Abstract

Color-vision-based applications for mobile phones has become a subject of special interest lately. It would be interesting to investigate an unsupervised, adaptive, and fast algorithm that can classify color components into color clusters. We propose a hierarchical clustering approach using a single-linkage algorithm and a k-means clustering approach to color classification for color-based image code recognition in mobile computing environments. We also measured the performance of the proposed algorithms by color channel stretch, which is a simple color-correction method. Experimental results show that the single-linkage method is more robust than previous algorithms used in experiments with varying cameras and print materials. In particular the k-means-based method with color channel stretching has the highest performance and is the most robust under varying environment conditions such as illuminants, cameras, and print materials.

© 2008 Optical Society of America

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  1. W. Johnson, H. Jellinek, L. Klotz, R. Rao, and S. Card, “Bridging the paper and electronic worlds: the paper user interface,” in Proceedings of Interact '93 and CHI'93 Conference on Human Factors in Computing Systems, S. Ashlund, K. Mullet, A. Henderson, E. Hollnagel, and T. White, eds. (Association for Computing Machinery Press, 1993), pp. 507-512.
  2. D. L. Hecht, “Printed embedded data graphical user interfaces,” IEEE Comput. Graphics Appl. 34, 47-55 (2001).
  3. L. Nelson, S. Ichimura, E. R. Pedersen, and L. Adams, “Palette: a paper interface for giving presentations,” in Proceedings of ACM SIGCHI Conference on Human Factors and Computing Systems, M. G. William and M. W. Altom, eds. (Association for Computing Machinery Press, 1999), pp. 354-361.
  4. T. Hautala, J. Kallenbach, M. Nuutinen, L. Salo, T. Venho, A. Bäck, C. Bäckström, L. Hakola, and T. Järvinen, “PrintAccess,” http://www.media.hut.fi/GTTS/GAiF/GAiF2_2005.htm#PrintAccess--Final Report.
  5. H. Usuda, M. Suzuku, and Maeda, Research result report on creation and transmission of digital contents using image recognition technology (summary version), Project Code IMS 0359, Sony Corporation, Japan, 2004.
  6. K. D. Hunter, “Automatic access of internet content with a camera-enabled cell phone,” U.S. patent 6,993,573 (United States Patent and Trademark Office, 2006).
  7. T. Pavlidis, J. Swartz, and Y. P. Wang, “Fundamentals of bar code information theory,” IEEE Comput. Graphics Appl. 23, 74-86 (1990).
  8. International Organization for Standardization, Information technology: automatic identification and data capture techniques--bar code symbology--data matrix, ISO/IEC 16022 (ISO/IEC, 2000).
  9. International Organization for Standardization, Information technology: automatic identification and data capture techniques--bar code symbology--PDF-417, ISO/IEC 15438 (ISO/IEC, 2001).
  10. International Organization for Standardization, Information technology: automatic identification and data capture techniques--bar code symbology--QR code, ISO/IEC 18004 (ISO/IEC, 2000).
  11. J. Rekimoto, The world through the computer: a new human-computer interaction style based on wearable computers, Technical Report SCSL-TR-94-013, Sony Computer Science Laboratories Inc., Japan, 1994.
  12. J. Rekimoto and Y. Ayatsuka, “Cyber code: designing augmented reality environments with visual tags,” in Proceedings Designing Augmented Reality Environments, W. E. Mackay, ed. (Association for Computing Machinery Press, 2000), pp. 1-10.
  13. P. Milgram and H. Colquhoun, “A taxonomy of real and virtual world displays integration,” in Mixed Reality--Merging Real and Virtual Worlds, Y. Ohta and H. Tamura, eds. (Ohmsha and Springer-Verlag, 1999), pp. 5-30.
  14. J. R. Vallino, “Interactive augmented reality,” Ph D. dissertation (University of Rochester, New York, 1998).
  15. R. Azuma, Y. Baillot, R. Behringer, S. Feiner, S. Julier, and B. MacIntyre, “Recent advances in augmented reality,” in IEEE Computer Graphics and Applications (IEEE, 2001), pp. 34-47.
  16. A. State, G. Hirota, D. T. Chen, W. F. Garrett, and M. A. Livingston, “Superior augmented reality registration by integrating landmark tracking and magnetic tracking,” in Proceedings of SIGGRAPH, J. Fujii, ed. (Association for Computing Machinery Press, 1996), pp. 429-438.
  17. H. Kato and M. Billinghurst, “Marker tracking and HMD calibration for a video-based augmented reality conferencing system,” in Proceedings of 2nd IEEE and ACM Int. Workshop on Augmented Reality, G. Klinker and T. U. München, eds. (IEEE Computer Society, 1999), pp. 85-94.
  18. H. Shimoda, H. Ishii, M. Maeshima, T. Nakai, Z. Bian, and H. Yoshikawa, “Development of a tracking method for augmented reality applied to nuclear plant maintenance work: (1) barcode marker,” in Proceeding of Halden Project VR Workshop (Halden Project Centre, 2005), http://hydro.energy.kyoto-u.ac.jp/Lab/staff/hirotake/paper/papers/VRWS2005_1.pdf.
  19. S. Sathyanath and F. Sahin, “AISIMAM: an artificial immune system based intelligent multi agent model and its application to a mine detection problem,” in Proceeding of International Centre for Advanced Research in Identification Science, S. Garrett, ed. (University of Kent at Canterbury, 2002), pp. 22-31.
  20. HITLab, “ARToolKit,” http://www.hitl.washington.edu/artoolkit.
  21. M. Fiala, “ARTag, a fiducial marker system using digital techniques,” in Proceedings of IEEE Computer Vision and Pattern Recognition, C.Schmid, S.Soatto, and C.Tomasi, eds. (IEEE Computer Society, 2005), Vol. 2, pp. 590-596.
  22. ColorZip Media, http://www.colorzip.co.jp/en.
  23. J. R. Kaufman and C. Hohberger, “Distortion resistant double-data correcting color transition barcode and method of generating and using same,” U.S. patent 6,070,805 (United States Patent and Trademark Office, 2000).
  24. V. L. Jaume, “Color constancy and image segmentation techniques for applications to mobile robotics,” Doctoral thesis (Universitat Politecnica de Catalunya, 2005).
  25. K. Barnard, V. Cardei, and B. Funt, “A comparison of computational color constancy algorithms-part I: methodology and experiments with synthesized data,” IEEE Trans. Image Process. 11, 972-984 (2002).
    [CrossRef]
  26. K. Barnard, L. Martin, A. Coath, and B. Funt, “A comparison of computational color constancy algorithms-part II: experiments with image data,” IEEE Trans. Image Process. 11, 985-996 (2002).
    [CrossRef]
  27. S. D. Hordley and G. D. Finlayson, “Reevaluation of color constancy algorithm performance,” J. Opt. Soc. Am. A 23, 1008-1020 (2006).
    [CrossRef]
  28. C. Cheong, N.-K. Lee, and T.-D. Han, “Apparatus and method for recognizing code,” U.S. patent 6,981,644 (United States Patent and Trademark Office, 2006).
  29. C. Cheong, D.-C. Kim, and T.-D. Han, “Color classification using quiet zone information for color-based image code recognition,” in Proceeding of First Korea-Japan Joint Workshop on Pattern Recognition, B. -K. Shin and K. Kise, eds. (Korea Information Science Society, Korea and The Institute of Electronics, Information and Communication Engineers, Japan, 2006), pp. 109-114.
  30. M. Ebner, “A parallel algorithm for color constancy,” Technical Report 296 (Universita¨t Wu¨rzburg, Lehrstuhl fu¨r Informatik II, April 2002).
  31. D. A. Brainard and B. A. Wandell, “Analysis of the retinex theory of color vision,” J. Opt. Soc. Am. A 3, 1651-1661 (1986).
  32. R. Gershon, A. D. Jepson, and J. K. Tsotsos, “From [R,G,B] to surface reflectance: computing color constant descriptors in images,” Perception 17, 755-758 (1988).
  33. K. J. Linnell and D. H. Foster, “Space-average scene colour used to extract illuminant information,” in Selected Proceedings of the Int. Conf. John Dalton's Colour Vision Legacy, C. Dickinson, I. Murray, and D. Carden, eds. (Taylor & Francis, 1997), pp. 501-509.
  34. J. J. McCann, S. P. McKee, and T. H. Taylor, “Quantitative studies in Retinex theory,” Vision Res. 16, 445-458 (1976).
    [CrossRef]
  35. B. K. P. Horn, “Determining lightness from an image,” Comput. Graph. Image Process. 3, 277-299 (1974).
    [CrossRef]
  36. B. V. Funt, K. Barnard, and L. Martin, “Is colour constancy good enough?,” in Proceedings of Fifth European Conference on Computer Vision, LNCS 1406, H.Burkhardt and B.Neumann, eds. (Springer-Verlag, 1998), pp. 445-459.
  37. C. Balkenius, A. J. Johansson, and A. Balkenius, “Color constancy in visual scene perception,” Lund University Cognitive Studies 98 (2003), http://www.lucs.lu.se/ftp/pub/LUCS_Studies/LUCSinlaga98.pdf.
  38. D. A. Forsyth, “A novel algorithm for color constancy,” Int. J. Comput. Vis. 5, 5-36 (1990).
    [CrossRef]
  39. G. D. Finlayson, “Color in perspective,” IEEE Transactions on Pattern Analysis and Machine Intelligence 18, 1034-1038(1996).
    [CrossRef]
  40. G. D. Finlayson and S. D. Hordley, “Improving gamut mapping color constancy,” IEEE Trans. Image Process. 9, 1774-1783(2000).
    [CrossRef]
  41. D. H. Brainard and W. T. Freeman, “Bayesian color constancy,” J. Opt. Soc. Am. A 14, 1393-1411 (1997).
    [CrossRef]
  42. E. H. Land, “An alternative technique for the computation of the designator in the Retinex theory of color vision,” Proc. Natl. Acad. Sci. U.S.A. 83, 3078-3080 (1986).
    [CrossRef]
  43. J. J. McCann, “Magnitude of color shifts from average quanta catch adaptation,” in Proceedings of IS&T/SID Fifth Color Imaging Conf.: Color Science, Systems and Application (The Society for Imaging Science and Technology, 1997), pp. 215-220.
  44. P. M. Hubel and G. Finlayson, “White point estimation using correlation matrix memory,” U.S. patent 6,038,339 (United States Patent and Trademark Office, 2000).
  45. G. Finlayson, S. Hordley, and P. Hubel, “Color by correlation: a simple, unifying framework for color constancy,” IEEE Transactions on Pattern Analysis and Machine Intelligence 23, 1209-1221 (2001).
    [CrossRef]
  46. V. C. Cardei, B. Funt, and K. Barnard, “Estimating the scene illuminant chromaticity by using a neural network,” J. Opt. Soc. Am. A 19, 2374-2386 (2002).
    [CrossRef]
  47. M. Ebner, “Evolving color constancy for an artificial retina,” in Genetic Programming: Proceedings of the 4th Europ. Conf., EuroGP 2001, J. Miller, M. Tomassini, P. L. Lanzi, C. Ryan, A. G. B. Tettamanzi, and W. B. Langdon, eds. (Springer-Verlag, 2001), pp. 11-22.
  48. V. C. Cardei and B. Funt, “Committee-based color constancy,” in Proceedings of the IS&T/SID 7th Color Imaging Conference: Color Science, Systems and Applications (The Society for Imaging Science and Technology, 1999), pp. 311-313, http://www.cs.sfu.ca/%7Ecolour/publications/IST-99/IST-99-CBCC.pdf.
  49. M. Ebner, “Combining white-patch retinex and the gray world assumption to achieve color constancy for multiple illuminants,” in Proceedings of the 25th DAGM Symposium on Pattern Recognition, LNCS 2781, B. Michaelis and G. Krell, eds. (Springer-Verlag, 2003), pp. 60-67.
  50. E. H. Land, “The retinex theory of color vision,” Sci. Am. 6, 108-128 (1977).
  51. “Using bar code,” Data Capture Institute, http://www.datacaptureinstitute.com/publications/book.htm.
  52. “2D (two dimensional) bar code symbologies,” Swing Labels, http://www.swinglabels.com/barcodes/symbology/2d.asp.
  53. A. R. Smith, “Color gamut transform pairs,” in Proceedings of the 5th annual conference on Computer graphics and interactive techniques, S. H. Chasen and R. L. Phillips, eds. (Association for Computing Machinery Press, 1978), pp. 12-19.
  54. M. Gardner, “Multivariate statistics: scaling, clustering, and factor analysis,” http://www.ed.utah.edu/edps/CourseMaterials/7570/MS14.
  55. P. Cimiano, A. Hotho, and S. Staab, “Comparing conceptual, divisive and agglomerative clustering for learning taxonomies from text,” in Proceedings of the 16th European Conference on Artificial Intelligence, R. L. Mántaras and L. Saitta, eds. (IOS Press, 2004), pp. 435-439.
  56. E. Gose, R. Johnsonbaugh, and S. Jost, Pattern Recognition and Image Analysis (Prentice Hall, 1996), pp. 338-346.
  57. K. N. Plataniotis and A. N. Venetsanopoulos, Color Image Processing and Application (Springer-Verlag, 2000), pp. 20-25.

2006 (4)

K. D. Hunter, “Automatic access of internet content with a camera-enabled cell phone,” U.S. patent 6,993,573 (United States Patent and Trademark Office, 2006).

S. D. Hordley and G. D. Finlayson, “Reevaluation of color constancy algorithm performance,” J. Opt. Soc. Am. A 23, 1008-1020 (2006).
[CrossRef]

C. Cheong, N.-K. Lee, and T.-D. Han, “Apparatus and method for recognizing code,” U.S. patent 6,981,644 (United States Patent and Trademark Office, 2006).

C. Cheong, D.-C. Kim, and T.-D. Han, “Color classification using quiet zone information for color-based image code recognition,” in Proceeding of First Korea-Japan Joint Workshop on Pattern Recognition, B. -K. Shin and K. Kise, eds. (Korea Information Science Society, Korea and The Institute of Electronics, Information and Communication Engineers, Japan, 2006), pp. 109-114.

2005 (3)

M. Fiala, “ARTag, a fiducial marker system using digital techniques,” in Proceedings of IEEE Computer Vision and Pattern Recognition, C.Schmid, S.Soatto, and C.Tomasi, eds. (IEEE Computer Society, 2005), Vol. 2, pp. 590-596.

V. L. Jaume, “Color constancy and image segmentation techniques for applications to mobile robotics,” Doctoral thesis (Universitat Politecnica de Catalunya, 2005).

H. Shimoda, H. Ishii, M. Maeshima, T. Nakai, Z. Bian, and H. Yoshikawa, “Development of a tracking method for augmented reality applied to nuclear plant maintenance work: (1) barcode marker,” in Proceeding of Halden Project VR Workshop (Halden Project Centre, 2005), http://hydro.energy.kyoto-u.ac.jp/Lab/staff/hirotake/paper/papers/VRWS2005_1.pdf.

2004 (2)

H. Usuda, M. Suzuku, and Maeda, Research result report on creation and transmission of digital contents using image recognition technology (summary version), Project Code IMS 0359, Sony Corporation, Japan, 2004.

P. Cimiano, A. Hotho, and S. Staab, “Comparing conceptual, divisive and agglomerative clustering for learning taxonomies from text,” in Proceedings of the 16th European Conference on Artificial Intelligence, R. L. Mántaras and L. Saitta, eds. (IOS Press, 2004), pp. 435-439.

2003 (2)

M. Ebner, “Combining white-patch retinex and the gray world assumption to achieve color constancy for multiple illuminants,” in Proceedings of the 25th DAGM Symposium on Pattern Recognition, LNCS 2781, B. Michaelis and G. Krell, eds. (Springer-Verlag, 2003), pp. 60-67.

C. Balkenius, A. J. Johansson, and A. Balkenius, “Color constancy in visual scene perception,” Lund University Cognitive Studies 98 (2003), http://www.lucs.lu.se/ftp/pub/LUCS_Studies/LUCSinlaga98.pdf.

2002 (4)

K. Barnard, V. Cardei, and B. Funt, “A comparison of computational color constancy algorithms-part I: methodology and experiments with synthesized data,” IEEE Trans. Image Process. 11, 972-984 (2002).
[CrossRef]

K. Barnard, L. Martin, A. Coath, and B. Funt, “A comparison of computational color constancy algorithms-part II: experiments with image data,” IEEE Trans. Image Process. 11, 985-996 (2002).
[CrossRef]

S. Sathyanath and F. Sahin, “AISIMAM: an artificial immune system based intelligent multi agent model and its application to a mine detection problem,” in Proceeding of International Centre for Advanced Research in Identification Science, S. Garrett, ed. (University of Kent at Canterbury, 2002), pp. 22-31.

V. C. Cardei, B. Funt, and K. Barnard, “Estimating the scene illuminant chromaticity by using a neural network,” J. Opt. Soc. Am. A 19, 2374-2386 (2002).
[CrossRef]

2001 (5)

M. Ebner, “Evolving color constancy for an artificial retina,” in Genetic Programming: Proceedings of the 4th Europ. Conf., EuroGP 2001, J. Miller, M. Tomassini, P. L. Lanzi, C. Ryan, A. G. B. Tettamanzi, and W. B. Langdon, eds. (Springer-Verlag, 2001), pp. 11-22.

G. Finlayson, S. Hordley, and P. Hubel, “Color by correlation: a simple, unifying framework for color constancy,” IEEE Transactions on Pattern Analysis and Machine Intelligence 23, 1209-1221 (2001).
[CrossRef]

R. Azuma, Y. Baillot, R. Behringer, S. Feiner, S. Julier, and B. MacIntyre, “Recent advances in augmented reality,” in IEEE Computer Graphics and Applications (IEEE, 2001), pp. 34-47.

D. L. Hecht, “Printed embedded data graphical user interfaces,” IEEE Comput. Graphics Appl. 34, 47-55 (2001).

International Organization for Standardization, Information technology: automatic identification and data capture techniques--bar code symbology--PDF-417, ISO/IEC 15438 (ISO/IEC, 2001).

2000 (7)

International Organization for Standardization, Information technology: automatic identification and data capture techniques--bar code symbology--QR code, ISO/IEC 18004 (ISO/IEC, 2000).

J. Rekimoto and Y. Ayatsuka, “Cyber code: designing augmented reality environments with visual tags,” in Proceedings Designing Augmented Reality Environments, W. E. Mackay, ed. (Association for Computing Machinery Press, 2000), pp. 1-10.

International Organization for Standardization, Information technology: automatic identification and data capture techniques--bar code symbology--data matrix, ISO/IEC 16022 (ISO/IEC, 2000).

J. R. Kaufman and C. Hohberger, “Distortion resistant double-data correcting color transition barcode and method of generating and using same,” U.S. patent 6,070,805 (United States Patent and Trademark Office, 2000).

G. D. Finlayson and S. D. Hordley, “Improving gamut mapping color constancy,” IEEE Trans. Image Process. 9, 1774-1783(2000).
[CrossRef]

P. M. Hubel and G. Finlayson, “White point estimation using correlation matrix memory,” U.S. patent 6,038,339 (United States Patent and Trademark Office, 2000).

K. N. Plataniotis and A. N. Venetsanopoulos, Color Image Processing and Application (Springer-Verlag, 2000), pp. 20-25.

1999 (4)

V. C. Cardei and B. Funt, “Committee-based color constancy,” in Proceedings of the IS&T/SID 7th Color Imaging Conference: Color Science, Systems and Applications (The Society for Imaging Science and Technology, 1999), pp. 311-313, http://www.cs.sfu.ca/%7Ecolour/publications/IST-99/IST-99-CBCC.pdf.

H. Kato and M. Billinghurst, “Marker tracking and HMD calibration for a video-based augmented reality conferencing system,” in Proceedings of 2nd IEEE and ACM Int. Workshop on Augmented Reality, G. Klinker and T. U. München, eds. (IEEE Computer Society, 1999), pp. 85-94.

P. Milgram and H. Colquhoun, “A taxonomy of real and virtual world displays integration,” in Mixed Reality--Merging Real and Virtual Worlds, Y. Ohta and H. Tamura, eds. (Ohmsha and Springer-Verlag, 1999), pp. 5-30.

L. Nelson, S. Ichimura, E. R. Pedersen, and L. Adams, “Palette: a paper interface for giving presentations,” in Proceedings of ACM SIGCHI Conference on Human Factors and Computing Systems, M. G. William and M. W. Altom, eds. (Association for Computing Machinery Press, 1999), pp. 354-361.

1998 (2)

J. R. Vallino, “Interactive augmented reality,” Ph D. dissertation (University of Rochester, New York, 1998).

B. V. Funt, K. Barnard, and L. Martin, “Is colour constancy good enough?,” in Proceedings of Fifth European Conference on Computer Vision, LNCS 1406, H.Burkhardt and B.Neumann, eds. (Springer-Verlag, 1998), pp. 445-459.

1997 (3)

K. J. Linnell and D. H. Foster, “Space-average scene colour used to extract illuminant information,” in Selected Proceedings of the Int. Conf. John Dalton's Colour Vision Legacy, C. Dickinson, I. Murray, and D. Carden, eds. (Taylor & Francis, 1997), pp. 501-509.

D. H. Brainard and W. T. Freeman, “Bayesian color constancy,” J. Opt. Soc. Am. A 14, 1393-1411 (1997).
[CrossRef]

J. J. McCann, “Magnitude of color shifts from average quanta catch adaptation,” in Proceedings of IS&T/SID Fifth Color Imaging Conf.: Color Science, Systems and Application (The Society for Imaging Science and Technology, 1997), pp. 215-220.

1996 (3)

G. D. Finlayson, “Color in perspective,” IEEE Transactions on Pattern Analysis and Machine Intelligence 18, 1034-1038(1996).
[CrossRef]

E. Gose, R. Johnsonbaugh, and S. Jost, Pattern Recognition and Image Analysis (Prentice Hall, 1996), pp. 338-346.

A. State, G. Hirota, D. T. Chen, W. F. Garrett, and M. A. Livingston, “Superior augmented reality registration by integrating landmark tracking and magnetic tracking,” in Proceedings of SIGGRAPH, J. Fujii, ed. (Association for Computing Machinery Press, 1996), pp. 429-438.

1994 (1)

J. Rekimoto, The world through the computer: a new human-computer interaction style based on wearable computers, Technical Report SCSL-TR-94-013, Sony Computer Science Laboratories Inc., Japan, 1994.

1993 (1)

W. Johnson, H. Jellinek, L. Klotz, R. Rao, and S. Card, “Bridging the paper and electronic worlds: the paper user interface,” in Proceedings of Interact '93 and CHI'93 Conference on Human Factors in Computing Systems, S. Ashlund, K. Mullet, A. Henderson, E. Hollnagel, and T. White, eds. (Association for Computing Machinery Press, 1993), pp. 507-512.

1990 (2)

T. Pavlidis, J. Swartz, and Y. P. Wang, “Fundamentals of bar code information theory,” IEEE Comput. Graphics Appl. 23, 74-86 (1990).

D. A. Forsyth, “A novel algorithm for color constancy,” Int. J. Comput. Vis. 5, 5-36 (1990).
[CrossRef]

1988 (1)

R. Gershon, A. D. Jepson, and J. K. Tsotsos, “From [R,G,B] to surface reflectance: computing color constant descriptors in images,” Perception 17, 755-758 (1988).

1986 (2)

E. H. Land, “An alternative technique for the computation of the designator in the Retinex theory of color vision,” Proc. Natl. Acad. Sci. U.S.A. 83, 3078-3080 (1986).
[CrossRef]

D. A. Brainard and B. A. Wandell, “Analysis of the retinex theory of color vision,” J. Opt. Soc. Am. A 3, 1651-1661 (1986).

1978 (1)

A. R. Smith, “Color gamut transform pairs,” in Proceedings of the 5th annual conference on Computer graphics and interactive techniques, S. H. Chasen and R. L. Phillips, eds. (Association for Computing Machinery Press, 1978), pp. 12-19.

1977 (1)

E. H. Land, “The retinex theory of color vision,” Sci. Am. 6, 108-128 (1977).

1976 (1)

J. J. McCann, S. P. McKee, and T. H. Taylor, “Quantitative studies in Retinex theory,” Vision Res. 16, 445-458 (1976).
[CrossRef]

1974 (1)

B. K. P. Horn, “Determining lightness from an image,” Comput. Graph. Image Process. 3, 277-299 (1974).
[CrossRef]

Adams, L.

L. Nelson, S. Ichimura, E. R. Pedersen, and L. Adams, “Palette: a paper interface for giving presentations,” in Proceedings of ACM SIGCHI Conference on Human Factors and Computing Systems, M. G. William and M. W. Altom, eds. (Association for Computing Machinery Press, 1999), pp. 354-361.

Ayatsuka, Y.

J. Rekimoto and Y. Ayatsuka, “Cyber code: designing augmented reality environments with visual tags,” in Proceedings Designing Augmented Reality Environments, W. E. Mackay, ed. (Association for Computing Machinery Press, 2000), pp. 1-10.

Azuma, R.

R. Azuma, Y. Baillot, R. Behringer, S. Feiner, S. Julier, and B. MacIntyre, “Recent advances in augmented reality,” in IEEE Computer Graphics and Applications (IEEE, 2001), pp. 34-47.

Bäck, A.

T. Hautala, J. Kallenbach, M. Nuutinen, L. Salo, T. Venho, A. Bäck, C. Bäckström, L. Hakola, and T. Järvinen, “PrintAccess,” http://www.media.hut.fi/GTTS/GAiF/GAiF2_2005.htm#PrintAccess--Final Report.

Bäckström, C.

T. Hautala, J. Kallenbach, M. Nuutinen, L. Salo, T. Venho, A. Bäck, C. Bäckström, L. Hakola, and T. Järvinen, “PrintAccess,” http://www.media.hut.fi/GTTS/GAiF/GAiF2_2005.htm#PrintAccess--Final Report.

Baillot, Y.

R. Azuma, Y. Baillot, R. Behringer, S. Feiner, S. Julier, and B. MacIntyre, “Recent advances in augmented reality,” in IEEE Computer Graphics and Applications (IEEE, 2001), pp. 34-47.

Balkenius, A.

C. Balkenius, A. J. Johansson, and A. Balkenius, “Color constancy in visual scene perception,” Lund University Cognitive Studies 98 (2003), http://www.lucs.lu.se/ftp/pub/LUCS_Studies/LUCSinlaga98.pdf.

Balkenius, C.

C. Balkenius, A. J. Johansson, and A. Balkenius, “Color constancy in visual scene perception,” Lund University Cognitive Studies 98 (2003), http://www.lucs.lu.se/ftp/pub/LUCS_Studies/LUCSinlaga98.pdf.

Barnard, K.

V. C. Cardei, B. Funt, and K. Barnard, “Estimating the scene illuminant chromaticity by using a neural network,” J. Opt. Soc. Am. A 19, 2374-2386 (2002).
[CrossRef]

K. Barnard, V. Cardei, and B. Funt, “A comparison of computational color constancy algorithms-part I: methodology and experiments with synthesized data,” IEEE Trans. Image Process. 11, 972-984 (2002).
[CrossRef]

K. Barnard, L. Martin, A. Coath, and B. Funt, “A comparison of computational color constancy algorithms-part II: experiments with image data,” IEEE Trans. Image Process. 11, 985-996 (2002).
[CrossRef]

B. V. Funt, K. Barnard, and L. Martin, “Is colour constancy good enough?,” in Proceedings of Fifth European Conference on Computer Vision, LNCS 1406, H.Burkhardt and B.Neumann, eds. (Springer-Verlag, 1998), pp. 445-459.

Behringer, R.

R. Azuma, Y. Baillot, R. Behringer, S. Feiner, S. Julier, and B. MacIntyre, “Recent advances in augmented reality,” in IEEE Computer Graphics and Applications (IEEE, 2001), pp. 34-47.

Bian, Z.

H. Shimoda, H. Ishii, M. Maeshima, T. Nakai, Z. Bian, and H. Yoshikawa, “Development of a tracking method for augmented reality applied to nuclear plant maintenance work: (1) barcode marker,” in Proceeding of Halden Project VR Workshop (Halden Project Centre, 2005), http://hydro.energy.kyoto-u.ac.jp/Lab/staff/hirotake/paper/papers/VRWS2005_1.pdf.

Billinghurst, M.

H. Kato and M. Billinghurst, “Marker tracking and HMD calibration for a video-based augmented reality conferencing system,” in Proceedings of 2nd IEEE and ACM Int. Workshop on Augmented Reality, G. Klinker and T. U. München, eds. (IEEE Computer Society, 1999), pp. 85-94.

Brainard, D. A.

Brainard, D. H.

Card, S.

W. Johnson, H. Jellinek, L. Klotz, R. Rao, and S. Card, “Bridging the paper and electronic worlds: the paper user interface,” in Proceedings of Interact '93 and CHI'93 Conference on Human Factors in Computing Systems, S. Ashlund, K. Mullet, A. Henderson, E. Hollnagel, and T. White, eds. (Association for Computing Machinery Press, 1993), pp. 507-512.

Cardei, V.

K. Barnard, V. Cardei, and B. Funt, “A comparison of computational color constancy algorithms-part I: methodology and experiments with synthesized data,” IEEE Trans. Image Process. 11, 972-984 (2002).
[CrossRef]

Cardei, V. C.

V. C. Cardei, B. Funt, and K. Barnard, “Estimating the scene illuminant chromaticity by using a neural network,” J. Opt. Soc. Am. A 19, 2374-2386 (2002).
[CrossRef]

V. C. Cardei and B. Funt, “Committee-based color constancy,” in Proceedings of the IS&T/SID 7th Color Imaging Conference: Color Science, Systems and Applications (The Society for Imaging Science and Technology, 1999), pp. 311-313, http://www.cs.sfu.ca/%7Ecolour/publications/IST-99/IST-99-CBCC.pdf.

Chen, D. T.

A. State, G. Hirota, D. T. Chen, W. F. Garrett, and M. A. Livingston, “Superior augmented reality registration by integrating landmark tracking and magnetic tracking,” in Proceedings of SIGGRAPH, J. Fujii, ed. (Association for Computing Machinery Press, 1996), pp. 429-438.

Cheong, C.

C. Cheong, N.-K. Lee, and T.-D. Han, “Apparatus and method for recognizing code,” U.S. patent 6,981,644 (United States Patent and Trademark Office, 2006).

C. Cheong, D.-C. Kim, and T.-D. Han, “Color classification using quiet zone information for color-based image code recognition,” in Proceeding of First Korea-Japan Joint Workshop on Pattern Recognition, B. -K. Shin and K. Kise, eds. (Korea Information Science Society, Korea and The Institute of Electronics, Information and Communication Engineers, Japan, 2006), pp. 109-114.

Cimiano, P.

P. Cimiano, A. Hotho, and S. Staab, “Comparing conceptual, divisive and agglomerative clustering for learning taxonomies from text,” in Proceedings of the 16th European Conference on Artificial Intelligence, R. L. Mántaras and L. Saitta, eds. (IOS Press, 2004), pp. 435-439.

Coath, A.

K. Barnard, L. Martin, A. Coath, and B. Funt, “A comparison of computational color constancy algorithms-part II: experiments with image data,” IEEE Trans. Image Process. 11, 985-996 (2002).
[CrossRef]

Colquhoun, H.

P. Milgram and H. Colquhoun, “A taxonomy of real and virtual world displays integration,” in Mixed Reality--Merging Real and Virtual Worlds, Y. Ohta and H. Tamura, eds. (Ohmsha and Springer-Verlag, 1999), pp. 5-30.

Ebner, M.

M. Ebner, “A parallel algorithm for color constancy,” Technical Report 296 (Universita¨t Wu¨rzburg, Lehrstuhl fu¨r Informatik II, April 2002).

M. Ebner, “Combining white-patch retinex and the gray world assumption to achieve color constancy for multiple illuminants,” in Proceedings of the 25th DAGM Symposium on Pattern Recognition, LNCS 2781, B. Michaelis and G. Krell, eds. (Springer-Verlag, 2003), pp. 60-67.

M. Ebner, “Evolving color constancy for an artificial retina,” in Genetic Programming: Proceedings of the 4th Europ. Conf., EuroGP 2001, J. Miller, M. Tomassini, P. L. Lanzi, C. Ryan, A. G. B. Tettamanzi, and W. B. Langdon, eds. (Springer-Verlag, 2001), pp. 11-22.

Feiner, S.

R. Azuma, Y. Baillot, R. Behringer, S. Feiner, S. Julier, and B. MacIntyre, “Recent advances in augmented reality,” in IEEE Computer Graphics and Applications (IEEE, 2001), pp. 34-47.

Fiala, M.

M. Fiala, “ARTag, a fiducial marker system using digital techniques,” in Proceedings of IEEE Computer Vision and Pattern Recognition, C.Schmid, S.Soatto, and C.Tomasi, eds. (IEEE Computer Society, 2005), Vol. 2, pp. 590-596.

Finlayson, G.

G. Finlayson, S. Hordley, and P. Hubel, “Color by correlation: a simple, unifying framework for color constancy,” IEEE Transactions on Pattern Analysis and Machine Intelligence 23, 1209-1221 (2001).
[CrossRef]

P. M. Hubel and G. Finlayson, “White point estimation using correlation matrix memory,” U.S. patent 6,038,339 (United States Patent and Trademark Office, 2000).

Finlayson, G. D.

S. D. Hordley and G. D. Finlayson, “Reevaluation of color constancy algorithm performance,” J. Opt. Soc. Am. A 23, 1008-1020 (2006).
[CrossRef]

G. D. Finlayson and S. D. Hordley, “Improving gamut mapping color constancy,” IEEE Trans. Image Process. 9, 1774-1783(2000).
[CrossRef]

G. D. Finlayson, “Color in perspective,” IEEE Transactions on Pattern Analysis and Machine Intelligence 18, 1034-1038(1996).
[CrossRef]

Forsyth, D. A.

D. A. Forsyth, “A novel algorithm for color constancy,” Int. J. Comput. Vis. 5, 5-36 (1990).
[CrossRef]

Foster, D. H.

K. J. Linnell and D. H. Foster, “Space-average scene colour used to extract illuminant information,” in Selected Proceedings of the Int. Conf. John Dalton's Colour Vision Legacy, C. Dickinson, I. Murray, and D. Carden, eds. (Taylor & Francis, 1997), pp. 501-509.

Freeman, W. T.

Funt, B.

V. C. Cardei, B. Funt, and K. Barnard, “Estimating the scene illuminant chromaticity by using a neural network,” J. Opt. Soc. Am. A 19, 2374-2386 (2002).
[CrossRef]

K. Barnard, L. Martin, A. Coath, and B. Funt, “A comparison of computational color constancy algorithms-part II: experiments with image data,” IEEE Trans. Image Process. 11, 985-996 (2002).
[CrossRef]

K. Barnard, V. Cardei, and B. Funt, “A comparison of computational color constancy algorithms-part I: methodology and experiments with synthesized data,” IEEE Trans. Image Process. 11, 972-984 (2002).
[CrossRef]

V. C. Cardei and B. Funt, “Committee-based color constancy,” in Proceedings of the IS&T/SID 7th Color Imaging Conference: Color Science, Systems and Applications (The Society for Imaging Science and Technology, 1999), pp. 311-313, http://www.cs.sfu.ca/%7Ecolour/publications/IST-99/IST-99-CBCC.pdf.

Funt, B. V.

B. V. Funt, K. Barnard, and L. Martin, “Is colour constancy good enough?,” in Proceedings of Fifth European Conference on Computer Vision, LNCS 1406, H.Burkhardt and B.Neumann, eds. (Springer-Verlag, 1998), pp. 445-459.

Gardner, M.

M. Gardner, “Multivariate statistics: scaling, clustering, and factor analysis,” http://www.ed.utah.edu/edps/CourseMaterials/7570/MS14.

Garrett, W. F.

A. State, G. Hirota, D. T. Chen, W. F. Garrett, and M. A. Livingston, “Superior augmented reality registration by integrating landmark tracking and magnetic tracking,” in Proceedings of SIGGRAPH, J. Fujii, ed. (Association for Computing Machinery Press, 1996), pp. 429-438.

Gershon, R.

R. Gershon, A. D. Jepson, and J. K. Tsotsos, “From [R,G,B] to surface reflectance: computing color constant descriptors in images,” Perception 17, 755-758 (1988).

Gose, E.

E. Gose, R. Johnsonbaugh, and S. Jost, Pattern Recognition and Image Analysis (Prentice Hall, 1996), pp. 338-346.

Hakola, L.

T. Hautala, J. Kallenbach, M. Nuutinen, L. Salo, T. Venho, A. Bäck, C. Bäckström, L. Hakola, and T. Järvinen, “PrintAccess,” http://www.media.hut.fi/GTTS/GAiF/GAiF2_2005.htm#PrintAccess--Final Report.

Han, T.-D.

C. Cheong, N.-K. Lee, and T.-D. Han, “Apparatus and method for recognizing code,” U.S. patent 6,981,644 (United States Patent and Trademark Office, 2006).

C. Cheong, D.-C. Kim, and T.-D. Han, “Color classification using quiet zone information for color-based image code recognition,” in Proceeding of First Korea-Japan Joint Workshop on Pattern Recognition, B. -K. Shin and K. Kise, eds. (Korea Information Science Society, Korea and The Institute of Electronics, Information and Communication Engineers, Japan, 2006), pp. 109-114.

Hautala, T.

T. Hautala, J. Kallenbach, M. Nuutinen, L. Salo, T. Venho, A. Bäck, C. Bäckström, L. Hakola, and T. Järvinen, “PrintAccess,” http://www.media.hut.fi/GTTS/GAiF/GAiF2_2005.htm#PrintAccess--Final Report.

Hecht, D. L.

D. L. Hecht, “Printed embedded data graphical user interfaces,” IEEE Comput. Graphics Appl. 34, 47-55 (2001).

Hirota, G.

A. State, G. Hirota, D. T. Chen, W. F. Garrett, and M. A. Livingston, “Superior augmented reality registration by integrating landmark tracking and magnetic tracking,” in Proceedings of SIGGRAPH, J. Fujii, ed. (Association for Computing Machinery Press, 1996), pp. 429-438.

Hohberger, C.

J. R. Kaufman and C. Hohberger, “Distortion resistant double-data correcting color transition barcode and method of generating and using same,” U.S. patent 6,070,805 (United States Patent and Trademark Office, 2000).

Hordley, S.

G. Finlayson, S. Hordley, and P. Hubel, “Color by correlation: a simple, unifying framework for color constancy,” IEEE Transactions on Pattern Analysis and Machine Intelligence 23, 1209-1221 (2001).
[CrossRef]

Hordley, S. D.

S. D. Hordley and G. D. Finlayson, “Reevaluation of color constancy algorithm performance,” J. Opt. Soc. Am. A 23, 1008-1020 (2006).
[CrossRef]

G. D. Finlayson and S. D. Hordley, “Improving gamut mapping color constancy,” IEEE Trans. Image Process. 9, 1774-1783(2000).
[CrossRef]

Horn, B. K. P.

B. K. P. Horn, “Determining lightness from an image,” Comput. Graph. Image Process. 3, 277-299 (1974).
[CrossRef]

Hotho, A.

P. Cimiano, A. Hotho, and S. Staab, “Comparing conceptual, divisive and agglomerative clustering for learning taxonomies from text,” in Proceedings of the 16th European Conference on Artificial Intelligence, R. L. Mántaras and L. Saitta, eds. (IOS Press, 2004), pp. 435-439.

Hubel, P.

G. Finlayson, S. Hordley, and P. Hubel, “Color by correlation: a simple, unifying framework for color constancy,” IEEE Transactions on Pattern Analysis and Machine Intelligence 23, 1209-1221 (2001).
[CrossRef]

Hubel, P. M.

P. M. Hubel and G. Finlayson, “White point estimation using correlation matrix memory,” U.S. patent 6,038,339 (United States Patent and Trademark Office, 2000).

Hunter, K. D.

K. D. Hunter, “Automatic access of internet content with a camera-enabled cell phone,” U.S. patent 6,993,573 (United States Patent and Trademark Office, 2006).

Ichimura, S.

L. Nelson, S. Ichimura, E. R. Pedersen, and L. Adams, “Palette: a paper interface for giving presentations,” in Proceedings of ACM SIGCHI Conference on Human Factors and Computing Systems, M. G. William and M. W. Altom, eds. (Association for Computing Machinery Press, 1999), pp. 354-361.

Ishii, H.

H. Shimoda, H. Ishii, M. Maeshima, T. Nakai, Z. Bian, and H. Yoshikawa, “Development of a tracking method for augmented reality applied to nuclear plant maintenance work: (1) barcode marker,” in Proceeding of Halden Project VR Workshop (Halden Project Centre, 2005), http://hydro.energy.kyoto-u.ac.jp/Lab/staff/hirotake/paper/papers/VRWS2005_1.pdf.

Järvinen, T.

T. Hautala, J. Kallenbach, M. Nuutinen, L. Salo, T. Venho, A. Bäck, C. Bäckström, L. Hakola, and T. Järvinen, “PrintAccess,” http://www.media.hut.fi/GTTS/GAiF/GAiF2_2005.htm#PrintAccess--Final Report.

Jaume, V. L.

V. L. Jaume, “Color constancy and image segmentation techniques for applications to mobile robotics,” Doctoral thesis (Universitat Politecnica de Catalunya, 2005).

Jellinek, H.

W. Johnson, H. Jellinek, L. Klotz, R. Rao, and S. Card, “Bridging the paper and electronic worlds: the paper user interface,” in Proceedings of Interact '93 and CHI'93 Conference on Human Factors in Computing Systems, S. Ashlund, K. Mullet, A. Henderson, E. Hollnagel, and T. White, eds. (Association for Computing Machinery Press, 1993), pp. 507-512.

Jepson, A. D.

R. Gershon, A. D. Jepson, and J. K. Tsotsos, “From [R,G,B] to surface reflectance: computing color constant descriptors in images,” Perception 17, 755-758 (1988).

Johansson, A. J.

C. Balkenius, A. J. Johansson, and A. Balkenius, “Color constancy in visual scene perception,” Lund University Cognitive Studies 98 (2003), http://www.lucs.lu.se/ftp/pub/LUCS_Studies/LUCSinlaga98.pdf.

Johnson, W.

W. Johnson, H. Jellinek, L. Klotz, R. Rao, and S. Card, “Bridging the paper and electronic worlds: the paper user interface,” in Proceedings of Interact '93 and CHI'93 Conference on Human Factors in Computing Systems, S. Ashlund, K. Mullet, A. Henderson, E. Hollnagel, and T. White, eds. (Association for Computing Machinery Press, 1993), pp. 507-512.

Johnsonbaugh, R.

E. Gose, R. Johnsonbaugh, and S. Jost, Pattern Recognition and Image Analysis (Prentice Hall, 1996), pp. 338-346.

Jost, S.

E. Gose, R. Johnsonbaugh, and S. Jost, Pattern Recognition and Image Analysis (Prentice Hall, 1996), pp. 338-346.

Julier, S.

R. Azuma, Y. Baillot, R. Behringer, S. Feiner, S. Julier, and B. MacIntyre, “Recent advances in augmented reality,” in IEEE Computer Graphics and Applications (IEEE, 2001), pp. 34-47.

Kallenbach, J.

T. Hautala, J. Kallenbach, M. Nuutinen, L. Salo, T. Venho, A. Bäck, C. Bäckström, L. Hakola, and T. Järvinen, “PrintAccess,” http://www.media.hut.fi/GTTS/GAiF/GAiF2_2005.htm#PrintAccess--Final Report.

Kato, H.

H. Kato and M. Billinghurst, “Marker tracking and HMD calibration for a video-based augmented reality conferencing system,” in Proceedings of 2nd IEEE and ACM Int. Workshop on Augmented Reality, G. Klinker and T. U. München, eds. (IEEE Computer Society, 1999), pp. 85-94.

Kaufman, J. R.

J. R. Kaufman and C. Hohberger, “Distortion resistant double-data correcting color transition barcode and method of generating and using same,” U.S. patent 6,070,805 (United States Patent and Trademark Office, 2000).

Kim, D.-C.

C. Cheong, D.-C. Kim, and T.-D. Han, “Color classification using quiet zone information for color-based image code recognition,” in Proceeding of First Korea-Japan Joint Workshop on Pattern Recognition, B. -K. Shin and K. Kise, eds. (Korea Information Science Society, Korea and The Institute of Electronics, Information and Communication Engineers, Japan, 2006), pp. 109-114.

Klotz, L.

W. Johnson, H. Jellinek, L. Klotz, R. Rao, and S. Card, “Bridging the paper and electronic worlds: the paper user interface,” in Proceedings of Interact '93 and CHI'93 Conference on Human Factors in Computing Systems, S. Ashlund, K. Mullet, A. Henderson, E. Hollnagel, and T. White, eds. (Association for Computing Machinery Press, 1993), pp. 507-512.

Land, E. H.

E. H. Land, “An alternative technique for the computation of the designator in the Retinex theory of color vision,” Proc. Natl. Acad. Sci. U.S.A. 83, 3078-3080 (1986).
[CrossRef]

E. H. Land, “The retinex theory of color vision,” Sci. Am. 6, 108-128 (1977).

Lee, N.-K.

C. Cheong, N.-K. Lee, and T.-D. Han, “Apparatus and method for recognizing code,” U.S. patent 6,981,644 (United States Patent and Trademark Office, 2006).

Linnell, K. J.

K. J. Linnell and D. H. Foster, “Space-average scene colour used to extract illuminant information,” in Selected Proceedings of the Int. Conf. John Dalton's Colour Vision Legacy, C. Dickinson, I. Murray, and D. Carden, eds. (Taylor & Francis, 1997), pp. 501-509.

Livingston, M. A.

A. State, G. Hirota, D. T. Chen, W. F. Garrett, and M. A. Livingston, “Superior augmented reality registration by integrating landmark tracking and magnetic tracking,” in Proceedings of SIGGRAPH, J. Fujii, ed. (Association for Computing Machinery Press, 1996), pp. 429-438.

MacIntyre, B.

R. Azuma, Y. Baillot, R. Behringer, S. Feiner, S. Julier, and B. MacIntyre, “Recent advances in augmented reality,” in IEEE Computer Graphics and Applications (IEEE, 2001), pp. 34-47.

Maeda,

H. Usuda, M. Suzuku, and Maeda, Research result report on creation and transmission of digital contents using image recognition technology (summary version), Project Code IMS 0359, Sony Corporation, Japan, 2004.

Maeshima, M.

H. Shimoda, H. Ishii, M. Maeshima, T. Nakai, Z. Bian, and H. Yoshikawa, “Development of a tracking method for augmented reality applied to nuclear plant maintenance work: (1) barcode marker,” in Proceeding of Halden Project VR Workshop (Halden Project Centre, 2005), http://hydro.energy.kyoto-u.ac.jp/Lab/staff/hirotake/paper/papers/VRWS2005_1.pdf.

Martin, L.

K. Barnard, L. Martin, A. Coath, and B. Funt, “A comparison of computational color constancy algorithms-part II: experiments with image data,” IEEE Trans. Image Process. 11, 985-996 (2002).
[CrossRef]

B. V. Funt, K. Barnard, and L. Martin, “Is colour constancy good enough?,” in Proceedings of Fifth European Conference on Computer Vision, LNCS 1406, H.Burkhardt and B.Neumann, eds. (Springer-Verlag, 1998), pp. 445-459.

McCann, J. J.

J. J. McCann, “Magnitude of color shifts from average quanta catch adaptation,” in Proceedings of IS&T/SID Fifth Color Imaging Conf.: Color Science, Systems and Application (The Society for Imaging Science and Technology, 1997), pp. 215-220.

J. J. McCann, S. P. McKee, and T. H. Taylor, “Quantitative studies in Retinex theory,” Vision Res. 16, 445-458 (1976).
[CrossRef]

McKee, S. P.

J. J. McCann, S. P. McKee, and T. H. Taylor, “Quantitative studies in Retinex theory,” Vision Res. 16, 445-458 (1976).
[CrossRef]

Milgram, P.

P. Milgram and H. Colquhoun, “A taxonomy of real and virtual world displays integration,” in Mixed Reality--Merging Real and Virtual Worlds, Y. Ohta and H. Tamura, eds. (Ohmsha and Springer-Verlag, 1999), pp. 5-30.

Nakai, T.

H. Shimoda, H. Ishii, M. Maeshima, T. Nakai, Z. Bian, and H. Yoshikawa, “Development of a tracking method for augmented reality applied to nuclear plant maintenance work: (1) barcode marker,” in Proceeding of Halden Project VR Workshop (Halden Project Centre, 2005), http://hydro.energy.kyoto-u.ac.jp/Lab/staff/hirotake/paper/papers/VRWS2005_1.pdf.

Nelson, L.

L. Nelson, S. Ichimura, E. R. Pedersen, and L. Adams, “Palette: a paper interface for giving presentations,” in Proceedings of ACM SIGCHI Conference on Human Factors and Computing Systems, M. G. William and M. W. Altom, eds. (Association for Computing Machinery Press, 1999), pp. 354-361.

Nuutinen, M.

T. Hautala, J. Kallenbach, M. Nuutinen, L. Salo, T. Venho, A. Bäck, C. Bäckström, L. Hakola, and T. Järvinen, “PrintAccess,” http://www.media.hut.fi/GTTS/GAiF/GAiF2_2005.htm#PrintAccess--Final Report.

Pavlidis, T.

T. Pavlidis, J. Swartz, and Y. P. Wang, “Fundamentals of bar code information theory,” IEEE Comput. Graphics Appl. 23, 74-86 (1990).

Pedersen, E. R.

L. Nelson, S. Ichimura, E. R. Pedersen, and L. Adams, “Palette: a paper interface for giving presentations,” in Proceedings of ACM SIGCHI Conference on Human Factors and Computing Systems, M. G. William and M. W. Altom, eds. (Association for Computing Machinery Press, 1999), pp. 354-361.

Plataniotis, K. N.

K. N. Plataniotis and A. N. Venetsanopoulos, Color Image Processing and Application (Springer-Verlag, 2000), pp. 20-25.

Rao, R.

W. Johnson, H. Jellinek, L. Klotz, R. Rao, and S. Card, “Bridging the paper and electronic worlds: the paper user interface,” in Proceedings of Interact '93 and CHI'93 Conference on Human Factors in Computing Systems, S. Ashlund, K. Mullet, A. Henderson, E. Hollnagel, and T. White, eds. (Association for Computing Machinery Press, 1993), pp. 507-512.

Rekimoto, J.

J. Rekimoto and Y. Ayatsuka, “Cyber code: designing augmented reality environments with visual tags,” in Proceedings Designing Augmented Reality Environments, W. E. Mackay, ed. (Association for Computing Machinery Press, 2000), pp. 1-10.

J. Rekimoto, The world through the computer: a new human-computer interaction style based on wearable computers, Technical Report SCSL-TR-94-013, Sony Computer Science Laboratories Inc., Japan, 1994.

Sahin, F.

S. Sathyanath and F. Sahin, “AISIMAM: an artificial immune system based intelligent multi agent model and its application to a mine detection problem,” in Proceeding of International Centre for Advanced Research in Identification Science, S. Garrett, ed. (University of Kent at Canterbury, 2002), pp. 22-31.

Salo, L.

T. Hautala, J. Kallenbach, M. Nuutinen, L. Salo, T. Venho, A. Bäck, C. Bäckström, L. Hakola, and T. Järvinen, “PrintAccess,” http://www.media.hut.fi/GTTS/GAiF/GAiF2_2005.htm#PrintAccess--Final Report.

Sathyanath, S.

S. Sathyanath and F. Sahin, “AISIMAM: an artificial immune system based intelligent multi agent model and its application to a mine detection problem,” in Proceeding of International Centre for Advanced Research in Identification Science, S. Garrett, ed. (University of Kent at Canterbury, 2002), pp. 22-31.

Shimoda, H.

H. Shimoda, H. Ishii, M. Maeshima, T. Nakai, Z. Bian, and H. Yoshikawa, “Development of a tracking method for augmented reality applied to nuclear plant maintenance work: (1) barcode marker,” in Proceeding of Halden Project VR Workshop (Halden Project Centre, 2005), http://hydro.energy.kyoto-u.ac.jp/Lab/staff/hirotake/paper/papers/VRWS2005_1.pdf.

Smith, A. R.

A. R. Smith, “Color gamut transform pairs,” in Proceedings of the 5th annual conference on Computer graphics and interactive techniques, S. H. Chasen and R. L. Phillips, eds. (Association for Computing Machinery Press, 1978), pp. 12-19.

Staab, S.

P. Cimiano, A. Hotho, and S. Staab, “Comparing conceptual, divisive and agglomerative clustering for learning taxonomies from text,” in Proceedings of the 16th European Conference on Artificial Intelligence, R. L. Mántaras and L. Saitta, eds. (IOS Press, 2004), pp. 435-439.

Standardization, International Organization for

International Organization for Standardization, Information technology: automatic identification and data capture techniques--bar code symbology--PDF-417, ISO/IEC 15438 (ISO/IEC, 2001).

International Organization for Standardization, Information technology: automatic identification and data capture techniques--bar code symbology--QR code, ISO/IEC 18004 (ISO/IEC, 2000).

International Organization for Standardization, Information technology: automatic identification and data capture techniques--bar code symbology--data matrix, ISO/IEC 16022 (ISO/IEC, 2000).

State, A.

A. State, G. Hirota, D. T. Chen, W. F. Garrett, and M. A. Livingston, “Superior augmented reality registration by integrating landmark tracking and magnetic tracking,” in Proceedings of SIGGRAPH, J. Fujii, ed. (Association for Computing Machinery Press, 1996), pp. 429-438.

Suzuku, M.

H. Usuda, M. Suzuku, and Maeda, Research result report on creation and transmission of digital contents using image recognition technology (summary version), Project Code IMS 0359, Sony Corporation, Japan, 2004.

Swartz, J.

T. Pavlidis, J. Swartz, and Y. P. Wang, “Fundamentals of bar code information theory,” IEEE Comput. Graphics Appl. 23, 74-86 (1990).

Taylor, T. H.

J. J. McCann, S. P. McKee, and T. H. Taylor, “Quantitative studies in Retinex theory,” Vision Res. 16, 445-458 (1976).
[CrossRef]

Tsotsos, J. K.

R. Gershon, A. D. Jepson, and J. K. Tsotsos, “From [R,G,B] to surface reflectance: computing color constant descriptors in images,” Perception 17, 755-758 (1988).

Usuda, H.

H. Usuda, M. Suzuku, and Maeda, Research result report on creation and transmission of digital contents using image recognition technology (summary version), Project Code IMS 0359, Sony Corporation, Japan, 2004.

Vallino, J. R.

J. R. Vallino, “Interactive augmented reality,” Ph D. dissertation (University of Rochester, New York, 1998).

Venetsanopoulos, A. N.

K. N. Plataniotis and A. N. Venetsanopoulos, Color Image Processing and Application (Springer-Verlag, 2000), pp. 20-25.

Venho, T.

T. Hautala, J. Kallenbach, M. Nuutinen, L. Salo, T. Venho, A. Bäck, C. Bäckström, L. Hakola, and T. Järvinen, “PrintAccess,” http://www.media.hut.fi/GTTS/GAiF/GAiF2_2005.htm#PrintAccess--Final Report.

Wandell, B. A.

Wang, Y. P.

T. Pavlidis, J. Swartz, and Y. P. Wang, “Fundamentals of bar code information theory,” IEEE Comput. Graphics Appl. 23, 74-86 (1990).

Yoshikawa, H.

H. Shimoda, H. Ishii, M. Maeshima, T. Nakai, Z. Bian, and H. Yoshikawa, “Development of a tracking method for augmented reality applied to nuclear plant maintenance work: (1) barcode marker,” in Proceeding of Halden Project VR Workshop (Halden Project Centre, 2005), http://hydro.energy.kyoto-u.ac.jp/Lab/staff/hirotake/paper/papers/VRWS2005_1.pdf.

Comput. Graph. Image Process. (1)

B. K. P. Horn, “Determining lightness from an image,” Comput. Graph. Image Process. 3, 277-299 (1974).
[CrossRef]

IEEE Comput. Graphics Appl. (2)

D. L. Hecht, “Printed embedded data graphical user interfaces,” IEEE Comput. Graphics Appl. 34, 47-55 (2001).

T. Pavlidis, J. Swartz, and Y. P. Wang, “Fundamentals of bar code information theory,” IEEE Comput. Graphics Appl. 23, 74-86 (1990).

IEEE Trans. Image Process. (3)

K. Barnard, V. Cardei, and B. Funt, “A comparison of computational color constancy algorithms-part I: methodology and experiments with synthesized data,” IEEE Trans. Image Process. 11, 972-984 (2002).
[CrossRef]

K. Barnard, L. Martin, A. Coath, and B. Funt, “A comparison of computational color constancy algorithms-part II: experiments with image data,” IEEE Trans. Image Process. 11, 985-996 (2002).
[CrossRef]

G. D. Finlayson and S. D. Hordley, “Improving gamut mapping color constancy,” IEEE Trans. Image Process. 9, 1774-1783(2000).
[CrossRef]

IEEE Transactions on Pattern Analysis and Machine Intelligence (2)

G. Finlayson, S. Hordley, and P. Hubel, “Color by correlation: a simple, unifying framework for color constancy,” IEEE Transactions on Pattern Analysis and Machine Intelligence 23, 1209-1221 (2001).
[CrossRef]

G. D. Finlayson, “Color in perspective,” IEEE Transactions on Pattern Analysis and Machine Intelligence 18, 1034-1038(1996).
[CrossRef]

Int. J. Comput. Vis. (1)

D. A. Forsyth, “A novel algorithm for color constancy,” Int. J. Comput. Vis. 5, 5-36 (1990).
[CrossRef]

J. Opt. Soc. Am. A (4)

Perception (1)

R. Gershon, A. D. Jepson, and J. K. Tsotsos, “From [R,G,B] to surface reflectance: computing color constant descriptors in images,” Perception 17, 755-758 (1988).

Proc. Natl. Acad. Sci. U.S.A. (1)

E. H. Land, “An alternative technique for the computation of the designator in the Retinex theory of color vision,” Proc. Natl. Acad. Sci. U.S.A. 83, 3078-3080 (1986).
[CrossRef]

Sci. Am. (1)

E. H. Land, “The retinex theory of color vision,” Sci. Am. 6, 108-128 (1977).

Vision Res. (1)

J. J. McCann, S. P. McKee, and T. H. Taylor, “Quantitative studies in Retinex theory,” Vision Res. 16, 445-458 (1976).
[CrossRef]

Other (40)

W. Johnson, H. Jellinek, L. Klotz, R. Rao, and S. Card, “Bridging the paper and electronic worlds: the paper user interface,” in Proceedings of Interact '93 and CHI'93 Conference on Human Factors in Computing Systems, S. Ashlund, K. Mullet, A. Henderson, E. Hollnagel, and T. White, eds. (Association for Computing Machinery Press, 1993), pp. 507-512.

K. J. Linnell and D. H. Foster, “Space-average scene colour used to extract illuminant information,” in Selected Proceedings of the Int. Conf. John Dalton's Colour Vision Legacy, C. Dickinson, I. Murray, and D. Carden, eds. (Taylor & Francis, 1997), pp. 501-509.

B. V. Funt, K. Barnard, and L. Martin, “Is colour constancy good enough?,” in Proceedings of Fifth European Conference on Computer Vision, LNCS 1406, H.Burkhardt and B.Neumann, eds. (Springer-Verlag, 1998), pp. 445-459.

C. Balkenius, A. J. Johansson, and A. Balkenius, “Color constancy in visual scene perception,” Lund University Cognitive Studies 98 (2003), http://www.lucs.lu.se/ftp/pub/LUCS_Studies/LUCSinlaga98.pdf.

C. Cheong, N.-K. Lee, and T.-D. Han, “Apparatus and method for recognizing code,” U.S. patent 6,981,644 (United States Patent and Trademark Office, 2006).

C. Cheong, D.-C. Kim, and T.-D. Han, “Color classification using quiet zone information for color-based image code recognition,” in Proceeding of First Korea-Japan Joint Workshop on Pattern Recognition, B. -K. Shin and K. Kise, eds. (Korea Information Science Society, Korea and The Institute of Electronics, Information and Communication Engineers, Japan, 2006), pp. 109-114.

M. Ebner, “A parallel algorithm for color constancy,” Technical Report 296 (Universita¨t Wu¨rzburg, Lehrstuhl fu¨r Informatik II, April 2002).

L. Nelson, S. Ichimura, E. R. Pedersen, and L. Adams, “Palette: a paper interface for giving presentations,” in Proceedings of ACM SIGCHI Conference on Human Factors and Computing Systems, M. G. William and M. W. Altom, eds. (Association for Computing Machinery Press, 1999), pp. 354-361.

T. Hautala, J. Kallenbach, M. Nuutinen, L. Salo, T. Venho, A. Bäck, C. Bäckström, L. Hakola, and T. Järvinen, “PrintAccess,” http://www.media.hut.fi/GTTS/GAiF/GAiF2_2005.htm#PrintAccess--Final Report.

H. Usuda, M. Suzuku, and Maeda, Research result report on creation and transmission of digital contents using image recognition technology (summary version), Project Code IMS 0359, Sony Corporation, Japan, 2004.

K. D. Hunter, “Automatic access of internet content with a camera-enabled cell phone,” U.S. patent 6,993,573 (United States Patent and Trademark Office, 2006).

International Organization for Standardization, Information technology: automatic identification and data capture techniques--bar code symbology--data matrix, ISO/IEC 16022 (ISO/IEC, 2000).

International Organization for Standardization, Information technology: automatic identification and data capture techniques--bar code symbology--PDF-417, ISO/IEC 15438 (ISO/IEC, 2001).

International Organization for Standardization, Information technology: automatic identification and data capture techniques--bar code symbology--QR code, ISO/IEC 18004 (ISO/IEC, 2000).

J. Rekimoto, The world through the computer: a new human-computer interaction style based on wearable computers, Technical Report SCSL-TR-94-013, Sony Computer Science Laboratories Inc., Japan, 1994.

J. Rekimoto and Y. Ayatsuka, “Cyber code: designing augmented reality environments with visual tags,” in Proceedings Designing Augmented Reality Environments, W. E. Mackay, ed. (Association for Computing Machinery Press, 2000), pp. 1-10.

P. Milgram and H. Colquhoun, “A taxonomy of real and virtual world displays integration,” in Mixed Reality--Merging Real and Virtual Worlds, Y. Ohta and H. Tamura, eds. (Ohmsha and Springer-Verlag, 1999), pp. 5-30.

J. R. Vallino, “Interactive augmented reality,” Ph D. dissertation (University of Rochester, New York, 1998).

R. Azuma, Y. Baillot, R. Behringer, S. Feiner, S. Julier, and B. MacIntyre, “Recent advances in augmented reality,” in IEEE Computer Graphics and Applications (IEEE, 2001), pp. 34-47.

A. State, G. Hirota, D. T. Chen, W. F. Garrett, and M. A. Livingston, “Superior augmented reality registration by integrating landmark tracking and magnetic tracking,” in Proceedings of SIGGRAPH, J. Fujii, ed. (Association for Computing Machinery Press, 1996), pp. 429-438.

H. Kato and M. Billinghurst, “Marker tracking and HMD calibration for a video-based augmented reality conferencing system,” in Proceedings of 2nd IEEE and ACM Int. Workshop on Augmented Reality, G. Klinker and T. U. München, eds. (IEEE Computer Society, 1999), pp. 85-94.

H. Shimoda, H. Ishii, M. Maeshima, T. Nakai, Z. Bian, and H. Yoshikawa, “Development of a tracking method for augmented reality applied to nuclear plant maintenance work: (1) barcode marker,” in Proceeding of Halden Project VR Workshop (Halden Project Centre, 2005), http://hydro.energy.kyoto-u.ac.jp/Lab/staff/hirotake/paper/papers/VRWS2005_1.pdf.

S. Sathyanath and F. Sahin, “AISIMAM: an artificial immune system based intelligent multi agent model and its application to a mine detection problem,” in Proceeding of International Centre for Advanced Research in Identification Science, S. Garrett, ed. (University of Kent at Canterbury, 2002), pp. 22-31.

HITLab, “ARToolKit,” http://www.hitl.washington.edu/artoolkit.

M. Fiala, “ARTag, a fiducial marker system using digital techniques,” in Proceedings of IEEE Computer Vision and Pattern Recognition, C.Schmid, S.Soatto, and C.Tomasi, eds. (IEEE Computer Society, 2005), Vol. 2, pp. 590-596.

ColorZip Media, http://www.colorzip.co.jp/en.

J. R. Kaufman and C. Hohberger, “Distortion resistant double-data correcting color transition barcode and method of generating and using same,” U.S. patent 6,070,805 (United States Patent and Trademark Office, 2000).

V. L. Jaume, “Color constancy and image segmentation techniques for applications to mobile robotics,” Doctoral thesis (Universitat Politecnica de Catalunya, 2005).

“Using bar code,” Data Capture Institute, http://www.datacaptureinstitute.com/publications/book.htm.

“2D (two dimensional) bar code symbologies,” Swing Labels, http://www.swinglabels.com/barcodes/symbology/2d.asp.

A. R. Smith, “Color gamut transform pairs,” in Proceedings of the 5th annual conference on Computer graphics and interactive techniques, S. H. Chasen and R. L. Phillips, eds. (Association for Computing Machinery Press, 1978), pp. 12-19.

M. Gardner, “Multivariate statistics: scaling, clustering, and factor analysis,” http://www.ed.utah.edu/edps/CourseMaterials/7570/MS14.

P. Cimiano, A. Hotho, and S. Staab, “Comparing conceptual, divisive and agglomerative clustering for learning taxonomies from text,” in Proceedings of the 16th European Conference on Artificial Intelligence, R. L. Mántaras and L. Saitta, eds. (IOS Press, 2004), pp. 435-439.

E. Gose, R. Johnsonbaugh, and S. Jost, Pattern Recognition and Image Analysis (Prentice Hall, 1996), pp. 338-346.

K. N. Plataniotis and A. N. Venetsanopoulos, Color Image Processing and Application (Springer-Verlag, 2000), pp. 20-25.

J. J. McCann, “Magnitude of color shifts from average quanta catch adaptation,” in Proceedings of IS&T/SID Fifth Color Imaging Conf.: Color Science, Systems and Application (The Society for Imaging Science and Technology, 1997), pp. 215-220.

P. M. Hubel and G. Finlayson, “White point estimation using correlation matrix memory,” U.S. patent 6,038,339 (United States Patent and Trademark Office, 2000).

M. Ebner, “Evolving color constancy for an artificial retina,” in Genetic Programming: Proceedings of the 4th Europ. Conf., EuroGP 2001, J. Miller, M. Tomassini, P. L. Lanzi, C. Ryan, A. G. B. Tettamanzi, and W. B. Langdon, eds. (Springer-Verlag, 2001), pp. 11-22.

V. C. Cardei and B. Funt, “Committee-based color constancy,” in Proceedings of the IS&T/SID 7th Color Imaging Conference: Color Science, Systems and Applications (The Society for Imaging Science and Technology, 1999), pp. 311-313, http://www.cs.sfu.ca/%7Ecolour/publications/IST-99/IST-99-CBCC.pdf.

M. Ebner, “Combining white-patch retinex and the gray world assumption to achieve color constancy for multiple illuminants,” in Proceedings of the 25th DAGM Symposium on Pattern Recognition, LNCS 2781, B. Michaelis and G. Krell, eds. (Springer-Verlag, 2003), pp. 60-67.

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Figures (9)

Fig. 1
Fig. 1

Examples of 2D image codes. (a)–(f) Black-and-white-based matrix-type 2D codes: QR code, Maxi code, Data Matrix, Cyber code, ARToolkit, and AR tag. (g)–(h) Stack-type 2D codes: PDF-417 and Ultra code. (i)–(m) Examples of ColorCodes.

Fig. 2
Fig. 2

HSV color space.

Fig. 3
Fig. 3

Examples of test corpus of color-based image codes on print materials [29]. Codes 1–10.

Fig. 4
Fig. 4

Variation trends in the correct recognition ratio of color-based code image for different S T s and illuminants. (a) SLACC and (b) KMACC (YUV).

Fig. 5
Fig. 5

Comparison of performance of the color-classification algorithms by illumination.

Fig. 6
Fig. 6

Variation trends in the correct recognition ratio of color-based code image for different S T s and devices. (a) SLACC and (b) KMACC (YUV).

Fig. 7
Fig. 7

Comparison of performance of the color-classification algorithms for varying devices.

Fig. 8
Fig. 8

Variation trends in the correct recognition ratio of color-based code image for different S T s and print materials. (a) SLACC and (b) KMACC (YUV).

Fig. 9
Fig. 9

Comparison of performance of the color-classification algorithms based on print material.

Tables (13)

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Table 1 Experimental Conditions: Illuminants, Cameras, and Print Materials [29]

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Table 2 Correct Recognition Ratio (%) for SLACC for Different S T s and Illuminants

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Table 3 Correct Recognition Ratio (%) for KMACC (YUV) for Different S T s and Illuminants

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Table 4 Comparison of the Performance of Algorithms Based on Illumination.

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Table 5 Comparison of Robustness of Algorithms Based on Illumination

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Table 6 Correct Recognition Ratio (%) for SLACC for Different S T s and Devices

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Table 7 Correct Recognition Ratio (%) for KMACC (YUV) for Different S T s and Devices

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Table 8 Comparison of the Performance of Algorithms Based on Device

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Table 9 Comparison of Robustness of Algorithms Based on Device

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Table 10 Correct Recognition Ratio (%) for SLACC for Different S T s and Print Materials

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Table 11 Correct Recognition Ratio (%) for KMACC (YUV) for Different S T s and Print Materials

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Table 12 Comparison of Robustness of Algorithms Based on Print Material

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Table 13 Comparison of the Performance of Algorithms Based on Print Material

Equations (19)

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ρ ( k ) = R ( k ) ( λ ) S ( λ ) E ( λ ) d λ ,
f MCC 1 ( P i ) = { black where     [ max ( P i ) , < T K 0     max ( P i ) min ( P i )     < T K 1 ] , or max ( P i ) < T K 2 non-black , otherwise .
f MCC 2 ( P i ) = { arg max ( P i ) where     max ( P i ) med ( P i ) > T j , j = arg max ( P i ) unknown otherwise .
P ci = [ I w / r ¯ w 0 0 0 I w / g ¯ w 0 0 0 I w / b ¯ w ] × [ r ¯ i g ¯ i b ¯ i ] .
f WBCC ( P ¯ i , P ci , P ¯ w ) = { black where     ( max ( P ci ) min ( P ci ) < T h K 1 ) , ( max ( P ¯ w ) max ( P ¯ i ) > T h K 2 ) red where     ( T h B < h ci 360 or 0 < h ci T h R ) , not black green where     T h R < h ci T h G , not black blue where     T h G < h ci T h B , not black .
f SLACC ( C i , C j ) = min x C i y C j d ( x , y ) = min x C i y C j | x y | .
f SLACC ( o h j | o h j C h i ) = { red where     d ( C h i , 0 ) = min [ d ( C h i , 0 ) , d ( C h i , 120 ) , d ( C h i , 240 ) ] green where     d ( C h i , 120 ) = min [ d ( C h i , 0 ) , d ( C h i , 120 ) , d ( C h i , 240 ) ] blue where     d ( C h i , 240 ) = min [ d ( C h i , 0 ) , d ( C h i , 120 ) , d ( C h i , 240 ) ] ,
f KMACC ( P h i ) = { red where     d ( μ R o h i ) = min { d ( μ R o h i ) , d ( μ G o h i ) , d ( μ B o h i ) } green where     d ( μ G o h i ) = min { d ( μ R o h i ) , d ( μ G o h i ' ) , d ( μ B o h i ) } blue otherwise .
μ i = ( r ¯ i + g ¯ i + b ¯ i ) / 3 ,
σ i = [ ( ( r ¯ i μ i ) 2 + ( g ¯ i μ i ) 2 + ( b ¯ i μ i ) 2 ) ) / 3 ] 1 / 2 ,
μ i = 0.3 r ¯ i + 0.59 g ¯ i + 0.11 b ¯ i ,
σ i = [ ( r ¯ i μ i ) 2 + ( b ¯ i μ i ) 2 ) ] 1 / 2 .
max j = max i = 1 n ( l i j ) , min j = min i = 1 n ( l i j ) , j = 1 , 2 , 3 max int = max j = 1 3 ( max j ) , min max int = min j = 1 3 ( max j ) , min int = min j = 1 3 ( min j ) .
l i j = min int + ( l i j min j ) ( max j min j ) × ( max int min int ) , where     l i j P i , max Int ST × min max Int .
R ( A | C ) = N A C / N P C .
f ( n ; x ) = ( n x ) p x ( 1 p ) n x , x = 0 , 1 , 2 , , n .
f ( n ; x r , x g , x b , x k ) = n ! x r ! x g ! x b ! x k ! ( n x ) ! p r x r p g x g p b x b p k x k q n x r x g x b x k , 0 x r , x g , x b , x k n , x = x r + x g + x b + x k , q = 1 ( p r + p g + p b + p k ) , 0 p r , p g , p b , p k 1 .
f ( n ; x r , x g , x b , x k ) = n ! x r ! x g ! x b ! x k ! p r x r p g x g p b x b p k x k , 0 x r , x g , x b , x k n , n = x r + x g + x b + x k .
L ( A | C ) = E [ R ( A | C ) ] V [ R ( A | C ) ] 1 / 2 , where     E [ R ( A | C ) ] = i = 1 t [ R ( A | c i ) / t and V [ R ( A | C ) ] = t = 1 t [ R ( A | c i ) E [ R ( A | C ) ] ] 2 / t .

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