Abstract

We demonstrate the validity of wavelet-based processing for recognition and classification of three-dimensional phase objects. One Fresnel digital hologram of each of the three-dimensional (3-D) phase objects to be classified is recorded. The electronic holograms are processed digitally to permit 3-D object information to be retrieved as two-dimensional digital complex images. We use a Mexican-hat wavelet- matched filter (WMF) to enhance the correlation peak and discriminate between the objects. The WMF performs a wavelet transform (WT) to enhance the significant features of the images and the correlation of the WT coefficients thus obtained. We compare the feasibility of a WMF-based object classifier with the matched-filter-based classifier to classify our four 3-D phase objects in a 3-D scene into true or false classes with minimal error.

© 2006 Optical Society of America

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References

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2006 (1)

A. Nelleri, U. Gopinathan, J. Joseph, and K. Singh, "Three-dimensional object recognition from digital Fresnel hologram by wavelet matched filtering," Opt. Commun. 259,499-506 (2006).
[CrossRef]

2005 (2)

2004 (2)

2002 (1)

2001 (4)

2000 (2)

1999 (1)

1997 (1)

1994 (2)

1993 (1)

1990 (1)

1986 (1)

1955 (1)

G. Nomarski, "Microinterféromètre différentiel à ondes polarisées," J. Phys. Radium 16, S9-S13 (1955).

1942 (1)

F. Zernike, "Phase contrast, a new method for the microscopic observation of transparent objects," Physica 9, 686-698 (1942).
[CrossRef]

Blu, T.

Carapezza, E.

Castro, M.

Colomb, T.

Cuche, E.

Depeursinge, C.

Emery, Y.

Frauel, Y.

Gopinathan, U.

A. Nelleri, U. Gopinathan, J. Joseph, and K. Singh, "Three-dimensional object recognition from digital Fresnel hologram by wavelet matched filtering," Opt. Commun. 259,499-506 (2006).
[CrossRef]

A. Nelleri, U. Gopinathan, J. Joseph, and K. Singh, "Wavelet based three-dimensional object recognition using single off-axis digital Fresnel hologram," in Opto-Ireland 2005, Photonic Engineering, B.W.Bowe, G.Byrne, A.J.Flanagan, T.J.Glynn, J.Magee, G.M.O'Connor, R.F.O'Dowd, G.D.O'Sullivan, and J.T.Sheridan, eds., Proc. SPIE 5827,30-37 (2005).

Hassebrook, L.

Javidi, B.

Joseph, J.

A. Nelleri, U. Gopinathan, J. Joseph, and K. Singh, "Three-dimensional object recognition from digital Fresnel hologram by wavelet matched filtering," Opt. Commun. 259,499-506 (2006).
[CrossRef]

A. Nelleri, U. Gopinathan, J. Joseph, and K. Singh, "Wavelet based three-dimensional object recognition using single off-axis digital Fresnel hologram," in Opto-Ireland 2005, Photonic Engineering, B.W.Bowe, G.Byrne, A.J.Flanagan, T.J.Glynn, J.Magee, G.M.O'Connor, R.F.O'Dowd, G.D.O'Sullivan, and J.T.Sheridan, eds., Proc. SPIE 5827,30-37 (2005).

Juptner, W.

Jutamulia, S.

F. T. S. Yu and S. Jutamulia, eds., Optical Pattern Recognition (Cambridge U. Press, 1998).

Kim, T.

Krumbugel, M. A.

Kumar, B. V. K. Vijaya

Liebling, M.

Lu, T.

Magistretti, P. J.

Marquet, P.

Matoba, O.

E. Tajahuerce, O. Matoba, and B. Javidi, "Shift-invariant three-dimensional object recognition by means of digital holography," Appl. Opt 40, 3877-3886 (2001).
[CrossRef]

Moon, I.

Nelleri, A.

A. Nelleri, U. Gopinathan, J. Joseph, and K. Singh, "Three-dimensional object recognition from digital Fresnel hologram by wavelet matched filtering," Opt. Commun. 259,499-506 (2006).
[CrossRef]

A. Nelleri, U. Gopinathan, J. Joseph, and K. Singh, "Wavelet based three-dimensional object recognition using single off-axis digital Fresnel hologram," in Opto-Ireland 2005, Photonic Engineering, B.W.Bowe, G.Byrne, A.J.Flanagan, T.J.Glynn, J.Magee, G.M.O'Connor, R.F.O'Dowd, G.D.O'Sullivan, and J.T.Sheridan, eds., Proc. SPIE 5827,30-37 (2005).

Nomarski, G.

G. Nomarski, "Microinterféromètre différentiel à ondes polarisées," J. Phys. Radium 16, S9-S13 (1955).

Poon, T.-C.

Rappaz, B.

Roberge, D.

Rosen, J.

Schnars, U.

Sheng, Y.

Sheppard, C. J. R.

Shin, S. H.

Singh, K.

A. Nelleri, U. Gopinathan, J. Joseph, and K. Singh, "Three-dimensional object recognition from digital Fresnel hologram by wavelet matched filtering," Opt. Commun. 259,499-506 (2006).
[CrossRef]

A. Nelleri, U. Gopinathan, J. Joseph, and K. Singh, "Wavelet based three-dimensional object recognition using single off-axis digital Fresnel hologram," in Opto-Ireland 2005, Photonic Engineering, B.W.Bowe, G.Byrne, A.J.Flanagan, T.J.Glynn, J.Magee, G.M.O'Connor, R.F.O'Dowd, G.D.O'Sullivan, and J.T.Sheridan, eds., Proc. SPIE 5827,30-37 (2005).

Stark, H.

Szu, H.

Tajahuerce, E.

Totzeck, M.

Unser, M.

Wu, R.

Yeom, S.

Yu, F. T. S.

F. T. S. Yu and S. Jutamulia, eds., Optical Pattern Recognition (Cambridge U. Press, 1998).

Zernike, F.

F. Zernike, "Phase contrast, a new method for the microscopic observation of transparent objects," Physica 9, 686-698 (1942).
[CrossRef]

Appl. Opt (1)

E. Tajahuerce, O. Matoba, and B. Javidi, "Shift-invariant three-dimensional object recognition by means of digital holography," Appl. Opt 40, 3877-3886 (2001).
[CrossRef]

Appl. Opt. (7)

J. Opt. Soc. Am. A (3)

J. Phys. Radium (1)

G. Nomarski, "Microinterféromètre différentiel à ondes polarisées," J. Phys. Radium 16, S9-S13 (1955).

Opt. Commun. (1)

A. Nelleri, U. Gopinathan, J. Joseph, and K. Singh, "Three-dimensional object recognition from digital Fresnel hologram by wavelet matched filtering," Opt. Commun. 259,499-506 (2006).
[CrossRef]

Opt. Express (1)

Opt. Lett. (6)

Physica (1)

F. Zernike, "Phase contrast, a new method for the microscopic observation of transparent objects," Physica 9, 686-698 (1942).
[CrossRef]

Other (4)

F. T. S. Yu and S. Jutamulia, eds., Optical Pattern Recognition (Cambridge U. Press, 1998).

B. Javidi, ed., Image Recognition and Classification (Marcel Dekker, 2002).
[CrossRef]

U. Schnars and W. Juptner, Digital Holography (Springer-Verlag, 2005).

A. Nelleri, U. Gopinathan, J. Joseph, and K. Singh, "Wavelet based three-dimensional object recognition using single off-axis digital Fresnel hologram," in Opto-Ireland 2005, Photonic Engineering, B.W.Bowe, G.Byrne, A.J.Flanagan, T.J.Glynn, J.Magee, G.M.O'Connor, R.F.O'Dowd, G.D.O'Sullivan, and J.T.Sheridan, eds., Proc. SPIE 5827,30-37 (2005).

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Figures (6)

Fig. 1
Fig. 1

3-D phase objects used in the experiment: (a) Rectangle–Triangle, (b) Rectangle–Circle, (c) Circle–Triangle, (d) Triangle–Rectangle. A magnesium fluoride film of uniform thickness (∼500 μm) over a glass plate is used to form the features Rectangle, Triangle, and Circle. Dimensions: Rectangle, 1.5 mm in the x and 2.5 mm in the y directions; Triangle, 2 mm base (x direction) and 2 mm in the y direction; Circle, 2 mm diameter. The distance between the faces of objects in each case is 1 cm in the z direction.

Fig. 2
Fig. 2

Experimental setup: SF-CL, spatial filter and beam collimator; BS1, BS2, beam splitters; M1, M2, mirrors.

Fig. 3
Fig. 3

(a) 3-D hologram of the object Rectangle–Triangle. The hologram's size is 576 × 768 pixels. (b) Reconstructed intensity of the object's wavefront in the plane through the center of the 3-D object at a distance of 12.1 cm from the CCD. (c) Reconstructed phase of the object's wavefront in (b). (d) 3-D profile of the reconstructed phase object.

Fig. 4
Fig. 4

Features extracted after the Mexican-hat WT for an optimum scale value of 13.82 of reconstructed (a) intensity and (b) phase of the phase object.

Fig. 5
Fig. 5

(Color online) (a) Correlation plane corresponding to correlation between objects Rectangle–Triangle, d = 12.1 cm, and Rectangle–Triangle, d = 14.1 cm, for classical matched filtering. (b) Correlation peak for wavelet-matched filtering.

Fig. 6
Fig. 6

Normalized correlation values for correlation between objects of the same class (true class) and of two different classes (true and false classes) for the WMF and the MF. The y axis shows the normalized correlation values ranging from 0 to 1. The x axis denotes the object pair label. 1–10, Object pairs from true class (intraclass correlations); 11–25, object pairs from true and false classes (interclass correlations).

Tables (2)

Tables Icon

Table 1 Performance Matrices for WMFs and MFs a

Tables Icon

Table 2 Intraclass and Interclass Correlation Peak Values a

Equations (27)

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U o ( x , y ) = { U i ( x , y ) exp [ i ϕ 1 ( x , y ) ] exp [ i π λ Δ z × ( x 2 + y 2 ) ] } exp [ i ϕ 2 ( x , y ) ] ,
I ( x , y , d ) = | U o ( x , y , d ) exp ( i k 1 r ) + exp ( i k 2 r ) | 2 .
K = k 1 k 2 = 4 π λ sin θ 2 ,
U ˜ o ( x , y , d ) = exp ( i k d ) i τ U o ( x , y , 0 ) exp i π τ × [ ( x x ) 2 + ( y y ) 2 ] d x d y ,
W t ( s x , s y , b x , b y ) = m = 1 N x n = 1 N y t ( m , n ) h s x , s y , b x , b y * ( m , n ) ,
h s x , s y , b x , b y * ( m , n ) = 1 s x s y h ( m b x s x , n b y s y ) .
W r ( s x , s y , b x , b y ) = m = 1 N x n = 1 N y r ( m , n ) h s x , s y , b x , b y * ( m , n ) .
W t W r = k = - ( N x / 2 ) ( N x / 2 ) 1 l = - ( N y / 2 ) ( N y / 2 ) 1 T ( k , l ) R * ( k , l ) × H s x , s y ( k , l ) H s x , s y * ( k , l ) × exp [ i 2 π ( m k N x + n l N y ) ] .
H ( k , l ) = k x     2 k 2 N x     2 exp ( 2 π 2 k x     2 k 2 N x     2 ) k y     2 l 2 N y     2 × exp ( 2 π 2 k y     2 l 2 N y     2 ) ,
ϕ { A d i , B d b , C d c , D d d } ,
d i { d 1 , , d i , , d N } ,
Class   true:   ω 1 { A d i } , d i { d 1 , , d i , , d N } ,
Class   false:   ω 2 { B d b , C d c , D d d } .
R ϕ { R A d i , R B d b , R C d c , R D d d } , d i { d 1 , , d i , , d N } .
Class   true:   R ω 1 { A d i } , d i { d 1 , , d i , , d N } ,
Class   false:   R ω 2 { B d b , C d c , D d d } .
A d 1 : Rectangle–Triangle   at   a   distance   of   12 .1   cm,
A d 2 : Rectangle–Triangle   at   a   distance   of   14. 1   cm,
A d 3 : Rectangle–Triangle   at   a   distance   of   16 .1   cm,
A d 4 : Rectangle–Triangle   at   a   distance   of   18 .1   cm,
A d 5 : Rectangle–Triangle  at  a  distance  of   20. 1  cm,
B d b : Rectangle–Circle   at   a   distance   of   11 .95   cm,
C d c : Circle–Triangle   at   a   distance   of   12 .2   cm,
D d d : Triangle–Rectangle   at   a   distance   of   12 .2   cm.
PCE   = Correlation   peak   intensity   value   at   the   center   of   the   correlation   plane Total   energy   in   the   correlation   plane .
DR  =   Minimum   intraclass   correlation   value   at   the   center   of   correlation   plane Maximum   interclass   correlation   value   at   the   center   of   correlation   plane .
DR = Min | C i | i R ω 1 Max | C i | i R ω 2 ,

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