Abstract

This paper addresses the generalization of a surface inspection methodology developed within an industrial context for the characterization of specular cylindrical surfaces. The principle relies on the interpretation of a stripe pattern, obtained after projecting a structured light onto the surface to be inspected. The main objective of this paper is to apply this technique to a broader range of surface geometries and types, i.e. to free-form rough and free-form specular shapes. One major purpose of this paper is to propose a general free-form stripe image interpretation approach on the basis of a four step procedure: (i) comparison of different feature-based image content description techniques, (ii) determination of optimal feature sub-groups, (iii) fusion of the most appropriate ones, and (iv) selection of the optimal features. The first part of this paper is dedicated to the general problem statement with the definition of different image data sets that correspond to various types of free-form rough and specular shapes recorded with a structured illumination. The second part deals with the definition and optimization of the most appropriate pattern recognition process. It is shown that this approach leads to an increase in the classification rates of more than 2 % between the initial fused set and the selected one. Then, it is demonstrated that with approximately a fourth of the initial features, similar high classification rates of free-form surfaces can be obtained.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Aceris-3D, "Fe substrate bump inspection system," Clark Graham 300, Baie D’Urfe, Quebec, Canada, (2005).
  2. Comet-AG, "Feinfocus fox, high resolution 2d/3d," Herrengasse 10, 31775 Flamatt, Switzerland, (2005).
  3. Solvision, "Precis 3d, wafer bump inspection solution," 50 De Lauzon, Suite 100, Boucherville, Qu´ebec, Canada, (2007).
  4. Y. Caulier, K. Spinnler, S. Bourennane, and T. Wittenberg, "New structured illumination technique for the inspection of high reflective surfaces," EURASIP Journal on Image and Video Processing, 2008, 14 pages, (2007).
  5. Y. Caulier, K. Spinnler, T. Wittenberg, and S. Bourennane, "Specific features for the analysis of fringe images," J. Opt. Eng. 47, 057201 (2008).
    [CrossRef]
  6. S. Kammel, "Deflektometrische Untersuchung spiegelnd reflektierender Freiformfl¨achen," Ph.D. dissertation, University of Karlsruhe (TH), Germany, (2004).
  7. S. J. Raudys and A. K. Jain, "Small sample size effects in statistical pattern recognition: Recommendations for practitioners," IEEE Trans. Pattern. Anal. Mach. Intell. 13, 252-264 (1991).
    [CrossRef]
  8. W. B. Li and T. J. Cui and X. Yin and Z. G. Qian and W. Hong, "Fast algorithms for large-scale periodic structures using subentire domain basis functions," IEEE Trans. Antennas Propag. 53, 1154-1162 (2005).
    [CrossRef]
  9. J. P. Besl and J. Ramesh, "Three-dimensional object recognition," ACM Comput. Surv. 17, 75-145 (1985).
    [CrossRef]
  10. G. Haulser, "Verfahren und Vorrichtung zur Ermittlung der Form oder der Abbildungseigenschaften von spiegelnden oder transparenter Objekten," Patent, (1999).
  11. A. Williams, "Streifenmuster im spiegelbild," Inspect Magazine, GIT Verlag GmbH & Co. KG, Darmstadt (2008).
  12. P. Marino, M. A. Dominguez, and M. Alonso, "Machine-vision based detection for sheet metal industries," in The 25th Annual Conf. of the IEEE Industrial Electronics Society (IECON’1999), 3, 1330-1335 (1999).
  13. I. Reindl, and P. O’Leary., "Instrumentation and measurement method for the inspection of peeled steel rods," in IEEE Conf. on Instrumentation and Measurement (IMTC’2007), (2007).
  14. F. Pernkopf., "3d surface inspection using coupled hmms," in Proc. of the 17th Int. Conf. on Pattern Recognition (ICPR’2004), (2004).
  15. M. Petz, and R. Tutsch, "Optical 3d measurement of reflecting free form surfaces," (2002).
  16. G. Delcroix, R. Seulin, B. Laalle, P. Gorria, and F. Merienne., "Study of the imaging conditions and processing for the aspect control of specular surfaces," Int.Society for Electronic Imaging 10, 196-202 (2001).
    [CrossRef]
  17. R. Seulin, F. Merienne, and P. Gorria, "Machine vision system for specular surface inspection: use of simulation process as a tool for design and optimization," in 5th Int. Conf. on Quality Control by Artificial Vision (QCAV’2001), (2001).
  18. S. K. Nayar, A.C. Sanderson, L. E. Weiss, and D. A. Simon, "Specular surface inspection using structured highlight and gaussian images," IEEE Trans. Rob. Autom. 6, 208-218 (1990).
    [CrossRef]
  19. F. Puente Leon, and J. Beyerer, "Active vision and sensor fusion for inspection of metallic surfaces," in Intelligent Robots and Computer Vision XVI: Algorithms, Techniques, Active Vision, and Materials Handling, D.P. Casasent (ed.), Proc. SPIE 3208, 394-405, (1997).
    [CrossRef]
  20. R. Woodham, Y. Iwahori, and R. Barman, "Photometric stereo: Lambertian reflectance and light sources with unknown direction and strength," University of British Columbia, Vancouver, BC, Canada, 1991, (1991).
  21. J. S. Weska, "A survey of threshold selection techniques," Comput. Graph. Image Process 7, 259-265 (1978).
    [CrossRef]
  22. H. Zhi, and R. B. Johansson, "Interpretation and classification of fringe patterns," in 11th Int. Conf. on Image, Speech and Signal Analysis (IAPR’1992) 3, 105-108 (1992).
  23. L. Lepisto, J. Rauhamaa, I. Kunttu, and A. Visa, "Fourier-based object description in defect image retrieval," Machine Vision Applications 17, 211-218 (2006).
    [CrossRef]
  24. Cem Unsalan, "Pattern recognition methods for texture analysis case study: Steel surface classification," Ph.D. dissertation, University of Hacettepe, Turkey, (1998).
  25. D. M. Tsai, and T. Y. Huang, "Automated surface inspection for statistical textures," Image Vision Comput. 21, 307-323 (2003).
    [CrossRef]
  26. H. S. Soon, K. Qian, and A. Asundi, Fringe 2005: Fault detection from temporal unusualness in fringe patterns. Stuttgart, Germany, (2005).
  27. T.M. Cover, and P.E. Hart, "Nearest neighbor pattern classification," IEEE Trans. Inf. Theory 13, 21-27 (1967).
    [CrossRef]
  28. R. Gutierrez-Osuna, "Pattern analysis for machine olfaction: A review," IEEE Sens. J. 2, 189-202 (2002).
    [CrossRef]
  29. R. Kohavi, "A study of cross-validation and bootstrap for accuracy estimation and model selection," in IJCAI, 1137-1145 (1995).
  30. I. H. Witten, and E. Frank, Data mining: Practical machine learning tools and techniques, 2nd ed., ser. The Morgan Kaufmann series in data management systems. Amsterdam: Morgan Kaufmann/Elsevier, (2008).

2006 (1)

L. Lepisto, J. Rauhamaa, I. Kunttu, and A. Visa, "Fourier-based object description in defect image retrieval," Machine Vision Applications 17, 211-218 (2006).
[CrossRef]

2005 (1)

W. B. Li and T. J. Cui and X. Yin and Z. G. Qian and W. Hong, "Fast algorithms for large-scale periodic structures using subentire domain basis functions," IEEE Trans. Antennas Propag. 53, 1154-1162 (2005).
[CrossRef]

2003 (1)

D. M. Tsai, and T. Y. Huang, "Automated surface inspection for statistical textures," Image Vision Comput. 21, 307-323 (2003).
[CrossRef]

2002 (1)

R. Gutierrez-Osuna, "Pattern analysis for machine olfaction: A review," IEEE Sens. J. 2, 189-202 (2002).
[CrossRef]

2001 (1)

G. Delcroix, R. Seulin, B. Laalle, P. Gorria, and F. Merienne., "Study of the imaging conditions and processing for the aspect control of specular surfaces," Int.Society for Electronic Imaging 10, 196-202 (2001).
[CrossRef]

1991 (1)

S. J. Raudys and A. K. Jain, "Small sample size effects in statistical pattern recognition: Recommendations for practitioners," IEEE Trans. Pattern. Anal. Mach. Intell. 13, 252-264 (1991).
[CrossRef]

1990 (1)

S. K. Nayar, A.C. Sanderson, L. E. Weiss, and D. A. Simon, "Specular surface inspection using structured highlight and gaussian images," IEEE Trans. Rob. Autom. 6, 208-218 (1990).
[CrossRef]

1985 (1)

J. P. Besl and J. Ramesh, "Three-dimensional object recognition," ACM Comput. Surv. 17, 75-145 (1985).
[CrossRef]

1978 (1)

J. S. Weska, "A survey of threshold selection techniques," Comput. Graph. Image Process 7, 259-265 (1978).
[CrossRef]

1967 (1)

T.M. Cover, and P.E. Hart, "Nearest neighbor pattern classification," IEEE Trans. Inf. Theory 13, 21-27 (1967).
[CrossRef]

Besl, J. P.

J. P. Besl and J. Ramesh, "Three-dimensional object recognition," ACM Comput. Surv. 17, 75-145 (1985).
[CrossRef]

Cover, T. M.

T.M. Cover, and P.E. Hart, "Nearest neighbor pattern classification," IEEE Trans. Inf. Theory 13, 21-27 (1967).
[CrossRef]

Cui, T. J.

W. B. Li and T. J. Cui and X. Yin and Z. G. Qian and W. Hong, "Fast algorithms for large-scale periodic structures using subentire domain basis functions," IEEE Trans. Antennas Propag. 53, 1154-1162 (2005).
[CrossRef]

Delcroix, G.

G. Delcroix, R. Seulin, B. Laalle, P. Gorria, and F. Merienne., "Study of the imaging conditions and processing for the aspect control of specular surfaces," Int.Society for Electronic Imaging 10, 196-202 (2001).
[CrossRef]

Gorria, P.

G. Delcroix, R. Seulin, B. Laalle, P. Gorria, and F. Merienne., "Study of the imaging conditions and processing for the aspect control of specular surfaces," Int.Society for Electronic Imaging 10, 196-202 (2001).
[CrossRef]

Gutierrez-Osuna, R.

R. Gutierrez-Osuna, "Pattern analysis for machine olfaction: A review," IEEE Sens. J. 2, 189-202 (2002).
[CrossRef]

Hart, P. E.

T.M. Cover, and P.E. Hart, "Nearest neighbor pattern classification," IEEE Trans. Inf. Theory 13, 21-27 (1967).
[CrossRef]

Hong, W.

W. B. Li and T. J. Cui and X. Yin and Z. G. Qian and W. Hong, "Fast algorithms for large-scale periodic structures using subentire domain basis functions," IEEE Trans. Antennas Propag. 53, 1154-1162 (2005).
[CrossRef]

Huang, T. Y.

D. M. Tsai, and T. Y. Huang, "Automated surface inspection for statistical textures," Image Vision Comput. 21, 307-323 (2003).
[CrossRef]

Jain, A. K.

S. J. Raudys and A. K. Jain, "Small sample size effects in statistical pattern recognition: Recommendations for practitioners," IEEE Trans. Pattern. Anal. Mach. Intell. 13, 252-264 (1991).
[CrossRef]

Kunttu, I.

L. Lepisto, J. Rauhamaa, I. Kunttu, and A. Visa, "Fourier-based object description in defect image retrieval," Machine Vision Applications 17, 211-218 (2006).
[CrossRef]

Laalle, B.

G. Delcroix, R. Seulin, B. Laalle, P. Gorria, and F. Merienne., "Study of the imaging conditions and processing for the aspect control of specular surfaces," Int.Society for Electronic Imaging 10, 196-202 (2001).
[CrossRef]

Lepist¨o, L.

L. Lepisto, J. Rauhamaa, I. Kunttu, and A. Visa, "Fourier-based object description in defect image retrieval," Machine Vision Applications 17, 211-218 (2006).
[CrossRef]

Li, W.B.

W. B. Li and T. J. Cui and X. Yin and Z. G. Qian and W. Hong, "Fast algorithms for large-scale periodic structures using subentire domain basis functions," IEEE Trans. Antennas Propag. 53, 1154-1162 (2005).
[CrossRef]

Merienne, F.

G. Delcroix, R. Seulin, B. Laalle, P. Gorria, and F. Merienne., "Study of the imaging conditions and processing for the aspect control of specular surfaces," Int.Society for Electronic Imaging 10, 196-202 (2001).
[CrossRef]

Nayar, S. K.

S. K. Nayar, A.C. Sanderson, L. E. Weiss, and D. A. Simon, "Specular surface inspection using structured highlight and gaussian images," IEEE Trans. Rob. Autom. 6, 208-218 (1990).
[CrossRef]

Qian, Z. G.

W. B. Li and T. J. Cui and X. Yin and Z. G. Qian and W. Hong, "Fast algorithms for large-scale periodic structures using subentire domain basis functions," IEEE Trans. Antennas Propag. 53, 1154-1162 (2005).
[CrossRef]

Ramesh, J.

J. P. Besl and J. Ramesh, "Three-dimensional object recognition," ACM Comput. Surv. 17, 75-145 (1985).
[CrossRef]

Raudys, S. J.

S. J. Raudys and A. K. Jain, "Small sample size effects in statistical pattern recognition: Recommendations for practitioners," IEEE Trans. Pattern. Anal. Mach. Intell. 13, 252-264 (1991).
[CrossRef]

Rauhamaa, J.

L. Lepisto, J. Rauhamaa, I. Kunttu, and A. Visa, "Fourier-based object description in defect image retrieval," Machine Vision Applications 17, 211-218 (2006).
[CrossRef]

Sanderson, A. C.

S. K. Nayar, A.C. Sanderson, L. E. Weiss, and D. A. Simon, "Specular surface inspection using structured highlight and gaussian images," IEEE Trans. Rob. Autom. 6, 208-218 (1990).
[CrossRef]

Seulin, R.

G. Delcroix, R. Seulin, B. Laalle, P. Gorria, and F. Merienne., "Study of the imaging conditions and processing for the aspect control of specular surfaces," Int.Society for Electronic Imaging 10, 196-202 (2001).
[CrossRef]

Simon, D. A.

S. K. Nayar, A.C. Sanderson, L. E. Weiss, and D. A. Simon, "Specular surface inspection using structured highlight and gaussian images," IEEE Trans. Rob. Autom. 6, 208-218 (1990).
[CrossRef]

Tsai, D. M.

D. M. Tsai, and T. Y. Huang, "Automated surface inspection for statistical textures," Image Vision Comput. 21, 307-323 (2003).
[CrossRef]

Visa, A.

L. Lepisto, J. Rauhamaa, I. Kunttu, and A. Visa, "Fourier-based object description in defect image retrieval," Machine Vision Applications 17, 211-218 (2006).
[CrossRef]

Weiss, L. E.

S. K. Nayar, A.C. Sanderson, L. E. Weiss, and D. A. Simon, "Specular surface inspection using structured highlight and gaussian images," IEEE Trans. Rob. Autom. 6, 208-218 (1990).
[CrossRef]

Weska, J. S.

J. S. Weska, "A survey of threshold selection techniques," Comput. Graph. Image Process 7, 259-265 (1978).
[CrossRef]

Yin, X.

W. B. Li and T. J. Cui and X. Yin and Z. G. Qian and W. Hong, "Fast algorithms for large-scale periodic structures using subentire domain basis functions," IEEE Trans. Antennas Propag. 53, 1154-1162 (2005).
[CrossRef]

ACM Comput. Surv. (1)

J. P. Besl and J. Ramesh, "Three-dimensional object recognition," ACM Comput. Surv. 17, 75-145 (1985).
[CrossRef]

Comput. Graph. Image Process. (1)

J. S. Weska, "A survey of threshold selection techniques," Comput. Graph. Image Process 7, 259-265 (1978).
[CrossRef]

IEEE Sens. J. (1)

R. Gutierrez-Osuna, "Pattern analysis for machine olfaction: A review," IEEE Sens. J. 2, 189-202 (2002).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

W. B. Li and T. J. Cui and X. Yin and Z. G. Qian and W. Hong, "Fast algorithms for large-scale periodic structures using subentire domain basis functions," IEEE Trans. Antennas Propag. 53, 1154-1162 (2005).
[CrossRef]

IEEE Trans. Inf. Theory (1)

T.M. Cover, and P.E. Hart, "Nearest neighbor pattern classification," IEEE Trans. Inf. Theory 13, 21-27 (1967).
[CrossRef]

IEEE Trans. Pattern. Anal. Mach. Intell. (1)

S. J. Raudys and A. K. Jain, "Small sample size effects in statistical pattern recognition: Recommendations for practitioners," IEEE Trans. Pattern. Anal. Mach. Intell. 13, 252-264 (1991).
[CrossRef]

IEEE Trans. Rob. Autom. (1)

S. K. Nayar, A.C. Sanderson, L. E. Weiss, and D. A. Simon, "Specular surface inspection using structured highlight and gaussian images," IEEE Trans. Rob. Autom. 6, 208-218 (1990).
[CrossRef]

Image Vision Comput. (1)

D. M. Tsai, and T. Y. Huang, "Automated surface inspection for statistical textures," Image Vision Comput. 21, 307-323 (2003).
[CrossRef]

Machine Vision Applications (1)

L. Lepisto, J. Rauhamaa, I. Kunttu, and A. Visa, "Fourier-based object description in defect image retrieval," Machine Vision Applications 17, 211-218 (2006).
[CrossRef]

Society for Electronic Imaging (1)

G. Delcroix, R. Seulin, B. Laalle, P. Gorria, and F. Merienne., "Study of the imaging conditions and processing for the aspect control of specular surfaces," Int.Society for Electronic Imaging 10, 196-202 (2001).
[CrossRef]

Other (20)

R. Seulin, F. Merienne, and P. Gorria, "Machine vision system for specular surface inspection: use of simulation process as a tool for design and optimization," in 5th Int. Conf. on Quality Control by Artificial Vision (QCAV’2001), (2001).

F. Puente Leon, and J. Beyerer, "Active vision and sensor fusion for inspection of metallic surfaces," in Intelligent Robots and Computer Vision XVI: Algorithms, Techniques, Active Vision, and Materials Handling, D.P. Casasent (ed.), Proc. SPIE 3208, 394-405, (1997).
[CrossRef]

R. Woodham, Y. Iwahori, and R. Barman, "Photometric stereo: Lambertian reflectance and light sources with unknown direction and strength," University of British Columbia, Vancouver, BC, Canada, 1991, (1991).

H. Zhi, and R. B. Johansson, "Interpretation and classification of fringe patterns," in 11th Int. Conf. on Image, Speech and Signal Analysis (IAPR’1992) 3, 105-108 (1992).

G. Haulser, "Verfahren und Vorrichtung zur Ermittlung der Form oder der Abbildungseigenschaften von spiegelnden oder transparenter Objekten," Patent, (1999).

A. Williams, "Streifenmuster im spiegelbild," Inspect Magazine, GIT Verlag GmbH & Co. KG, Darmstadt (2008).

P. Marino, M. A. Dominguez, and M. Alonso, "Machine-vision based detection for sheet metal industries," in The 25th Annual Conf. of the IEEE Industrial Electronics Society (IECON’1999), 3, 1330-1335 (1999).

I. Reindl, and P. O’Leary., "Instrumentation and measurement method for the inspection of peeled steel rods," in IEEE Conf. on Instrumentation and Measurement (IMTC’2007), (2007).

F. Pernkopf., "3d surface inspection using coupled hmms," in Proc. of the 17th Int. Conf. on Pattern Recognition (ICPR’2004), (2004).

M. Petz, and R. Tutsch, "Optical 3d measurement of reflecting free form surfaces," (2002).

Aceris-3D, "Fe substrate bump inspection system," Clark Graham 300, Baie D’Urfe, Quebec, Canada, (2005).

Comet-AG, "Feinfocus fox, high resolution 2d/3d," Herrengasse 10, 31775 Flamatt, Switzerland, (2005).

Solvision, "Precis 3d, wafer bump inspection solution," 50 De Lauzon, Suite 100, Boucherville, Qu´ebec, Canada, (2007).

Y. Caulier, K. Spinnler, S. Bourennane, and T. Wittenberg, "New structured illumination technique for the inspection of high reflective surfaces," EURASIP Journal on Image and Video Processing, 2008, 14 pages, (2007).

Y. Caulier, K. Spinnler, T. Wittenberg, and S. Bourennane, "Specific features for the analysis of fringe images," J. Opt. Eng. 47, 057201 (2008).
[CrossRef]

S. Kammel, "Deflektometrische Untersuchung spiegelnd reflektierender Freiformfl¨achen," Ph.D. dissertation, University of Karlsruhe (TH), Germany, (2004).

Cem Unsalan, "Pattern recognition methods for texture analysis case study: Steel surface classification," Ph.D. dissertation, University of Hacettepe, Turkey, (1998).

H. S. Soon, K. Qian, and A. Asundi, Fringe 2005: Fault detection from temporal unusualness in fringe patterns. Stuttgart, Germany, (2005).

R. Kohavi, "A study of cross-validation and bootstrap for accuracy estimation and model selection," in IJCAI, 1137-1145 (1995).

I. H. Witten, and E. Frank, Data mining: Practical machine learning tools and techniques, 2nd ed., ser. The Morgan Kaufmann series in data management systems. Amsterdam: Morgan Kaufmann/Elsevier, (2008).

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 (8)

Fig. 1.
Fig. 1.

Six examples taken from the reference initial set of images Φ 0 0 made of 252 patterns. This set has been used for the qualification of the industrial system for the cylindrical specular surfaces inspection. All the patterns have been classified into distinct classes: Acceptable Ω A , rejected (non-acceptable) Ω R,3D , and Ω R,2D . All other 246 patterns depict similar structures, i.e. correspond to similar geometry and/or grey level changes/perturbations.

Fig. 2.
Fig. 2.

(a) Surface inspection principle: A camera C records the object surfaces to be inspected S, illuminated by a lighting L. (b) Recordings of one free-form rough surface and one free-form specular surface, both are illuminated by a structured light pattern.

Fig. 3.
Fig. 3.

Left and middle: Two different examples of stripe deformations arising when (a1) and (b1) free-formed rough or (a2) and (b2) free-formed specular objects are recorded. These two examples show that depending on the surface geometry, similar stripe deformations can be observed for rough or specular objects. These two examples show the inspection of a surface S illuminated by a lighting L and recorded by a line-scan camera C during its linear movement along V. Right: One possible bright/dark structure example in case of a round (spherical) object. Upper image shows a sphere with 3 surface portions of different sizes. Lower images show the corresponding image structures if a light pattern is projected.

Fig. 4.
Fig. 4.

Left: Reference patterns for the classification of free-form rough and specular surfaces. These image patterns correspond to three different surface shapes illuminated with a regular periodical structured illumination: -0- for surfaces inducing no deformations, and -1- and -2- for surfaces inducing perspective and cylindrical distortions. Φ0 0 corresponds to patterns without distortion related to the shape of the object. These patterns have been measured. Φ4 1 and Φ4 2 corresponds to patterns with a maximal perspective distortion of type -1- and a maximal cylindrical distortion of type -2-. These patterns have been simulated by transforming patterns Φ0 0 with perspective and cylindrical distortions. All the patterns have a size of 64 × 64 pixel. Right: Bright/dark geometry and reflectance characteristics: Surface: Period dL,P and coefficient ρS ; Defect: Size [dD,u × dD,v ] and coefficient ρD .

Fig. 5.
Fig. 5.

Image characterization from amounts of values in the Fourier spectrum, according to [21]. Four different spectral regions are considered: The radial P̄ r 1,r 2 , directional P̄ θ1θ2, horizontal P̄ v 1,v 2 and vertical P̄ u 1,u 2 spectral ones.

Fig. 6.
Fig. 6.

Typical “projected” and “interferometric” bright/dark structures. The three upper images correspond to ideal “projected” structures, the three lower ones to more complex “interferometric” fringe structures. The first “vertical stripes” feature group was defined for the characterization of the former, whereas the second “free-form” feature group was developed for description of the latter. For illustration purpose, the equations of one adapted “vertical stripes” “minimum distance” feature c 02 and one adapted “free-form stripe” “tangent” feature c 08 are listed. The results of corresponding operators are written for one central blue marked pixel (B) si c . Both are the average results of operators O02 and O08 applied to all bright stripes central pixel elements (B) si c of the considered image F.

Fig. 7.
Fig. 7.

The detection rates were computed for different image sets and correspond to increasing distortions of type -1- and of type -2-. Left to right values: detection rates for image set Φ0 0 to image sets Φ4 1 and Φ4 2.

Fig. 8.
Fig. 8.

The detection rates were computed for different image sets and correspond to increasing distortions of type -1- and of type -2-. Left to right values: detection rates for image set Φ0 0 to image sets Φ4 1 and Φ4 2.

Tables (4)

Tables Icon

Table 1. Notation and names of the 20 considered adapted features of the stripe feature vector c S. These features characterize the bright and the dark stripe depicted in a pattern.

Tables Icon

Table 2. Rates R of correctly classified patterns for image set Φ0 0 with Fourier’s textural features and stripe adapted features by means of a 1-NN classifier.

Tables Icon

Table 3. Selected features when a wrapper 1-NN approach is used, for increasing distortion of type -1-. The maximum number of times a feature can be selected is 10. The variables Nc,sub on the left give the total number of selected features after the 10 runs. The 10 time, 9 time and 8 time selected features are marked with ***, ** and *. Results for all relevant features are marked in bold.

Tables Icon

Table 4. Selected features when a wrapper 1-NN approach is used, for increasing distortion of type -2-. The maximum number of times a feature can be selected is 10. The variables Nc,sub on the left give the total number of selected features after the 10 runs. The 10 time, 9 time and 8 time selected features are marked with ***, ** and *. Results for all relevant features are marked in bold.

Equations (4)

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

d D , u > d L , P 4 . r C , u and d D , v 2 . r C , u
ρ D / ρ S > α
c r , θ , v , u F = { c r F ; c θ F ; c v F ; c u F } : N c = 33 c r F : N c = 8 c θ F : N c = 10 c v F : N c = 5 c u F : N c = 10
c S = { c 06 S ; c 14 S } N c = 20 c 06 S = c S ( [ 00 : 05 ] ) : N c = 06 c 14 S = c S ( [ 06 : 19 ] ) : N c = 14

Metrics