Abstract

We propose a class of generalized moment functions (GMFs) that can be used to determine a set of geometric points, namely, generalized centroids (G centroids), within an object. Based on a linear GMF, a mass centroid and its subcentroids can be defined and extracted, which provide information on the location and orientation of an object. Similar to traditional moment functions, GMFs can also be used to describe the global shape of an object, including symmetry and fullness. However, GMFs, along with G centroids and subcentroids, can further serve to construct a feature vector of an object, which is critical for image registration and invariant pattern recognition. One can extract more distinguishing features from the same object by changing the combination of GMFs. We present results that show simulations of pattern recognition from uniform backgrounds.

© 2005 Optical Society of America

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References

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  1. A. Rosenfeld, A. C. Kak, Digital Picture Processing, 2nd ed. (Academic, Orlando, Fla., 1982), pp. 286–290.
  2. R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, New York, 1992), pp. 514–518.
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    [CrossRef]
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  6. N. G. Chen, Q. Zhu, “Characterization of small absorbers inside turbid media,” Opt. Lett. 27, 252–254 (2002).
    [CrossRef]
  7. J. Flusser, J. Boldy, B. Zitova, “Invariants to convolution in arbitrary dimensions,” J. Math. Imag. Vis. 13, 101–113 (2000).
    [CrossRef]
  8. F. M. Candocia, “Moment relations and blur invariant conditions for finite-extent signals in one, two and N-dimensions,” Pattern Recogn. Lett. 25, 437–447 (2004).
    [CrossRef]
  9. S. Chang, C. P. Grover, “Centroid detection based on optical correlation,” Opt. Eng. 41, 2479–2486 (2002).
    [CrossRef]
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    [CrossRef]

2004 (1)

F. M. Candocia, “Moment relations and blur invariant conditions for finite-extent signals in one, two and N-dimensions,” Pattern Recogn. Lett. 25, 437–447 (2004).
[CrossRef]

2002 (2)

S. Chang, C. P. Grover, “Centroid detection based on optical correlation,” Opt. Eng. 41, 2479–2486 (2002).
[CrossRef]

N. G. Chen, Q. Zhu, “Characterization of small absorbers inside turbid media,” Opt. Lett. 27, 252–254 (2002).
[CrossRef]

2000 (2)

J. Flusser, J. Boldy, B. Zitova, “Invariants to convolution in arbitrary dimensions,” J. Math. Imag. Vis. 13, 101–113 (2000).
[CrossRef]

S. Chang, H. H. Arsenault, P. Garcia-Martinez, C. P. Grover, “Invariant pattern recognition based on centroids,” Appl. Opt. 39, 6641 (2000).
[CrossRef]

1999 (2)

1987 (1)

1962 (1)

M. K. Hu, “Visual pattern recognition by moment invariants,” IRE Trans. Inf. Theory IT-8, 179–187 (1962).

Arsenault, H. H.

Boldy, J.

J. Flusser, J. Boldy, B. Zitova, “Invariants to convolution in arbitrary dimensions,” J. Math. Imag. Vis. 13, 101–113 (2000).
[CrossRef]

Candocia, F. M.

F. M. Candocia, “Moment relations and blur invariant conditions for finite-extent signals in one, two and N-dimensions,” Pattern Recogn. Lett. 25, 437–447 (2004).
[CrossRef]

Caprari, R. S.

Chang, S.

S. Chang, C. P. Grover, “Centroid detection based on optical correlation,” Opt. Eng. 41, 2479–2486 (2002).
[CrossRef]

S. Chang, H. H. Arsenault, P. Garcia-Martinez, C. P. Grover, “Invariant pattern recognition based on centroids,” Appl. Opt. 39, 6641 (2000).
[CrossRef]

Chen, N. G.

Flusser, J.

J. Flusser, J. Boldy, B. Zitova, “Invariants to convolution in arbitrary dimensions,” J. Math. Imag. Vis. 13, 101–113 (2000).
[CrossRef]

Freeman, M. O.

Garcia-Martinez, P.

Gonzalez, R. C.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, New York, 1992), pp. 514–518.

Grover, C. P.

S. Chang, C. P. Grover, “Centroid detection based on optical correlation,” Opt. Eng. 41, 2479–2486 (2002).
[CrossRef]

S. Chang, H. H. Arsenault, P. Garcia-Martinez, C. P. Grover, “Invariant pattern recognition based on centroids,” Appl. Opt. 39, 6641 (2000).
[CrossRef]

Hu, M. K.

M. K. Hu, “Visual pattern recognition by moment invariants,” IRE Trans. Inf. Theory IT-8, 179–187 (1962).

Kak, A. C.

A. Rosenfeld, A. C. Kak, Digital Picture Processing, 2nd ed. (Academic, Orlando, Fla., 1982), pp. 286–290.

Miller, P. C.

Rosenfeld, A.

A. Rosenfeld, A. C. Kak, Digital Picture Processing, 2nd ed. (Academic, Orlando, Fla., 1982), pp. 286–290.

Saleh, B. E. A.

Woods, R. E.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, New York, 1992), pp. 514–518.

Zhu, Q.

Zitova, B.

J. Flusser, J. Boldy, B. Zitova, “Invariants to convolution in arbitrary dimensions,” J. Math. Imag. Vis. 13, 101–113 (2000).
[CrossRef]

Appl. Opt. (4)

IRE Trans. Inf. Theory (1)

M. K. Hu, “Visual pattern recognition by moment invariants,” IRE Trans. Inf. Theory IT-8, 179–187 (1962).

J. Math. Imag. Vis. (1)

J. Flusser, J. Boldy, B. Zitova, “Invariants to convolution in arbitrary dimensions,” J. Math. Imag. Vis. 13, 101–113 (2000).
[CrossRef]

Opt. Eng. (1)

S. Chang, C. P. Grover, “Centroid detection based on optical correlation,” Opt. Eng. 41, 2479–2486 (2002).
[CrossRef]

Opt. Lett. (1)

Pattern Recogn. Lett. (1)

F. M. Candocia, “Moment relations and blur invariant conditions for finite-extent signals in one, two and N-dimensions,” Pattern Recogn. Lett. 25, 437–447 (2004).
[CrossRef]

Other (2)

A. Rosenfeld, A. C. Kak, Digital Picture Processing, 2nd ed. (Academic, Orlando, Fla., 1982), pp. 286–290.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, New York, 1992), pp. 514–518.

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Figures (10)

Fig. 1
Fig. 1

Centroid and zero-crossing point.

Fig. 2
Fig. 2

G centroids generated by various GMFs. C0 is the mass centroid.

Fig. 3
Fig. 3

Error distances Ed between G centroids obtained from an object and its Gaussian noisy version: diamonds, result obtained from the conventional centroid detection method; squares, result obtained by convolution-based centroid detection; stars and circles, results from G centroids detected by probing functions (L3 + iL3) and (H3 + iH3), respectively.

Fig. 4
Fig. 4

Centroid and subcentroids.

Fig. 5
Fig. 5

Mass centroids, subcentroids, and synthetic centroids of nine aircraft.

Fig. 6
Fig. 6

G centroids change their relative positions to become mass centroids when the object rotates.

Fig. 7
Fig. 7

Four objects and their five G centroids.

Fig. 8
Fig. 8

Feature point, feature phasor, and feature vector.

Fig. 9
Fig. 9

Test animals: left to right, pig, hen, ox, fox, goat, elephant, cow, and horse.

Fig. 10
Fig. 10

Nine aircraft used in testing.

Tables (6)

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Table 1 Centroid Position (Xn, Yn) Detected from a Noisy Imagea

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Table 2 Orientation Angles Detected by Synthetic Subcentroids

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Table 3 Positions of G Centroids of Six Objects, O1–O6

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Table 4 Feature Distances between Animalsa

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Table 5 Feature Invariant of Nine Aircrafta

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Table 6 Recognition Results Obtained by a Neural Network

Equations (21)

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m p q = - - f ( x , y ) x p y q d x d y ,
m p q = - - f ( x , y ) ( x - x 0 ) p ( y - y 0 ) q d x d y .
Φ 3 = ( η 30 - 3 η 12 ) 2 + ( 3 η 21 - η 03 ) 2 ,
m p q ( x , y ) = f ( x , y ) ( x p , y q ) .
m 10 = f ( x , y ) x ,
m 01 = f ( x , y ) y .
m 10 ( x 0 , y ) = 0.
m 01 ( x , y 0 ) = 0.
Centroid = location { [ f ( x , y ) ( x + i y ) ] = 0 inside f ( x , y ) } .
Centroid = location { Max [ | f ( x , y ) × m f ( x , y ) G ( x , y ) ] } ,
m w ( x , y ) = [ S r ( x ) + i S i ( y ) ] circ ( 2 r / w ) ,
GMF ( x , y ) = f ( x , y ) m w ( x , y ) .
S r ( - x ) = - S r ( x ) ,             S i ( - y ) = - S i ( y ) .
GMF ( s , t ) = [ f ( x , y ) + n ( x , y ) ] m w ( x , y ) = f ( x , y ) m w ( x , y ) + n ( x , y ) m w ( x , y ) = f ( x , y ) m w ( x , y ) + n ( x , y ) S r × ( x - s ) d x d y + i n ( x , y ) S i ( y - t ) d x d y = f ( x , y ) m w ( x , y ) + S r ( x - s ) × [ n ( x , y ) d y ] d x + i S i ( y - t ) × [ n ( x , y ) d x ] d y f ( x , y ) m w ( x , y ) .
P 1 = P 1 ( x , y ) - P m ( x , y ) ,
P 2 = P 2 ( x , y ) - P m ( x , y ) .
P = C 0 ( x 0 , y 0 ) - C 1 ( x 1 , y 1 ) = p 01 exp ( i φ 01 ) ,
V = [ P 1 , P 2 , P n ] .
D f = V 1 - V 2 .
m = p i j 2 / M 0 ,
M 0 = - - f ( x , y ) d x d y .

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