at the location of the training target. The input ladar range image in Fig. 3 is applied to the filter in Ref. 12. Correlation output without the background noise model at the target depth level of (a) 25, (b) 24, (c) 26.

Fig. 5
Fig. 5

Optimum nonlinear filter outputs with the background noise model at the location of the training target. The input ladar range image in Fig. 3 is applied to the filter in Eq. (19). Correlation output of the optimum nonlinear filter with the background noise model at the target depth level of (a) 25, (b) 24, (c) 26.

Fig. 6
Fig. 6

Nine 2D-encoded ladar images of the true-class training target set. The azimuth and elevation of the true-class training targets are 60°, 70°, 80° (left to right) and 20°, 30°, 40° (bottom to top), respectively, and the distance of the targets from the ladar range sensor is 900 m.

Fig. 7
Fig. 7

2D-encoded input ladar image with the training target in the bottom right-hand corner and the true class nontraining target in the upper right-hand corner. The distance, elevation, and azimuth of the training target are 900 m, 70°, and 30°, respectively. The distance, elevation, and azimuth of the true-class nontraining target with respect to the ladar range sensor are 1000 m, 75°, and 35°, respectively.

Fig. 8
Fig. 8

Optimum nonlinear filter outputs with the background noise model at the location of the training target. The input ladar range image in Fig. 7 is applied to the filter in Eq. (19). Correlation output of the optimum nonlinear filter with the background noise model at the target depth level of (a) 25, (b) 24, (c) 26.

Fig. 9
Fig. 9

Optimum nonlinear filter outputs with the background noise model at the location of the true class nontraining target. The input ladar range image in Fig. 7 is applied to the filter in Eq. (19). Correlation output of the optimum nonlinear filter with the background noise model at the target depth level of (a) 74, (b) 73, (c) 75.

Equations (40)

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st=i=1T virit-τi+nbtwt-i=1T viwrit-τi+natwt,
ot=τ=0M-1 hτ-t*sτ,
oi0=t=0M-1 ht*rit=Ci,
k=0M-1 Hk*Rik=MCi,
E1Mk=0M-1 |Hk|2|Nk|2=1Mk=0M-1 |Hk|2E|Nk|2,
E|Nk|2=1MTi=1TΦb0k|Wk|2+|Wrik|2-2 |Wk|2dReWrik+1M Φa0k|Wk|2+1Ti=1Tmb2|Wk|2+|Wrik|2-2 |Wk|2dReWrik+2mamb|Wk|2×Re1-Wrikd+ma2|Wk|2,
1Mk=0M-1 |Hk|2|Sk|2,
wnMk=0M-1 |Hk|2E|Nk|2+wdMk=0M-1 |Hk|2|Sk|2,
k=0M-1 Hk*Rik=k=0M-1ak-jbkcik+jdik=k=0M-1akcik+bkdik+jakdik-bkcik=MCi.
k=0M-1akcik+bkdik=MCi  for i=1, 2,, T,
k=0M-1akdik-bkcik=0  for i=1, 2,, T.
wnMk=0M-1 |Hk|2E|Nk|2+wdMk=0M-1 |Hk|2|Sk|2=k=0M-1ak2+bk2Dk
Jk=0M-1ak2+bk2Dk+i=1T λ1iMCi-k=0M-1 akcik-k=0M-1 bkdik+i=1T λ2i0-k=0M-1 akdik+k=0M-1 bkcik.
Jak=2akDk-i=1T λ1icik-i=1T λ2idik=0,
Jbk=2bkDk-i=1T λ1idik+i=1T λ2icik=0.
δkl=1,k=l0,kl.
ak=i=1Tλ1icik+λ2idik2Dk,
bk=i=1Tλ1idik-λ2icik2Dk,
k=0M-112Dki=1Tλ1icikcpk+dikdpk+λ2idikcpk-cikdpk=MCp for p=1, 2,, T,
k=0M-112Dki=1Tλ1icikdpk-dikcpk+λ2idikdpk+cikcpk=0 for p=1, 2,, T.
λ1λ11 λ12  λ1Tt, λ2λ21 λ22  λ2Tt, CC1 C2  CTt, Ax,yk=0M-1ReRxkReRyk+ImRxkImRyk2Dk=k=0M-1cxkcyk+dxkdyk2Dk, Bx,yk=0M-1ImRxkReRyk-ReRxkImRyk2Dk=k=0M-1dxkcyk-cxkdyk2Dk,
λ1tA+λ2tB=MCt,
-λ1tB+λ2tA=0t.
λ1t=MCtA+BA-1B-1,
λ2t=MCtA+BA-1B-1BA-1.
ak+jbk=12Dki=1Tλ1icik+jdik+λ2idik-jcik=12Dki=1Tλ1i-jλ2icik+jdik.
Hk=i=1Tλ1i-jλ2iRik1MTi=1TΦb0k|Wk|2+|Wrik|2-2 |Wk|2d×ReWrik+1M Φa0k|Wk|2+1Ti=1Tmb2|Wk|2+|Wrik|2-2 |Wk|2dReWrik+2mamb|Wk|2Re1-Wrikd+ma2|Wk|2+|Sk|2
st=i=1T virit-τi+nbtwt-i=1T viwrit-τi+natwt,
st=i=1T virit-τi+nbtwt-writ-τi+natwt-i=1T vi-1natwt+nbtwt.
st=i=1T virit-τi+nbtwt-writ-τi+natwt.
|Wcik|2=Wk-Wrikexp-j2πkτiM2=|Wk|2+|Wrik|2-2ReWkexpj2πkτiMWri*k,
Eτiexp-j2πkτiM=Wkd,
Eτiexpj2πkτiM=Wk*d.
E|Nk|2=EνiEτiEnaEnbi=1T viNik2=1Ti=1T EτiEn|Nik|2,
En|Nik|2=EnFnbtwcit+natwt[nb-twci-t+na-tw-t.
En|Nik|2=En(Fnb0t+mbwcitnb0-t+mbwci-t+nb0t+mbwcitna0-t+maw-t+na0t+mawtnb0-t+mbwci-t+na0t+mawtna0-t+maw-t).
En|Nik|2=FRnb0t×wcitwci-t+FRna0t×wtw-t+mb2|Wcik|2+ma2|Wk|2+2mambReWcikW*k.
En|Nik|2=1M Φb0k|Wk|2+|Wrik|2-2ReWkexpj2πkτiMWri*k+1M Φa0k|Wk|2+mb2|Wk|2+|Wrik|2-2ReWkexpj2πkτiM×Wri*k+ma2|Wk|2+2mamb×Re|Wk|2-WrikW*k×exp-j2πkτiM.
EτiEn|Nik|2=1M Φb0k|Wk|2+|Wrik|2-2 |Wk|2dReWrik+1M Φa0k|Wk|2+mb2|Wk|2+|Wrik|2-2 |Wk|2dReWrik+ma2|Wk|2+2mamb|Wk|2Re1-Wrikd.
E|Nk|2=1MTi=1TΦb0k|Wk|2+|Wrik|2-2 |Wk|2dReWrik+1M Φa0k|k|2+1Ti=1Tmb2|Wk|2+|Wrik|2-2 |Wk|2dReWrik +2mamb|Wk|2Re1-Wrik2d+ma2|Wk|2.

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