Abstract

Gabor wavelets are applied to develop an unsupervised novelty method for defect detection and segmentation that is fully automatic and free of any adjustable parameter. The algorithm combines the Gabor analysis of the sample image with a statistical analysis of the wavelet coefficients corresponding to each detail. The statistical distribution of the coefficients corresponding to the defect-free background texture is calculated from the coefficient’s distribution of the sample under inspection. Once the background texture features are estimated, a threshold is automatically fixed and applied to all the details, whose information is merged into a single binary output image in which the defect appears segmented from the background. The method is applicable to random, nonperiodic, and periodic textures. Since all the information to inspect a sample is obtained from the sample itself, the method is proof against heterogeneities between different samples of the material, in-plane positioning errors, scale variations, and lack of homogeneous illumination. Experimental results are presented. Some results are compared with other unsupervised methods designed for defect segmentation in periodic textures.

© 2009 Optical Society of America

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References

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  1. X. Xie, “A review of recent advances in surface defect detection using texture analysis techniques,” Elec. Lett. Comp. Vision Imag. Anal. 7, 1-22 (2008).
  2. J. Escofet, R. Navarro, M. S. Millán, and J. Pladellorens, “Detection of local defects in textile webs using Gabor filters,” Opt. Eng. (Bellingham) 37, 2297-2307 (1998).
    [CrossRef]
  3. A. Bodnarova, M. Bennamoun, and S. Latham, “Optimal Gabor filters for textile flaw detection,” Pattern Recogn. 35, 2973-2991 (2002).
    [CrossRef]
  4. Z. Hou and J. M. Parker, “Texture defect detection using support vector machines with adaptative gabor wavelet features,” in Proceedings of IEEE Workshop on Applications of Computer Vision (IEEE, 2005), pp. 275-280.
  5. K. L. Mak and P. Peng, “An automated inspection system for textile fabrics based on Gabor filters,” Rob. Comput.-Integr. Manufact. 24, 359-369 (2008).
    [CrossRef]
  6. H. Sari-Sarraf and J. Goddard, “Vision systems for on-loom fabric inspection,” IEEE Trans. Ind. Appl. 35, 1252-1259 (1999).
    [CrossRef]
  7. M. C. Hu and I. S. Tsai, “Fabric inspection based on best wavelet packet bases,” Text. Res. J. 70, 662-670 (2000).
    [CrossRef]
  8. S. C. Kim and T. J. Kang, “Automated defect detection system using wavelet packet frame and Gaussian mixture model,” J. Opt. Soc. Am. A 23, 2690-2701 (2006).
    [CrossRef]
  9. F. Truchetet and O. Laligant, “A review on industrial applications of wavelet and multiresolution based signal-image processing,” J. Electron. Imaging 17, 031102 (2008).
    [CrossRef]
  10. M. Markou and S. Singh, “Novelty detection: a review-part 1: statistical approaches,” Signal Process. 83, 2481-2497 (2003).
    [CrossRef]
  11. D. R. Rohrmus, “Invariant and adaptive geometrical texture features for defect detection and classification,” Pattern Recogn. 38, 1546-1556 (2005).
    [CrossRef]
  12. D. M. Tsai and T. Y. Huang, “Automated surface inspection for statistical textures,” Image Vis. Comput. 21, 302-323 (2003).
    [CrossRef]
  13. A. Abouelela, H. M. Abbas, H. Eldeeb, A. A. Wahdan, and S. M. Nassar, “Automated vision system for localizing structural defects in textile fabrics,” Pattern Recogn. Lett. 26, 1435-1443 (2005).
    [CrossRef]
  14. M. Ralló, M. S. Millán, and J. Escofet, “Referenceless segmentation of flaws in woven fabrics,” Appl. Opt. 46, 6688-6699 (2007).
    [CrossRef] [PubMed]
  15. A. Gururajan, H. Sari-Sarraf, and E. F. Hequet, “Statistical approach to unsupervised defect detection and multiscale localization in two-texture images,” Opt. Eng. (Bellingham) 47, 027202 (2008).
    [CrossRef]
  16. M. S. Millán and J. Escofet, “Fabric inspection by near-infrared machine vision,” Opt. Lett. 29, 1440-1442 (2004).
    [CrossRef] [PubMed]
  17. M. S. Millán and J. Escofet, “NIR imaging of non-uniform colored webs: Application to fabric inspection,” Proc. SPIE 5622, 188-193 (2004).
    [CrossRef]
  18. F. Meriaudeau, F. Truchetet, O. Laligant, and P. Bourgeat, “Gabor filters in industrial inspection: a review. Application to semiconductor industry,” Proc. SPIE 6001, 53-62 (2005).
  19. R. Navarro and A. Tabernero, “Gaussian wavelet transform: two alternative fast implementation for images,” Multidimens. Syst. Signal Process. 2, 421-436 (1991).
    [CrossRef]
  20. O. Nestares, R. Navarro, J. Portilla, and A. Tabernero, “Efficient spatial-domain implementation of a multiscale image representation based on Gabor functions,” J. Electron. Imaging 7, 166-173 (1998).
    [CrossRef]
  21. M. S. Crouse, R. D. Nowak, and R. G. Baraniuk, “Wavelet-based statistical signal processing using hidden markov models,” IEEE Trans. Signal Process. 46, 886-902 (1998).
    [CrossRef]
  22. S. C. Kim and T. J. Kang, “Texture classification and segmentation using wavelet packet frame and Gaussian mixture model,” Pattern Recogn. 40, 1207-1221 (2007).
    [CrossRef]
  23. P. J. Huber, Robust Statistics (Wiley, 1981), p. 107.

2008 (4)

X. Xie, “A review of recent advances in surface defect detection using texture analysis techniques,” Elec. Lett. Comp. Vision Imag. Anal. 7, 1-22 (2008).

K. L. Mak and P. Peng, “An automated inspection system for textile fabrics based on Gabor filters,” Rob. Comput.-Integr. Manufact. 24, 359-369 (2008).
[CrossRef]

F. Truchetet and O. Laligant, “A review on industrial applications of wavelet and multiresolution based signal-image processing,” J. Electron. Imaging 17, 031102 (2008).
[CrossRef]

A. Gururajan, H. Sari-Sarraf, and E. F. Hequet, “Statistical approach to unsupervised defect detection and multiscale localization in two-texture images,” Opt. Eng. (Bellingham) 47, 027202 (2008).
[CrossRef]

2007 (2)

S. C. Kim and T. J. Kang, “Texture classification and segmentation using wavelet packet frame and Gaussian mixture model,” Pattern Recogn. 40, 1207-1221 (2007).
[CrossRef]

M. Ralló, M. S. Millán, and J. Escofet, “Referenceless segmentation of flaws in woven fabrics,” Appl. Opt. 46, 6688-6699 (2007).
[CrossRef] [PubMed]

2006 (1)

2005 (3)

D. R. Rohrmus, “Invariant and adaptive geometrical texture features for defect detection and classification,” Pattern Recogn. 38, 1546-1556 (2005).
[CrossRef]

A. Abouelela, H. M. Abbas, H. Eldeeb, A. A. Wahdan, and S. M. Nassar, “Automated vision system for localizing structural defects in textile fabrics,” Pattern Recogn. Lett. 26, 1435-1443 (2005).
[CrossRef]

F. Meriaudeau, F. Truchetet, O. Laligant, and P. Bourgeat, “Gabor filters in industrial inspection: a review. Application to semiconductor industry,” Proc. SPIE 6001, 53-62 (2005).

2004 (2)

M. S. Millán and J. Escofet, “NIR imaging of non-uniform colored webs: Application to fabric inspection,” Proc. SPIE 5622, 188-193 (2004).
[CrossRef]

M. S. Millán and J. Escofet, “Fabric inspection by near-infrared machine vision,” Opt. Lett. 29, 1440-1442 (2004).
[CrossRef] [PubMed]

2003 (2)

D. M. Tsai and T. Y. Huang, “Automated surface inspection for statistical textures,” Image Vis. Comput. 21, 302-323 (2003).
[CrossRef]

M. Markou and S. Singh, “Novelty detection: a review-part 1: statistical approaches,” Signal Process. 83, 2481-2497 (2003).
[CrossRef]

2002 (1)

A. Bodnarova, M. Bennamoun, and S. Latham, “Optimal Gabor filters for textile flaw detection,” Pattern Recogn. 35, 2973-2991 (2002).
[CrossRef]

2000 (1)

M. C. Hu and I. S. Tsai, “Fabric inspection based on best wavelet packet bases,” Text. Res. J. 70, 662-670 (2000).
[CrossRef]

1999 (1)

H. Sari-Sarraf and J. Goddard, “Vision systems for on-loom fabric inspection,” IEEE Trans. Ind. Appl. 35, 1252-1259 (1999).
[CrossRef]

1998 (3)

J. Escofet, R. Navarro, M. S. Millán, and J. Pladellorens, “Detection of local defects in textile webs using Gabor filters,” Opt. Eng. (Bellingham) 37, 2297-2307 (1998).
[CrossRef]

O. Nestares, R. Navarro, J. Portilla, and A. Tabernero, “Efficient spatial-domain implementation of a multiscale image representation based on Gabor functions,” J. Electron. Imaging 7, 166-173 (1998).
[CrossRef]

M. S. Crouse, R. D. Nowak, and R. G. Baraniuk, “Wavelet-based statistical signal processing using hidden markov models,” IEEE Trans. Signal Process. 46, 886-902 (1998).
[CrossRef]

1991 (1)

R. Navarro and A. Tabernero, “Gaussian wavelet transform: two alternative fast implementation for images,” Multidimens. Syst. Signal Process. 2, 421-436 (1991).
[CrossRef]

Abbas, H. M.

A. Abouelela, H. M. Abbas, H. Eldeeb, A. A. Wahdan, and S. M. Nassar, “Automated vision system for localizing structural defects in textile fabrics,” Pattern Recogn. Lett. 26, 1435-1443 (2005).
[CrossRef]

Abouelela, A.

A. Abouelela, H. M. Abbas, H. Eldeeb, A. A. Wahdan, and S. M. Nassar, “Automated vision system for localizing structural defects in textile fabrics,” Pattern Recogn. Lett. 26, 1435-1443 (2005).
[CrossRef]

Baraniuk, R. G.

M. S. Crouse, R. D. Nowak, and R. G. Baraniuk, “Wavelet-based statistical signal processing using hidden markov models,” IEEE Trans. Signal Process. 46, 886-902 (1998).
[CrossRef]

Bennamoun, M.

A. Bodnarova, M. Bennamoun, and S. Latham, “Optimal Gabor filters for textile flaw detection,” Pattern Recogn. 35, 2973-2991 (2002).
[CrossRef]

Bodnarova, A.

A. Bodnarova, M. Bennamoun, and S. Latham, “Optimal Gabor filters for textile flaw detection,” Pattern Recogn. 35, 2973-2991 (2002).
[CrossRef]

Bourgeat, P.

F. Meriaudeau, F. Truchetet, O. Laligant, and P. Bourgeat, “Gabor filters in industrial inspection: a review. Application to semiconductor industry,” Proc. SPIE 6001, 53-62 (2005).

Crouse, M. S.

M. S. Crouse, R. D. Nowak, and R. G. Baraniuk, “Wavelet-based statistical signal processing using hidden markov models,” IEEE Trans. Signal Process. 46, 886-902 (1998).
[CrossRef]

Eldeeb, H.

A. Abouelela, H. M. Abbas, H. Eldeeb, A. A. Wahdan, and S. M. Nassar, “Automated vision system for localizing structural defects in textile fabrics,” Pattern Recogn. Lett. 26, 1435-1443 (2005).
[CrossRef]

Escofet, J.

M. Ralló, M. S. Millán, and J. Escofet, “Referenceless segmentation of flaws in woven fabrics,” Appl. Opt. 46, 6688-6699 (2007).
[CrossRef] [PubMed]

M. S. Millán and J. Escofet, “Fabric inspection by near-infrared machine vision,” Opt. Lett. 29, 1440-1442 (2004).
[CrossRef] [PubMed]

M. S. Millán and J. Escofet, “NIR imaging of non-uniform colored webs: Application to fabric inspection,” Proc. SPIE 5622, 188-193 (2004).
[CrossRef]

J. Escofet, R. Navarro, M. S. Millán, and J. Pladellorens, “Detection of local defects in textile webs using Gabor filters,” Opt. Eng. (Bellingham) 37, 2297-2307 (1998).
[CrossRef]

Goddard, J.

H. Sari-Sarraf and J. Goddard, “Vision systems for on-loom fabric inspection,” IEEE Trans. Ind. Appl. 35, 1252-1259 (1999).
[CrossRef]

Gururajan, A.

A. Gururajan, H. Sari-Sarraf, and E. F. Hequet, “Statistical approach to unsupervised defect detection and multiscale localization in two-texture images,” Opt. Eng. (Bellingham) 47, 027202 (2008).
[CrossRef]

Hequet, E. F.

A. Gururajan, H. Sari-Sarraf, and E. F. Hequet, “Statistical approach to unsupervised defect detection and multiscale localization in two-texture images,” Opt. Eng. (Bellingham) 47, 027202 (2008).
[CrossRef]

Hou, Z.

Z. Hou and J. M. Parker, “Texture defect detection using support vector machines with adaptative gabor wavelet features,” in Proceedings of IEEE Workshop on Applications of Computer Vision (IEEE, 2005), pp. 275-280.

Hu, M. C.

M. C. Hu and I. S. Tsai, “Fabric inspection based on best wavelet packet bases,” Text. Res. J. 70, 662-670 (2000).
[CrossRef]

Huang, T. Y.

D. M. Tsai and T. Y. Huang, “Automated surface inspection for statistical textures,” Image Vis. Comput. 21, 302-323 (2003).
[CrossRef]

Huber, P. J.

P. J. Huber, Robust Statistics (Wiley, 1981), p. 107.

Kang, T. J.

S. C. Kim and T. J. Kang, “Texture classification and segmentation using wavelet packet frame and Gaussian mixture model,” Pattern Recogn. 40, 1207-1221 (2007).
[CrossRef]

S. C. Kim and T. J. Kang, “Automated defect detection system using wavelet packet frame and Gaussian mixture model,” J. Opt. Soc. Am. A 23, 2690-2701 (2006).
[CrossRef]

Kim, S. C.

S. C. Kim and T. J. Kang, “Texture classification and segmentation using wavelet packet frame and Gaussian mixture model,” Pattern Recogn. 40, 1207-1221 (2007).
[CrossRef]

S. C. Kim and T. J. Kang, “Automated defect detection system using wavelet packet frame and Gaussian mixture model,” J. Opt. Soc. Am. A 23, 2690-2701 (2006).
[CrossRef]

Laligant, O.

F. Truchetet and O. Laligant, “A review on industrial applications of wavelet and multiresolution based signal-image processing,” J. Electron. Imaging 17, 031102 (2008).
[CrossRef]

F. Meriaudeau, F. Truchetet, O. Laligant, and P. Bourgeat, “Gabor filters in industrial inspection: a review. Application to semiconductor industry,” Proc. SPIE 6001, 53-62 (2005).

Latham, S.

A. Bodnarova, M. Bennamoun, and S. Latham, “Optimal Gabor filters for textile flaw detection,” Pattern Recogn. 35, 2973-2991 (2002).
[CrossRef]

Mak, K. L.

K. L. Mak and P. Peng, “An automated inspection system for textile fabrics based on Gabor filters,” Rob. Comput.-Integr. Manufact. 24, 359-369 (2008).
[CrossRef]

Markou, M.

M. Markou and S. Singh, “Novelty detection: a review-part 1: statistical approaches,” Signal Process. 83, 2481-2497 (2003).
[CrossRef]

Meriaudeau, F.

F. Meriaudeau, F. Truchetet, O. Laligant, and P. Bourgeat, “Gabor filters in industrial inspection: a review. Application to semiconductor industry,” Proc. SPIE 6001, 53-62 (2005).

Millán, M. S.

M. Ralló, M. S. Millán, and J. Escofet, “Referenceless segmentation of flaws in woven fabrics,” Appl. Opt. 46, 6688-6699 (2007).
[CrossRef] [PubMed]

M. S. Millán and J. Escofet, “Fabric inspection by near-infrared machine vision,” Opt. Lett. 29, 1440-1442 (2004).
[CrossRef] [PubMed]

M. S. Millán and J. Escofet, “NIR imaging of non-uniform colored webs: Application to fabric inspection,” Proc. SPIE 5622, 188-193 (2004).
[CrossRef]

J. Escofet, R. Navarro, M. S. Millán, and J. Pladellorens, “Detection of local defects in textile webs using Gabor filters,” Opt. Eng. (Bellingham) 37, 2297-2307 (1998).
[CrossRef]

Nassar, S. M.

A. Abouelela, H. M. Abbas, H. Eldeeb, A. A. Wahdan, and S. M. Nassar, “Automated vision system for localizing structural defects in textile fabrics,” Pattern Recogn. Lett. 26, 1435-1443 (2005).
[CrossRef]

Navarro, R.

J. Escofet, R. Navarro, M. S. Millán, and J. Pladellorens, “Detection of local defects in textile webs using Gabor filters,” Opt. Eng. (Bellingham) 37, 2297-2307 (1998).
[CrossRef]

O. Nestares, R. Navarro, J. Portilla, and A. Tabernero, “Efficient spatial-domain implementation of a multiscale image representation based on Gabor functions,” J. Electron. Imaging 7, 166-173 (1998).
[CrossRef]

R. Navarro and A. Tabernero, “Gaussian wavelet transform: two alternative fast implementation for images,” Multidimens. Syst. Signal Process. 2, 421-436 (1991).
[CrossRef]

Nestares, O.

O. Nestares, R. Navarro, J. Portilla, and A. Tabernero, “Efficient spatial-domain implementation of a multiscale image representation based on Gabor functions,” J. Electron. Imaging 7, 166-173 (1998).
[CrossRef]

Nowak, R. D.

M. S. Crouse, R. D. Nowak, and R. G. Baraniuk, “Wavelet-based statistical signal processing using hidden markov models,” IEEE Trans. Signal Process. 46, 886-902 (1998).
[CrossRef]

Parker, J. M.

Z. Hou and J. M. Parker, “Texture defect detection using support vector machines with adaptative gabor wavelet features,” in Proceedings of IEEE Workshop on Applications of Computer Vision (IEEE, 2005), pp. 275-280.

Peng, P.

K. L. Mak and P. Peng, “An automated inspection system for textile fabrics based on Gabor filters,” Rob. Comput.-Integr. Manufact. 24, 359-369 (2008).
[CrossRef]

Pladellorens, J.

J. Escofet, R. Navarro, M. S. Millán, and J. Pladellorens, “Detection of local defects in textile webs using Gabor filters,” Opt. Eng. (Bellingham) 37, 2297-2307 (1998).
[CrossRef]

Portilla, J.

O. Nestares, R. Navarro, J. Portilla, and A. Tabernero, “Efficient spatial-domain implementation of a multiscale image representation based on Gabor functions,” J. Electron. Imaging 7, 166-173 (1998).
[CrossRef]

Ralló, M.

Rohrmus, D. R.

D. R. Rohrmus, “Invariant and adaptive geometrical texture features for defect detection and classification,” Pattern Recogn. 38, 1546-1556 (2005).
[CrossRef]

Sari-Sarraf, H.

A. Gururajan, H. Sari-Sarraf, and E. F. Hequet, “Statistical approach to unsupervised defect detection and multiscale localization in two-texture images,” Opt. Eng. (Bellingham) 47, 027202 (2008).
[CrossRef]

H. Sari-Sarraf and J. Goddard, “Vision systems for on-loom fabric inspection,” IEEE Trans. Ind. Appl. 35, 1252-1259 (1999).
[CrossRef]

Singh, S.

M. Markou and S. Singh, “Novelty detection: a review-part 1: statistical approaches,” Signal Process. 83, 2481-2497 (2003).
[CrossRef]

Tabernero, A.

O. Nestares, R. Navarro, J. Portilla, and A. Tabernero, “Efficient spatial-domain implementation of a multiscale image representation based on Gabor functions,” J. Electron. Imaging 7, 166-173 (1998).
[CrossRef]

R. Navarro and A. Tabernero, “Gaussian wavelet transform: two alternative fast implementation for images,” Multidimens. Syst. Signal Process. 2, 421-436 (1991).
[CrossRef]

Truchetet, F.

F. Truchetet and O. Laligant, “A review on industrial applications of wavelet and multiresolution based signal-image processing,” J. Electron. Imaging 17, 031102 (2008).
[CrossRef]

F. Meriaudeau, F. Truchetet, O. Laligant, and P. Bourgeat, “Gabor filters in industrial inspection: a review. Application to semiconductor industry,” Proc. SPIE 6001, 53-62 (2005).

Tsai, D. M.

D. M. Tsai and T. Y. Huang, “Automated surface inspection for statistical textures,” Image Vis. Comput. 21, 302-323 (2003).
[CrossRef]

Tsai, I. S.

M. C. Hu and I. S. Tsai, “Fabric inspection based on best wavelet packet bases,” Text. Res. J. 70, 662-670 (2000).
[CrossRef]

Wahdan, A. A.

A. Abouelela, H. M. Abbas, H. Eldeeb, A. A. Wahdan, and S. M. Nassar, “Automated vision system for localizing structural defects in textile fabrics,” Pattern Recogn. Lett. 26, 1435-1443 (2005).
[CrossRef]

Xie, X.

X. Xie, “A review of recent advances in surface defect detection using texture analysis techniques,” Elec. Lett. Comp. Vision Imag. Anal. 7, 1-22 (2008).

Appl. Opt. (1)

Elec. Lett. Comp. Vision Imag. Anal. (1)

X. Xie, “A review of recent advances in surface defect detection using texture analysis techniques,” Elec. Lett. Comp. Vision Imag. Anal. 7, 1-22 (2008).

IEEE Trans. Ind. Appl. (1)

H. Sari-Sarraf and J. Goddard, “Vision systems for on-loom fabric inspection,” IEEE Trans. Ind. Appl. 35, 1252-1259 (1999).
[CrossRef]

IEEE Trans. Signal Process. (1)

M. S. Crouse, R. D. Nowak, and R. G. Baraniuk, “Wavelet-based statistical signal processing using hidden markov models,” IEEE Trans. Signal Process. 46, 886-902 (1998).
[CrossRef]

Image Vis. Comput. (1)

D. M. Tsai and T. Y. Huang, “Automated surface inspection for statistical textures,” Image Vis. Comput. 21, 302-323 (2003).
[CrossRef]

J. Electron. Imaging (2)

F. Truchetet and O. Laligant, “A review on industrial applications of wavelet and multiresolution based signal-image processing,” J. Electron. Imaging 17, 031102 (2008).
[CrossRef]

O. Nestares, R. Navarro, J. Portilla, and A. Tabernero, “Efficient spatial-domain implementation of a multiscale image representation based on Gabor functions,” J. Electron. Imaging 7, 166-173 (1998).
[CrossRef]

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

Multidimens. Syst. Signal Process. (1)

R. Navarro and A. Tabernero, “Gaussian wavelet transform: two alternative fast implementation for images,” Multidimens. Syst. Signal Process. 2, 421-436 (1991).
[CrossRef]

Opt. Eng. (Bellingham) (2)

J. Escofet, R. Navarro, M. S. Millán, and J. Pladellorens, “Detection of local defects in textile webs using Gabor filters,” Opt. Eng. (Bellingham) 37, 2297-2307 (1998).
[CrossRef]

A. Gururajan, H. Sari-Sarraf, and E. F. Hequet, “Statistical approach to unsupervised defect detection and multiscale localization in two-texture images,” Opt. Eng. (Bellingham) 47, 027202 (2008).
[CrossRef]

Opt. Lett. (1)

Pattern Recogn. (3)

A. Bodnarova, M. Bennamoun, and S. Latham, “Optimal Gabor filters for textile flaw detection,” Pattern Recogn. 35, 2973-2991 (2002).
[CrossRef]

D. R. Rohrmus, “Invariant and adaptive geometrical texture features for defect detection and classification,” Pattern Recogn. 38, 1546-1556 (2005).
[CrossRef]

S. C. Kim and T. J. Kang, “Texture classification and segmentation using wavelet packet frame and Gaussian mixture model,” Pattern Recogn. 40, 1207-1221 (2007).
[CrossRef]

Pattern Recogn. Lett. (1)

A. Abouelela, H. M. Abbas, H. Eldeeb, A. A. Wahdan, and S. M. Nassar, “Automated vision system for localizing structural defects in textile fabrics,” Pattern Recogn. Lett. 26, 1435-1443 (2005).
[CrossRef]

Proc. SPIE (2)

M. S. Millán and J. Escofet, “NIR imaging of non-uniform colored webs: Application to fabric inspection,” Proc. SPIE 5622, 188-193 (2004).
[CrossRef]

F. Meriaudeau, F. Truchetet, O. Laligant, and P. Bourgeat, “Gabor filters in industrial inspection: a review. Application to semiconductor industry,” Proc. SPIE 6001, 53-62 (2005).

Rob. Comput.-Integr. Manufact. (1)

K. L. Mak and P. Peng, “An automated inspection system for textile fabrics based on Gabor filters,” Rob. Comput.-Integr. Manufact. 24, 359-369 (2008).
[CrossRef]

Signal Process. (1)

M. Markou and S. Singh, “Novelty detection: a review-part 1: statistical approaches,” Signal Process. 83, 2481-2497 (2003).
[CrossRef]

Text. Res. J. (1)

M. C. Hu and I. S. Tsai, “Fabric inspection based on best wavelet packet bases,” Text. Res. J. 70, 662-670 (2000).
[CrossRef]

Other (2)

Z. Hou and J. M. Parker, “Texture defect detection using support vector machines with adaptative gabor wavelet features,” in Proceedings of IEEE Workshop on Applications of Computer Vision (IEEE, 2005), pp. 275-280.

P. J. Huber, Robust Statistics (Wiley, 1981), p. 107.

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Figures (10)

Fig. 1
Fig. 1

Examples of twill fabrics affected by subtle and tiny flaws that do not alter the intensity of the background texture. In (a), the mispick defect looks like a phase shift of a periodic pattern, while in (b) the small down heddle defect appears repeated. These are photographic images of real texture samples.

Fig. 2
Fig. 2

(a) Photographic image of a piece of fabric with two local defects. (b)–(g) Some examples of the similarity of the coefficients obtained using Gabor filters of different parity (even and odd). (b), (c), (d) Even parts and (e), (f), (g) odd parts of Gabor filters of p q = 31 , 42 , 44 .

Fig. 3
Fig. 3

Decomposition of a model flawed texture s ( x , y ) as the sum of a background defect-free texture t ( x , y ) and a defect d ( x , y ) . In the example, s ( x , y ) has been obtained by producing a numerical local alteration (flaw) on the photographic image of a real sample of rough paper (random texture).

Fig. 4
Fig. 4

Wavelet coefficients of s ( x , y ) , t ( x , y ) , and d ( x , y ) (as in Fig. 3) yielded by the imaginary Gabor filter g 33 o . Gray areas correspond to coefficients with values close to zero, bright areas to positive coefficients, and dark areas to negative coefficients.

Fig. 5
Fig. 5

(a), (b) Histograms of the wavelet coefficients of the details s 33 o and t 33 o . (c), (d) Truncated histograms of (a), (b) at N = 100 .

Fig. 6
Fig. 6

Histogram of the wavelet coefficients of detail s 33 o [Fig. 5a, but grouped in a lower number of bins] as a mixture of two zero-mean normal probability distributions, ( 1 α ) f p q d ( i ) and α f p q t ( i ) with α = 0.8121 , σ p q t = 1.668 , σ p q d = 2.829 .

Fig. 7
Fig. 7

(a) Segmentation of s 33 o . (b) Integration of the information provided by all the scales and orientations. (c) Opening of (b).

Fig. 8
Fig. 8

Photographic images of real fabric samples of the first experiment (left) and results of defect detection and segmentation obtained by two unsupervised novelty methods: center, the Gabor-filtering-based-method described in this paper; right, the method designed for periodic textures described in [14]. (Continues on next page.)

Fig. 8, part 2
Fig. 8, part 2

Continued from Fig. 8(a).

Fig. 9
Fig. 9

Photographic images of real test samples of the second experiment (left) and the corresponding results obtained by the unsupervised-Gabor-filtering-based method (right).

Equations (6)

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

g p q ( x , y ) = exp [ π a p 2 ( x 2 + y 2 ) ] exp [ i 2 π f p ( x cos θ q + y sin θ q ) ] ,
s p q e ( x , y ) = s ( x , y ) g p q e ( x , y ) , s p q o ( x , y ) = s ( x , y ) g p q o ( x , y ) ,
f p q ( i ) = α f p q t ( i ) + ( 1 α ) f p q d ( i ) ,
MAD { s p q } = median i | s p q ( i ) median j [ s p q ( j ) ] | ,
MAD p q = p p q , 0.75 t ( N ) 0.674492 σ p q t .
s p q ( x , y ) = { 1 , if | s p q ( x , y ) | > 3 σ p q t 0 , if | s p q ( x , y ) | 3 σ p q t } .

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