Abstract

A modified wavelet transform, the scale-adapted wavelet transform (SAWT), is proposed. The scale factor is adaptively changed according to the local structure of the input signal. The transformed image keeps the same dimensions as the input signal without losing the meaningful multiresolution representation. Some simple applications of the SAWT are discussed.

© 1996 Optical Society of America

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References

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  1. A. Grossman, Morlet, SIAM J. Math. 15, 723 (1984).
    [CrossRef]
  2. S. G. Mallat, IEEE Trans. Acoust. Speech Signal Process. 32, 699 (1989).
  3. H. H. Szu, B. A. Telfer, Opt. Eng. 33, 2111 (1989).
    [CrossRef]
  4. S. Kadambe, P. Srinivasan, Opt. Eng. 33, 2204 (1994).
    [CrossRef]
  5. G. Davis, S. Mallat, Z. Zhang, Opt. Eng. 33, 2183 (1994).
    [CrossRef]
  6. Y. Sheng, D. Roberge, H. Szu, T. Lu, Opt. Lett. 18, 299 (1993).
    [CrossRef] [PubMed]
  7. D. P. Casasent, J. S. Smokelin, A. Ye, Opt. Eng. 31, 1893 (1992).
    [CrossRef]

1994

S. Kadambe, P. Srinivasan, Opt. Eng. 33, 2204 (1994).
[CrossRef]

G. Davis, S. Mallat, Z. Zhang, Opt. Eng. 33, 2183 (1994).
[CrossRef]

1993

1992

D. P. Casasent, J. S. Smokelin, A. Ye, Opt. Eng. 31, 1893 (1992).
[CrossRef]

1989

S. G. Mallat, IEEE Trans. Acoust. Speech Signal Process. 32, 699 (1989).

H. H. Szu, B. A. Telfer, Opt. Eng. 33, 2111 (1989).
[CrossRef]

1984

A. Grossman, Morlet, SIAM J. Math. 15, 723 (1984).
[CrossRef]

Casasent, D. P.

D. P. Casasent, J. S. Smokelin, A. Ye, Opt. Eng. 31, 1893 (1992).
[CrossRef]

Davis, G.

G. Davis, S. Mallat, Z. Zhang, Opt. Eng. 33, 2183 (1994).
[CrossRef]

Grossman, A.

A. Grossman, Morlet, SIAM J. Math. 15, 723 (1984).
[CrossRef]

Kadambe, S.

S. Kadambe, P. Srinivasan, Opt. Eng. 33, 2204 (1994).
[CrossRef]

Lu, T.

Mallat, S.

G. Davis, S. Mallat, Z. Zhang, Opt. Eng. 33, 2183 (1994).
[CrossRef]

Mallat, S. G.

S. G. Mallat, IEEE Trans. Acoust. Speech Signal Process. 32, 699 (1989).

Morlet,

A. Grossman, Morlet, SIAM J. Math. 15, 723 (1984).
[CrossRef]

Roberge, D.

Sheng, Y.

Smokelin, J. S.

D. P. Casasent, J. S. Smokelin, A. Ye, Opt. Eng. 31, 1893 (1992).
[CrossRef]

Srinivasan, P.

S. Kadambe, P. Srinivasan, Opt. Eng. 33, 2204 (1994).
[CrossRef]

Szu, H.

Szu, H. H.

H. H. Szu, B. A. Telfer, Opt. Eng. 33, 2111 (1989).
[CrossRef]

Telfer, B. A.

H. H. Szu, B. A. Telfer, Opt. Eng. 33, 2111 (1989).
[CrossRef]

Ye, A.

D. P. Casasent, J. S. Smokelin, A. Ye, Opt. Eng. 31, 1893 (1992).
[CrossRef]

Zhang, Z.

G. Davis, S. Mallat, Z. Zhang, Opt. Eng. 33, 2183 (1994).
[CrossRef]

IEEE Trans. Acoust. Speech Signal Process

S. G. Mallat, IEEE Trans. Acoust. Speech Signal Process. 32, 699 (1989).

Opt. Eng.

H. H. Szu, B. A. Telfer, Opt. Eng. 33, 2111 (1989).
[CrossRef]

S. Kadambe, P. Srinivasan, Opt. Eng. 33, 2204 (1994).
[CrossRef]

G. Davis, S. Mallat, Z. Zhang, Opt. Eng. 33, 2183 (1994).
[CrossRef]

D. P. Casasent, J. S. Smokelin, A. Ye, Opt. Eng. 31, 1893 (1992).
[CrossRef]

Opt. Lett.

SIAM J. Math.

A. Grossman, Morlet, SIAM J. Math. 15, 723 (1984).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Relationship between s(x, y) and ▽f(x, y).

Fig. 2
Fig. 2

Binary square Mexican hat. The numbers denote the values of the areas.

Fig. 3
Fig. 3

(a) Space shuttle and (b) its SAWTed images.

Fig. 4
Fig. 4

(a) Lena, (b) edge image of Lena detected by the SAWT, (c) edge image of Lena detected by the Laplacian operator.

Fig. 5
Fig. 5

Pattern recognition system based on the SAWT.

Fig. 6
Fig. 6

(a) Autocorrelation peak of SAWTed space shuttle. (b) Autocorrelation peak of the space shuttle’s edge image detected by a Laplacian operator.

Fig. 7
Fig. 7

Eight aircraft used in discrimination testing. They are numbered from left to right, top to bottom. The reference object is number 3.

Tables (1)

Tables Icon

Table 1 Cross Correlations of Eight Aircraft

Equations (3)

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W f ( s x , s y , u , v ) = f ( x , y ) 1 s x , s y × h ( x u s x , y v s y ) d x d y ,
W f ( u , v ) = f ( x , y ) 1 s ( x , y ) h × [ x u s ( x , y ) , y v s ( x , y ) ] d x d y .
s ( x , y ) = { 1 | f ( x , y ) | > D max s max ( s max 1 ) | f ( x , y ) | D max otherwise ,

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