Abstract

The periodic woven structures of fabrics can be defined on the basis of the convolution theorem. Here an elementary unit with the minimum number of thread crossings and a nonrectangular two-dimensional comb function for the pattern of repetition is used to define woven structures. The expression derived is more compact than the conventional diagram for weaving, and the parameters that one needs to determine a given fabric can easily be extracted from its Fourier transform. Several results with real samples of the most common structures—plain, twill, and satin—are presented.

© 2001 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. O. Reynolds, J. B. DeVelis, G. B. Parrent, B. J. Thompson, The New Optics Notebook: Tutorial in Fourier Optics (Society for Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1989).
    [CrossRef]
  2. B. J. Thompson, “Optical transforms and coherent processing systems with insights from crystallography,” in Optical Data Processing, D. Casasent, ed. (Springer-Verlag, Berlin, 1978), pp. 17–52.
    [CrossRef]
  3. E. J. Wood, “Applying Fourier and associated transforms to pattern characterization in textiles,” Textile Res. J. 60, 212–220 (1990).
    [CrossRef]
  4. B. Xu, “Identifying fabric structures with fast Fourier transform techniques,” Textile Res. J. 66, 496–506 (1996).
    [CrossRef]
  5. M. S. Millán, J. Escofet, “Fourier-domain-based angular correlation for quasiperiodic pattern recognition. Applications to web inspection,” Appl. Opt. 35, 6253–6260 (1996).
    [CrossRef] [PubMed]
  6. T. J. Kang, C. H. Kim, K. W. Oh, “Automatic recognition of fabric weave patterns by digital image analysis,” Textile Res. J. 69, 77–83 (1999).
    [CrossRef]
  7. T. J. Kang, S. H. Choi, S. M. Kim, K. W. Oh, “Automatic structure analysis and objective evaluation of woven fabric using image analysis,” Textile Res. J. 71, 261–270 (2001).
    [CrossRef]
  8. T. Matsuyama, S.-I. Miura, M. Nagao, “Structural analysis of natural textures by Fourier transformation,” Comput. Vision Graph. Image Process. 24, 347–362 (1983).
    [CrossRef]

2001 (1)

T. J. Kang, S. H. Choi, S. M. Kim, K. W. Oh, “Automatic structure analysis and objective evaluation of woven fabric using image analysis,” Textile Res. J. 71, 261–270 (2001).
[CrossRef]

1999 (1)

T. J. Kang, C. H. Kim, K. W. Oh, “Automatic recognition of fabric weave patterns by digital image analysis,” Textile Res. J. 69, 77–83 (1999).
[CrossRef]

1996 (2)

1990 (1)

E. J. Wood, “Applying Fourier and associated transforms to pattern characterization in textiles,” Textile Res. J. 60, 212–220 (1990).
[CrossRef]

1983 (1)

T. Matsuyama, S.-I. Miura, M. Nagao, “Structural analysis of natural textures by Fourier transformation,” Comput. Vision Graph. Image Process. 24, 347–362 (1983).
[CrossRef]

Choi, S. H.

T. J. Kang, S. H. Choi, S. M. Kim, K. W. Oh, “Automatic structure analysis and objective evaluation of woven fabric using image analysis,” Textile Res. J. 71, 261–270 (2001).
[CrossRef]

DeVelis, J. B.

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, B. J. Thompson, The New Optics Notebook: Tutorial in Fourier Optics (Society for Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1989).
[CrossRef]

Escofet, J.

Kang, T. J.

T. J. Kang, S. H. Choi, S. M. Kim, K. W. Oh, “Automatic structure analysis and objective evaluation of woven fabric using image analysis,” Textile Res. J. 71, 261–270 (2001).
[CrossRef]

T. J. Kang, C. H. Kim, K. W. Oh, “Automatic recognition of fabric weave patterns by digital image analysis,” Textile Res. J. 69, 77–83 (1999).
[CrossRef]

Kim, C. H.

T. J. Kang, C. H. Kim, K. W. Oh, “Automatic recognition of fabric weave patterns by digital image analysis,” Textile Res. J. 69, 77–83 (1999).
[CrossRef]

Kim, S. M.

T. J. Kang, S. H. Choi, S. M. Kim, K. W. Oh, “Automatic structure analysis and objective evaluation of woven fabric using image analysis,” Textile Res. J. 71, 261–270 (2001).
[CrossRef]

Matsuyama, T.

T. Matsuyama, S.-I. Miura, M. Nagao, “Structural analysis of natural textures by Fourier transformation,” Comput. Vision Graph. Image Process. 24, 347–362 (1983).
[CrossRef]

Millán, M. S.

Miura, S.-I.

T. Matsuyama, S.-I. Miura, M. Nagao, “Structural analysis of natural textures by Fourier transformation,” Comput. Vision Graph. Image Process. 24, 347–362 (1983).
[CrossRef]

Nagao, M.

T. Matsuyama, S.-I. Miura, M. Nagao, “Structural analysis of natural textures by Fourier transformation,” Comput. Vision Graph. Image Process. 24, 347–362 (1983).
[CrossRef]

Oh, K. W.

T. J. Kang, S. H. Choi, S. M. Kim, K. W. Oh, “Automatic structure analysis and objective evaluation of woven fabric using image analysis,” Textile Res. J. 71, 261–270 (2001).
[CrossRef]

T. J. Kang, C. H. Kim, K. W. Oh, “Automatic recognition of fabric weave patterns by digital image analysis,” Textile Res. J. 69, 77–83 (1999).
[CrossRef]

Parrent, G. B.

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, B. J. Thompson, The New Optics Notebook: Tutorial in Fourier Optics (Society for Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1989).
[CrossRef]

Reynolds, G. O.

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, B. J. Thompson, The New Optics Notebook: Tutorial in Fourier Optics (Society for Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1989).
[CrossRef]

Thompson, B. J.

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, B. J. Thompson, The New Optics Notebook: Tutorial in Fourier Optics (Society for Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1989).
[CrossRef]

B. J. Thompson, “Optical transforms and coherent processing systems with insights from crystallography,” in Optical Data Processing, D. Casasent, ed. (Springer-Verlag, Berlin, 1978), pp. 17–52.
[CrossRef]

Wood, E. J.

E. J. Wood, “Applying Fourier and associated transforms to pattern characterization in textiles,” Textile Res. J. 60, 212–220 (1990).
[CrossRef]

Xu, B.

B. Xu, “Identifying fabric structures with fast Fourier transform techniques,” Textile Res. J. 66, 496–506 (1996).
[CrossRef]

Appl. Opt. (1)

Comput. Vision Graph. Image Process. (1)

T. Matsuyama, S.-I. Miura, M. Nagao, “Structural analysis of natural textures by Fourier transformation,” Comput. Vision Graph. Image Process. 24, 347–362 (1983).
[CrossRef]

Textile Res. J. (4)

E. J. Wood, “Applying Fourier and associated transforms to pattern characterization in textiles,” Textile Res. J. 60, 212–220 (1990).
[CrossRef]

B. Xu, “Identifying fabric structures with fast Fourier transform techniques,” Textile Res. J. 66, 496–506 (1996).
[CrossRef]

T. J. Kang, C. H. Kim, K. W. Oh, “Automatic recognition of fabric weave patterns by digital image analysis,” Textile Res. J. 69, 77–83 (1999).
[CrossRef]

T. J. Kang, S. H. Choi, S. M. Kim, K. W. Oh, “Automatic structure analysis and objective evaluation of woven fabric using image analysis,” Textile Res. J. 71, 261–270 (2001).
[CrossRef]

Other (2)

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, B. J. Thompson, The New Optics Notebook: Tutorial in Fourier Optics (Society for Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1989).
[CrossRef]

B. J. Thompson, “Optical transforms and coherent processing systems with insights from crystallography,” in Optical Data Processing, D. Casasent, ed. (Springer-Verlag, Berlin, 1978), pp. 17–52.
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Plain fabric structure as the convolution of the base and the repetition pattern (rectangular 2D comb function).

Fig. 2
Fig. 2

(a) Plain fabric structure of Fig. 1 as the convolution of a minimum base and a nonrectangular repetition pattern. (b) Minimum bases b m (x, y) that generate the plain fabric of (a).

Fig. 3
Fig. 3

Twill fabric structure as the convolution of a minimum base and a nonrectangular repetition pattern. Rectangle C corresponds to the weaving diagram conventionally used to represent this twill structure.

Fig. 4
Fig. 4

Satin fabric structure as the convolution of a minimum base and a nonrectangular repetition pattern. Rectangle C corresponds to the weaving diagram conventionally used to represent this satin structure.

Fig. 5
Fig. 5

Convolution theorem applied to the twill structure of Fig. 3.

Fig. 6
Fig. 6

Schematic of correspondence between the spatial and the frequency domains for a fabric structure. We extracted parameters p, q, n, and θ from the Fourier transform (right) to determine the set {a m , b m , b m (x, y)} that defines the fabric structure in the spatial domain (left) and the tilt angle of the fringes. Warp threads are vertical and weft threads horizontal in the fabric image.

Fig. 7
Fig. 7

Schematic as for Fig. 6 but including a second, alternative, set {a2m = (1, 2), b 2m = (0, 5), b 2m (x, y)} to define equivalently the same woven structure. The set {a1m = (3, 1), b 1m = (5, 0), b 1m (x, y)} is the same as that represented in Fig. 6.

Fig. 8
Fig. 8

Top, plain fabric and bottom, its Fourier-transform magnitude. From the peak distribution in the marked triangle, p = 1, q = 1, n = 2.

Fig. 9
Fig. 9

Top, twill fabrics and bottom, their Fourier-transform magnitudes. (a) p = 1, q = 1, n = 4; (b) p = 1, q = 1, n = 3. The minimum bases are marked in the magnified sectors of the fabric images in the spatial domain.

Fig. 10
Fig. 10

Top, satin fabrics and (bottom) their Fourier-transform magnitudes. (a) p = 3, q = 1, n = 5; (b) p = 2, q = 1, n = 5. The minimum bases are marked in the magnified sectors of the fabric images in the spatial domain.

Equations (3)

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

tx, y=bx, y  hx, y,
hx, y=n1,n2Z δx-n1a, y-n2b,
Tu, v=Bmu, vHmu, v,

Metrics