Abstract

To quantify the concept of similarity between classes of images three measures and algorithms of calculation are proposed. The first measure is calculated through the frequency of misclassification of subimages sampled randomly from images. The second one is calculated through the cross membership of the mass center of a class in a feature space. The third measure is defined through the membership of subimages, using the distance between each subimage and the mass center of a class in a feature space. We study these measures, classifying images in the coordinated clusters representation (CCR) feature space with the minimum distance classifier. A database of images of Rosa Porriño granite tiles, previously classified by three human experts, is used in the experiments. The calculated similarity between classes is in excellent accordance with the qualitative evaluation by the human experts.

© 2007 Optical Society of America

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References

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  1. G. Gimel'farb, Image Textures and Gibbs Random Fields (Kluwer Academic, 1999).
  2. K. Hoang, W. Wen, A. Nachimuthu, and X. L. Jiang, "Achieving automation in leather surface inspection," Comput. Ind. 34, 43-54 (1997).
    [CrossRef]
  3. C. Boukouvalas, F. De Natale, G. De Toni, J. Kittler, R. Marik, M. Mirmehdi, M. Petrou, P. Le Roy, R. Salñgari, and G. Vernazza, "ASSIST: automatic system for surface inspection and sorting of tiles," J. Mater. Process. Technol. 82, 179-188 (1998).
    [CrossRef]
  4. S. Kukkonen, H. Kalviainen, and J. Parkkinen, "Color features for quality control in ceramic tile industry," Opt. Eng. 40, 170-177 (2001).
    [CrossRef]
  5. M. Deviren, M. Koray, U. Murat, and M. Severcan, "A feature extraction method for marble classification," in Proceedings of the Third International Conference on Computer Vision, Pattern Recognition and Image Processing (CVPRIP) (Atlantic City, USA, 2000), pp. 25-28.
  6. A. Fernández, E. González, and X. A. Leiceaga, "Caracterización de la apariencia visual de superficies pulidas de granito "Rosa Porriño" mediante procesamiento digital de imagen," in Actas del XIV Congreso Internacional de Ingeniería Gráfica (Santander, 2002), pp. 330-335.
  7. A. Bodnarova, M. Bennamoun, and S. Latham, "Optimal Gabor filters for textile flaw detection," Pattern Recogn. 35, 1799-1814 (2002).
    [CrossRef]
  8. M. Turtinen, M. Pietikainen, O. Silvén, T. Maenpaa, and M. Niskanen, "Paper characterization by texture using visualization-based training," Int. J. Adv. Manuf. Technol. 22, 890-898 (2003).
    [CrossRef]
  9. O. Silvén, M. Niskanen, and H. Kauppinen, "Wood inspection with nonsupervised clustering," Mach. Vision Appl. 13, 275-285 (2003).
    [CrossRef]
  10. O. Ghita, P. F. Whelan, T. Carew, and P. Nammalwar, "Quality grading of painted slates using texture analysis," Comput. Ind. 56, 802-815 (2005).
    [CrossRef]
  11. R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification, 2nd ed. (Wiley, 2001).
  12. AENOR, Norma UNE 22-170-85: Granitos ornamentales, características generales (1985).
  13. AENOR, Norma UNE 22-171-85: Granitos ornamentales, tamaño de grano (1985).
  14. A. Tversky, "Features of similarity," Psychol. Rev. 84, 327-352 (1977).
    [CrossRef]
  15. R. Jain, S. N. Murthy, L. Tran, and S. Chatterjee, "Similarity Measures for Image Databases," in SPIE Proceedings on Storage and Retrieval for Image and Video Databases III, Proc. SPIE 2420, 58-65 (1995).
    [CrossRef]
  16. P. Rogelj and S. Kovacic, "Local similarity measures of multimodal image matching," in First International Workshop on Image and Signal Processing and Analysis (Pula, 2000), pp. 81-86.
    [CrossRef]
  17. N. Abbadeni, "Content representation and similarity matching for texture-based image retrieval," in Proceedings of the 5th ACM SIGMM International Workshop on Multimedia Information Retrieval (Berkeley, Calif., USA, 2003), pp. 63-70.
  18. J. F. Omhover, M. Detyniecki, M. Rifqi, and B. Bouchon-Meunier, "Ranking invariance between fuzzy similarity measures applied to image retrieval," in Proceedings of the IEEE International Conference on Fuzzy Systems (IEEE, 2004), pp. 1367-1372.
  19. P. Vacha, "Texture similarity measure," in Proceedings of the 14th Annual Conference of Doctoral Students (WDS 2005), Part 1 (Prague, June 2005), pp. 47-52.
  20. T. Yokoyama, T. Watanabe, and H. Koga, "Similarity-based retrieval method for fractal coded images in the compressed data domain," in Proceedings of International Conference on Image and Video Retrieval (Singapore, 2005), pp. 385-394.
  21. E. V. Kurmyshev and R. E. Sánchez-Yáñez, "Texture classification based on image representation by coordinated clusters," in Proceedings of Image and Vision Computing (Dunedin, 2001), pp. 213-217.
  22. R. E. Sánchez Yáñez, E. V. Kurmyshev, and F. J. Cuevas, "A framework for texture classification using the coordinated clusters representation," Pattern Recogn. Lett. 24, 21-31 (2003).
    [CrossRef]
  23. E. V. Kurmyshev, F. J. Cuevas, and R. E. Sánchez Yáñez, "Noisy binary texture recognition using the coordinated cluster transform," Computación y Sistemas 6, 196-203 (2003).
  24. R. E. Sánchez Yáñez, E. V. Kurmyshev, and A. Fernández, "One-class texture classifier in the CCR feature space," Pattern Recogn. Lett. 24, 1503-1511 (2003).
    [CrossRef]
  25. E. V. Kurmyshev and R. E. Sánchez Yáñez, "Comparative experiment with color texture classifiers using the CCR feature space," Pattern Recogn. Lett. 26, 1346-1353 (2005).
    [CrossRef]
  26. E. V. Kurmyshev, M. Poterasu, and J. T. Guillen-Bonilla, "Image scale determination for optimal texture classification using coordinated clusters representation of images," Appl. Opt. 46, 1467-1476 (2007).
    [CrossRef]
  27. P. Brodatz, A Photographic Album for Artists and Designers (Dover, 1996).
  28. VisTex Vision Texture Database, http://www.white.media.mit.edu/vismod/imagery/Vision Texture/Vistex.html (1997).
  29. OuTex, Texture Database, http://www.outex.oulu.fi/temp/.

2007 (1)

2005 (2)

E. V. Kurmyshev and R. E. Sánchez Yáñez, "Comparative experiment with color texture classifiers using the CCR feature space," Pattern Recogn. Lett. 26, 1346-1353 (2005).
[CrossRef]

O. Ghita, P. F. Whelan, T. Carew, and P. Nammalwar, "Quality grading of painted slates using texture analysis," Comput. Ind. 56, 802-815 (2005).
[CrossRef]

2003 (5)

M. Turtinen, M. Pietikainen, O. Silvén, T. Maenpaa, and M. Niskanen, "Paper characterization by texture using visualization-based training," Int. J. Adv. Manuf. Technol. 22, 890-898 (2003).
[CrossRef]

O. Silvén, M. Niskanen, and H. Kauppinen, "Wood inspection with nonsupervised clustering," Mach. Vision Appl. 13, 275-285 (2003).
[CrossRef]

R. E. Sánchez Yáñez, E. V. Kurmyshev, and F. J. Cuevas, "A framework for texture classification using the coordinated clusters representation," Pattern Recogn. Lett. 24, 21-31 (2003).
[CrossRef]

E. V. Kurmyshev, F. J. Cuevas, and R. E. Sánchez Yáñez, "Noisy binary texture recognition using the coordinated cluster transform," Computación y Sistemas 6, 196-203 (2003).

R. E. Sánchez Yáñez, E. V. Kurmyshev, and A. Fernández, "One-class texture classifier in the CCR feature space," Pattern Recogn. Lett. 24, 1503-1511 (2003).
[CrossRef]

2002 (1)

A. Bodnarova, M. Bennamoun, and S. Latham, "Optimal Gabor filters for textile flaw detection," Pattern Recogn. 35, 1799-1814 (2002).
[CrossRef]

2001 (1)

S. Kukkonen, H. Kalviainen, and J. Parkkinen, "Color features for quality control in ceramic tile industry," Opt. Eng. 40, 170-177 (2001).
[CrossRef]

1998 (1)

C. Boukouvalas, F. De Natale, G. De Toni, J. Kittler, R. Marik, M. Mirmehdi, M. Petrou, P. Le Roy, R. Salñgari, and G. Vernazza, "ASSIST: automatic system for surface inspection and sorting of tiles," J. Mater. Process. Technol. 82, 179-188 (1998).
[CrossRef]

1997 (1)

K. Hoang, W. Wen, A. Nachimuthu, and X. L. Jiang, "Achieving automation in leather surface inspection," Comput. Ind. 34, 43-54 (1997).
[CrossRef]

1995 (1)

R. Jain, S. N. Murthy, L. Tran, and S. Chatterjee, "Similarity Measures for Image Databases," in SPIE Proceedings on Storage and Retrieval for Image and Video Databases III, Proc. SPIE 2420, 58-65 (1995).
[CrossRef]

1977 (1)

A. Tversky, "Features of similarity," Psychol. Rev. 84, 327-352 (1977).
[CrossRef]

Appl. Opt. (1)

Comput. Ind. (2)

K. Hoang, W. Wen, A. Nachimuthu, and X. L. Jiang, "Achieving automation in leather surface inspection," Comput. Ind. 34, 43-54 (1997).
[CrossRef]

O. Ghita, P. F. Whelan, T. Carew, and P. Nammalwar, "Quality grading of painted slates using texture analysis," Comput. Ind. 56, 802-815 (2005).
[CrossRef]

Computación y Sistemas (1)

E. V. Kurmyshev, F. J. Cuevas, and R. E. Sánchez Yáñez, "Noisy binary texture recognition using the coordinated cluster transform," Computación y Sistemas 6, 196-203 (2003).

Int. J. Adv. Manuf. Technol. (1)

M. Turtinen, M. Pietikainen, O. Silvén, T. Maenpaa, and M. Niskanen, "Paper characterization by texture using visualization-based training," Int. J. Adv. Manuf. Technol. 22, 890-898 (2003).
[CrossRef]

J. Mater. Process. Technol. (1)

C. Boukouvalas, F. De Natale, G. De Toni, J. Kittler, R. Marik, M. Mirmehdi, M. Petrou, P. Le Roy, R. Salñgari, and G. Vernazza, "ASSIST: automatic system for surface inspection and sorting of tiles," J. Mater. Process. Technol. 82, 179-188 (1998).
[CrossRef]

Mach. Vision Appl. (1)

O. Silvén, M. Niskanen, and H. Kauppinen, "Wood inspection with nonsupervised clustering," Mach. Vision Appl. 13, 275-285 (2003).
[CrossRef]

Opt. Eng. (1)

S. Kukkonen, H. Kalviainen, and J. Parkkinen, "Color features for quality control in ceramic tile industry," Opt. Eng. 40, 170-177 (2001).
[CrossRef]

Pattern Recogn. (1)

A. Bodnarova, M. Bennamoun, and S. Latham, "Optimal Gabor filters for textile flaw detection," Pattern Recogn. 35, 1799-1814 (2002).
[CrossRef]

Pattern Recogn. Lett. (3)

R. E. Sánchez Yáñez, E. V. Kurmyshev, and A. Fernández, "One-class texture classifier in the CCR feature space," Pattern Recogn. Lett. 24, 1503-1511 (2003).
[CrossRef]

E. V. Kurmyshev and R. E. Sánchez Yáñez, "Comparative experiment with color texture classifiers using the CCR feature space," Pattern Recogn. Lett. 26, 1346-1353 (2005).
[CrossRef]

R. E. Sánchez Yáñez, E. V. Kurmyshev, and F. J. Cuevas, "A framework for texture classification using the coordinated clusters representation," Pattern Recogn. Lett. 24, 21-31 (2003).
[CrossRef]

Proc. SPIE (1)

R. Jain, S. N. Murthy, L. Tran, and S. Chatterjee, "Similarity Measures for Image Databases," in SPIE Proceedings on Storage and Retrieval for Image and Video Databases III, Proc. SPIE 2420, 58-65 (1995).
[CrossRef]

Psychol. Rev. (1)

A. Tversky, "Features of similarity," Psychol. Rev. 84, 327-352 (1977).
[CrossRef]

Other (15)

P. Brodatz, A Photographic Album for Artists and Designers (Dover, 1996).

VisTex Vision Texture Database, http://www.white.media.mit.edu/vismod/imagery/Vision Texture/Vistex.html (1997).

OuTex, Texture Database, http://www.outex.oulu.fi/temp/.

P. Rogelj and S. Kovacic, "Local similarity measures of multimodal image matching," in First International Workshop on Image and Signal Processing and Analysis (Pula, 2000), pp. 81-86.
[CrossRef]

N. Abbadeni, "Content representation and similarity matching for texture-based image retrieval," in Proceedings of the 5th ACM SIGMM International Workshop on Multimedia Information Retrieval (Berkeley, Calif., USA, 2003), pp. 63-70.

J. F. Omhover, M. Detyniecki, M. Rifqi, and B. Bouchon-Meunier, "Ranking invariance between fuzzy similarity measures applied to image retrieval," in Proceedings of the IEEE International Conference on Fuzzy Systems (IEEE, 2004), pp. 1367-1372.

P. Vacha, "Texture similarity measure," in Proceedings of the 14th Annual Conference of Doctoral Students (WDS 2005), Part 1 (Prague, June 2005), pp. 47-52.

T. Yokoyama, T. Watanabe, and H. Koga, "Similarity-based retrieval method for fractal coded images in the compressed data domain," in Proceedings of International Conference on Image and Video Retrieval (Singapore, 2005), pp. 385-394.

E. V. Kurmyshev and R. E. Sánchez-Yáñez, "Texture classification based on image representation by coordinated clusters," in Proceedings of Image and Vision Computing (Dunedin, 2001), pp. 213-217.

R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification, 2nd ed. (Wiley, 2001).

AENOR, Norma UNE 22-170-85: Granitos ornamentales, características generales (1985).

AENOR, Norma UNE 22-171-85: Granitos ornamentales, tamaño de grano (1985).

G. Gimel'farb, Image Textures and Gibbs Random Fields (Kluwer Academic, 1999).

M. Deviren, M. Koray, U. Murat, and M. Severcan, "A feature extraction method for marble classification," in Proceedings of the Third International Conference on Computer Vision, Pattern Recognition and Image Processing (CVPRIP) (Atlantic City, USA, 2000), pp. 25-28.

A. Fernández, E. González, and X. A. Leiceaga, "Caracterización de la apariencia visual de superficies pulidas de granito "Rosa Porriño" mediante procesamiento digital de imagen," in Actas del XIV Congreso Internacional de Ingeniería Gráfica (Santander, 2002), pp. 330-335.

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Figures (1)

Fig. 1
Fig. 1

Images of Rosa Porriño granite tiles used in classification experiments.

Tables (6)

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Table 1 Classification of Rosa Porriño Granite Tiles by Human Experts

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Table 2 Source Images of Classes Used in Experiments

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Table 3 Classification of Images of Rosa Porriño Granite Tiles in Eight Classes, Using a Minimum Distance Multiclass Classifier in the CCR Feature Space

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Table 4 Average Membership of Test Images of Rosa Porriño Granite Tiles in Eight Classes, Using the Frequency of Assignment of Sunimages

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Table 5 Cross Membership of Classes of Images of Rosa Porriño Granite Tiles, Using the Hamming Distance in the CCR Feature Space

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Table 6 Cross Membership of Classes of Images of Rosa Porriño Granite Tiles, Using the Hamming Distance of Subimages in the CCR Feature Space

Equations (33)

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

μ m = k m / K .
sim 1 ( l , m ) = 1 2 ( ( i μ i , m ) / ( i μ i , l ) + ( j μ j , l ) / ( j μ j , m ) ) ,
F ˜ l = 1 I l i = 1 I l F i , l .
μ ( F ˜ l , F m ) = d 1 ( F ˜ l , F m ) / m d 1 ( F ˜ l , F m ) ,
m μ ( F ˜ l , F m ) = 1 , 0 μ ( F ˜ m , F m ) 1 ,
sim 2 ( l , m ) = 1 2 ( μ ( F ˜ l , F m ) μ ( F ˜ l , F l ) + μ ( F ˜ m , F l ) μ ( F ˜ m , F m ) ) = sim 2 ( m , l ) .
μ ( F i , l α , F m ) = d 1 ( F i , l α , F m ) / m d 1 ( F i , l α , F m ) ,
μ ( F i , l , F m ) = P 1 α = 1 P μ ( F i , l α , F m ) .
sim 3 ( l , m ) = 1 2 ( μ ( l , m ) μ ( l , l ) + μ ( m , l ) μ ( m , m ) ) = sim 3 ( m , l ) ,
μ ( l , m ) = I l 1 i = 1 I l μ ( F i , l , F m ) = I l 1 i = 1 I l P 1 α = 1 P μ ( F i , l α , F m ) .
F q , m ( b ) = 1 P α = 1 P F q , m α ( b ) .
F m ( b ) = 1 Q q = 1 Q F q , m ( b ) = 1 P Q q = 1 Q α = 1 P F q , m α ( b ) .
F ( b ) = 1 K β = 1 K F β ( b ) .
d ( F , F m ) = b | F ( b ) F m ( b ) | .
d ( F , F m ) = min m [ 1 , , M ] ( b | F ( b ) F m ( b ) | ) .
sim 1 ( 2 , 7 ) = sim 1 ( 7 , 2 ) = ( 27 / 32 + 25 / 33 ) / 2 = 0.80 ,
sim 1 ( 5 , 7 ) = sim 1 ( 7 , 5 ) = ( 22 / 34 + 25 / 33 ) / 2 = 0.70 ,
sim 1 ( 2 , 5 ) = sim 1 ( 5 , 2 ) = ( 20 / 32 + 19 / 34 ) / 2 = 0.59 ,
sim 1 ( 3 , 4 ) = sim 1 ( 4 , 3 ) = ( 14 / 40 + 14 / 41 ) / 2 = 0.34 ,
sim 1 ( 4 , 6 ) = sim 1 ( 6 , 4 ) = ( 12 / 41 + 13 / 42 ) / 2 = 0.30 ,
sim 1 ( 1 , 8 ) = sim 1 ( 8 , 1 ) = ( 17 / 54 + 17 / 59 ) / 2 = 0.30 .
sim 2 ( 2 , 7 ) = sim 2 ( 7 , 2 ) = ( 0.27 / 0.34 + 0.26 / 0.34 ) / 2 = 0.78 ,
sim 2 ( 5 , 7 ) = sim 2 ( 7 , 5 ) = ( 0.23 / 0.35 + 0.25 / 0.34 ) / 2 = 0.696 ,
sim 2 ( 2 , 5 ) = sim 2 ( 5 , 2 ) = ( 0.21 / 0.34 + 0.21 / 0.35 ) / 2 = 0.60 ,
sim 2 ( 3 , 4 ) = sim 2 ( 4 , 3 ) = ( 0.15 / 0.40 + 0.15 / 0.42 ) / 2 = 0.36 ,
sim 2 ( 4 , 6 ) = sim 2 ( 6 , 4 ) = ( 0.15 / 0.42 + 0.14 / 0.45 ) / 2 = 0.33 ,
sim 2 ( 1 , 8 ) = sim 2 ( 8 , 1 ) = ( 0.16 / 0.48 + 0.19 / 0.57 ) / 2 = 0.33 .
sim 3 ( 2 , 7 ) = sim 3 ( 7 , 2 ) = ( 0. 273 / 0.322 + 0.256 / 0.337 ) / 2 = 0.80 3 ,
sim 3 ( 5 , 7 ) = sim 3 ( 7 , 5 ) = ( 0. 224 / 0.345 + 0.257 / 0.337 ) / 2 = 0.70 5 ,
sim 3 ( 2 , 5 ) = sim 3 ( 5 , 2 ) = ( 0. 201 / 0.322 + 0.195 / 0.345 ) / 2 = 0.595 ,
sim 3 ( 3 , 4 ) = sim 3 ( 4 , 3 ) = ( 0.145 / 0.403 + 0. 135 / 0.417 ) / 2 = 0.34 1 ,
sim 3 ( 4 , 6 ) = sim 3 ( 6 , 4 ) = ( 0.124 / 0.417 + 0. 131 / 0.421 ) / 2 = 0.30 4 ,
sim 3 ( 1 , 8 ) = sim 3 ( 8 , 1 ) = ( 0.165 / 0.537 + 0.176 / 0.593 ) / 2 = 0.30 2.

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