Abstract

We address three-dimensional (3D) object classification with computational holographic imaging. A 3D object can be reconstructed at different planes by use of a single hologram. We apply principal component and Fisher linear discriminant analyses based on Gabor-wavelet feature vectors to classify 3D objects measured by digital interferometry. Experimental and simulation results are presented for regional filtering concentrated at specific positions and for overall grid filtering. The proposed technique substantially reduces the dimensionality of the 3D classification problem. To the best of our knowledge, this is the first report on the use of the proposed technique for 3D object classification.

© 2004 Optical Society of America

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    [CrossRef]

2002 (2)

Y. Frauel, B. Javidi, “Digital three-dimensional image correlation by use of computer-reconstructed integral imaging,” Appl. Opt. 41, 5488–5496 (2002).
[CrossRef] [PubMed]

C. Liu, H. Wechsler, “Gabor feature based classification using the enhanced Fisher linear discriminant model for face recognition,” IEEE Trans. Image Process. 11, 467–476 (2002).
[CrossRef]

2001 (3)

2000 (1)

1999 (2)

J. J. Esteve-Taboada, D. Mas, J. Garcia, “Three-dimensional object recognition by Fourier transform profilometry,” Appl. Opt. 38, 4760–4765 (1999).
[CrossRef]

M. J. Lyons, J. Budynek, S. Akamatsu, “Automatic classification of single facial images,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 1357–1362 (1999).
[CrossRef]

1998 (1)

1997 (2)

I. Yamaguchi, T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
[CrossRef] [PubMed]

P. N. Belhumer, J. P. Hespanha, D. J. Kriegman, “Eigenfaces vs. Fisherfaces: recognition using class specific linear projection,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 711–720 (1997).
[CrossRef]

1996 (2)

D. L. Swets, J. Weng, “Using discriminant eigenfeatures for image retrieval,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 831–836 (1996).
[CrossRef]

T. S. Lee, “Image representation using 2D Gabor wavelets,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 959–971 (1996).
[CrossRef]

1993 (1)

M. Lades, J. C. Vorbruggen, J. Buhmann, J. Lange, C. v.d. Malsburg, R. P. Wurtz, W. Konen, “Distortion invariant object recognition in the dynamic link architecture,” IEEE Trans. Comput. 42, 300–311 (1993).
[CrossRef]

1988 (1)

J. G. Daugman, “Complete discrete 2-D Gabor transforms by neural networks for image analysis and compression,” IEEE Trans. Acoust. Speech Signal Process. 36, 1169–1179 (1988).
[CrossRef]

1985 (1)

Akamatsu, S.

M. J. Lyons, J. Budynek, S. Akamatsu, “Automatic classification of single facial images,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 1357–1362 (1999).
[CrossRef]

Belhumer, P. N.

P. N. Belhumer, J. P. Hespanha, D. J. Kriegman, “Eigenfaces vs. Fisherfaces: recognition using class specific linear projection,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 711–720 (1997).
[CrossRef]

Budynek, J.

M. J. Lyons, J. Budynek, S. Akamatsu, “Automatic classification of single facial images,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 1357–1362 (1999).
[CrossRef]

Buhmann, J.

M. Lades, J. C. Vorbruggen, J. Buhmann, J. Lange, C. v.d. Malsburg, R. P. Wurtz, W. Konen, “Distortion invariant object recognition in the dynamic link architecture,” IEEE Trans. Comput. 42, 300–311 (1993).
[CrossRef]

Castro, M.

Daugman, J. G.

J. G. Daugman, “Complete discrete 2-D Gabor transforms by neural networks for image analysis and compression,” IEEE Trans. Acoust. Speech Signal Process. 36, 1169–1179 (1988).
[CrossRef]

J. G. Daugman, “Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters,” J. Opt. Soc. Am. A 2, 1160–1169 (1985).
[CrossRef] [PubMed]

Duda, R. O.

R. O. Duda, P. E. Hart, D. G. Stork, Pattern Classification 2nd, (Wiley, New York, 2001).

Esteve-Taboada, J. J.

Frauel, Y.

Garcia, J.

Goudail, F.

F. Goudail, P. Réfrégier, “Statistical algorithms for target detection in coherent active polarimetric images,” J. Opt. Soc. Am. 18, 3049–3060 (2001).
[CrossRef]

Hart, P. E.

R. O. Duda, P. E. Hart, D. G. Stork, Pattern Classification 2nd, (Wiley, New York, 2001).

Hespanha, J. P.

P. N. Belhumer, J. P. Hespanha, D. J. Kriegman, “Eigenfaces vs. Fisherfaces: recognition using class specific linear projection,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 711–720 (1997).
[CrossRef]

Javidi, B.

Konen, W.

M. Lades, J. C. Vorbruggen, J. Buhmann, J. Lange, C. v.d. Malsburg, R. P. Wurtz, W. Konen, “Distortion invariant object recognition in the dynamic link architecture,” IEEE Trans. Comput. 42, 300–311 (1993).
[CrossRef]

Kriegman, D. J.

P. N. Belhumer, J. P. Hespanha, D. J. Kriegman, “Eigenfaces vs. Fisherfaces: recognition using class specific linear projection,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 711–720 (1997).
[CrossRef]

Lades, M.

M. Lades, J. C. Vorbruggen, J. Buhmann, J. Lange, C. v.d. Malsburg, R. P. Wurtz, W. Konen, “Distortion invariant object recognition in the dynamic link architecture,” IEEE Trans. Comput. 42, 300–311 (1993).
[CrossRef]

Lange, J.

M. Lades, J. C. Vorbruggen, J. Buhmann, J. Lange, C. v.d. Malsburg, R. P. Wurtz, W. Konen, “Distortion invariant object recognition in the dynamic link architecture,” IEEE Trans. Comput. 42, 300–311 (1993).
[CrossRef]

Lee, T. S.

T. S. Lee, “Image representation using 2D Gabor wavelets,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 959–971 (1996).
[CrossRef]

Liu, C.

C. Liu, H. Wechsler, “Gabor feature based classification using the enhanced Fisher linear discriminant model for face recognition,” IEEE Trans. Image Process. 11, 467–476 (2002).
[CrossRef]

Lyons, M. J.

M. J. Lyons, J. Budynek, S. Akamatsu, “Automatic classification of single facial images,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 1357–1362 (1999).
[CrossRef]

Mahalanobis, A.

A. Mahalanobis, “Review of correlation filters and their application for scene matching,” in Optoelectronic Devices and Systems for Processing, B. Javidi, K. M. Johnson, eds., Proc. SPIECR65, 240–260 (1996).

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

Mas, D.

Norris-Zachery, K.

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

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

Perona, M. T.

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

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

Réfrégier, P.

F. Goudail, P. Réfrégier, “Statistical algorithms for target detection in coherent active polarimetric images,” J. Opt. Soc. Am. 18, 3049–3060 (2001).
[CrossRef]

Rosen, J.

Sadjadi, F. A.

F. A. Sadjadi, “New results in the use of polarization diversity for classification of radar targets,” in Automatic Target Recognition XII, F. A. Sadjadi, ed., Proc. SPIE4726, 26–34 (2002).
[CrossRef]

Stork, D. G.

R. O. Duda, P. E. Hart, D. G. Stork, Pattern Classification 2nd, (Wiley, New York, 2001).

Swets, D. L.

D. L. Swets, J. Weng, “Using discriminant eigenfeatures for image retrieval,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 831–836 (1996).
[CrossRef]

Tajahuerce, E.

v.d. Malsburg, C.

M. Lades, J. C. Vorbruggen, J. Buhmann, J. Lange, C. v.d. Malsburg, R. P. Wurtz, W. Konen, “Distortion invariant object recognition in the dynamic link architecture,” IEEE Trans. Comput. 42, 300–311 (1993).
[CrossRef]

Vorbruggen, J. C.

M. Lades, J. C. Vorbruggen, J. Buhmann, J. Lange, C. v.d. Malsburg, R. P. Wurtz, W. Konen, “Distortion invariant object recognition in the dynamic link architecture,” IEEE Trans. Comput. 42, 300–311 (1993).
[CrossRef]

Wechsler, H.

C. Liu, H. Wechsler, “Gabor feature based classification using the enhanced Fisher linear discriminant model for face recognition,” IEEE Trans. Image Process. 11, 467–476 (2002).
[CrossRef]

Weng, J.

D. L. Swets, J. Weng, “Using discriminant eigenfeatures for image retrieval,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 831–836 (1996).
[CrossRef]

Wurtz, R. P.

M. Lades, J. C. Vorbruggen, J. Buhmann, J. Lange, C. v.d. Malsburg, R. P. Wurtz, W. Konen, “Distortion invariant object recognition in the dynamic link architecture,” IEEE Trans. Comput. 42, 300–311 (1993).
[CrossRef]

Yamaguchi, I.

Zhang, T.

Appl. Opt. (4)

IEEE Trans. Acoust. Speech Signal Process. (1)

J. G. Daugman, “Complete discrete 2-D Gabor transforms by neural networks for image analysis and compression,” IEEE Trans. Acoust. Speech Signal Process. 36, 1169–1179 (1988).
[CrossRef]

IEEE Trans. Comput. (1)

M. Lades, J. C. Vorbruggen, J. Buhmann, J. Lange, C. v.d. Malsburg, R. P. Wurtz, W. Konen, “Distortion invariant object recognition in the dynamic link architecture,” IEEE Trans. Comput. 42, 300–311 (1993).
[CrossRef]

IEEE Trans. Image Process. (1)

C. Liu, H. Wechsler, “Gabor feature based classification using the enhanced Fisher linear discriminant model for face recognition,” IEEE Trans. Image Process. 11, 467–476 (2002).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (4)

T. S. Lee, “Image representation using 2D Gabor wavelets,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 959–971 (1996).
[CrossRef]

P. N. Belhumer, J. P. Hespanha, D. J. Kriegman, “Eigenfaces vs. Fisherfaces: recognition using class specific linear projection,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 711–720 (1997).
[CrossRef]

D. L. Swets, J. Weng, “Using discriminant eigenfeatures for image retrieval,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 831–836 (1996).
[CrossRef]

M. J. Lyons, J. Budynek, S. Akamatsu, “Automatic classification of single facial images,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 1357–1362 (1999).
[CrossRef]

J. Opt. Soc. Am. (1)

F. Goudail, P. Réfrégier, “Statistical algorithms for target detection in coherent active polarimetric images,” J. Opt. Soc. Am. 18, 3049–3060 (2001).
[CrossRef]

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

Opt. Lett. (3)

Other (6)

F. A. Sadjadi, “New results in the use of polarization diversity for classification of radar targets,” in Automatic Target Recognition XII, F. A. Sadjadi, ed., Proc. SPIE4726, 26–34 (2002).
[CrossRef]

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

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

A. Mahalanobis, “Review of correlation filters and their application for scene matching,” in Optoelectronic Devices and Systems for Processing, B. Javidi, K. M. Johnson, eds., Proc. SPIECR65, 240–260 (1996).

R. O. Duda, P. E. Hart, D. G. Stork, Pattern Classification 2nd, (Wiley, New York, 2001).

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Figures (19)

Fig. 1
Fig. 1

Three-dimensional object classification: U O is the reconstructed hologram of the 3D object; W P and W F are the weights for the PCA and FLD, respectively; m z j is the sample mean of class j; Σ̂ zz j is the sample covariance of class j.

Fig. 2
Fig. 2

Optical sensing system for 3D object: (a) phase-shift interferometry to detect the Fresnel pattern, (b) hologram reconstruction at specific longitudinal depths.

Fig. 3
Fig. 3

Reconstructed images of the class 1 object at different longitudinal distances: (a) d = -922.5 mm, (b) d = -882.5 mm, (c) d = -842.5 mm, (d) d = -823.5 mm.

Fig. 4
Fig. 4

Reconstructed images of the class 2 object at different longitudinal distances: (a) d = -922.5 mm, (b) d = -882.5 mm, (c) d = -842.5 mm, (d) d = -823.5 mm.

Fig. 5
Fig. 5

Gabor jets for the object shown in Fig. 4(c) when n = 1: (a) m = 1, (b) m = 3, (c) m = 5.

Fig. 6
Fig. 6

Gabor jets for the object shown in Fig. 4(c) when n = 2: (a) m = 1, (b) m = 3, (c) m = 5.

Fig. 7
Fig. 7

Gabor jets for the object shown in Fig. 4(c) when n = 3: (a) m = 1, (b) m = 3, (c) m = 5.

Fig. 8
Fig. 8

Gabor jets for the object shown in Fig. 4(c) when n = 4: (a) m = 1, (b) m = 3, (c) m = 5.

Fig. 9
Fig. 9

Gabor jets for the object shown in Fig. 4(c) when n = 5: (a) m = 1, (b) m = 3, (c) m = 5.

Fig. 10
Fig. 10

Basis images for the subspace for six randomly chosen training Gabor jets when n = 1 and m = 1: (a) PCA1, (b) PCA2, (c) PCA3, (d) FLD.

Fig. 11
Fig. 11

Basis images for the subspace for six randomly chosen training Gabor jets when n = 2 and m = 2: (a) PCA1, (b) PCA2, (c) PCA3, (d) FLD.

Fig. 12
Fig. 12

Basis images for the subspace for six randomly chosen training Gabor jets when n = 3 and m = 3: (a) PCA1, (b) PCA2, (c) PCA3, (d) FLD.

Fig. 13
Fig. 13

Basis images for the subspace for six randomly chosen training Gabor jets when n = 4 and m = 4: (a) PCA1, (b) PCA2, (c) PCA3, (d) FLD.

Fig. 14
Fig. 14

Basis images for the subspace for six randomly chosen training Gabor jets when n = 5 and m = 5: (a) PCA1, (b) PCA2, (c) PCA3, (d) FLD.

Fig. 15
Fig. 15

Feature vectors from headlights.

Fig. 16
Fig. 16

Correct decision rate (percent) of feature vectors from the left headlight; n = ALL (implies that 30 components of the Gabor jets were used).

Fig. 17
Fig. 17

Feature vectors formed at the nodes of a rectangular grid.

Fig. 18
Fig. 18

Correct decision rates (percent) of feature vectors from the overall grid (l = 2); n = ALL (implies that 1350 components of the Gabor jets were used).

Fig. 19
Fig. 19

Correct decision rates (percent) of feature vectors from the overall grid (l = 4); n = ALL (implies that 1350 components of the Gabor jets were used).

Equations (9)

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

UOm, n, d=expiπλdΔx2m2+Δy2n2×m=0Nx-1n=0Ny-1HOm, n×expiπλdΔx2m2+Δy2n2×exp-i2πmmNx+nnNy,
gx=|k|2σ2exp-|k|2|x|22σ2expjk · x-exp-σ22,
Gk=2πexp-σ22|k|2 |k-k|2-exp-σ22|k|2|k|2+|k|2.
ST=SB+SW=k=1ntxk-mxk-mt,
S˜B=WFtSBWF=j=1c njm˜j-m˜m˜j-m˜t,
S˜W=WFtSWWF=j=1ci=1njyi-m˜jyi-m˜jt,
Jxˆ=Ex-xˆ2  when xˆ=μx+k=1l ykek.
JWF, WP=|WFtWPtSBWPWF|/|WFtWPtSWWPWF|.
zCĵifĵ=argminjgjz,

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