Abstract

This paper introduces a lattice algebra procedure that can be used for the multispectral analysis of historical documents and artworks. Assuming the presence of linearly mixed spectral pixels captured in a multispectral scene, the proposed method computes the scaled min- and max-lattice associative memories to determine the purest pixels that best represent the spectra of single pigments. The estimation of fractional proportions of pure spectra at each image pixel is used to build pigment abundance maps that can be used for subsequent restoration of damaged parts. Application examples include multispectral images acquired from the Archimedes Palimpsest and a Mexican pre-Hispanic codex.

© 2013 Optical Society of America

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  1. R. L. Easton and W. Noel, “Infinite possibilities: ten years of study of the Archimedes Palimpsest,” in Proc. Am. Philos. Soc. 154, 50–76 (2010).
  2. M. Lettner and R. Sablatnig, “Multispectral imaging for analyzing ancient manuscripts,” in Proceedings of the 17th European Signal Processing Conference (EURASIP, 2009), pp. 1200–1204.
  3. K. Rapantzikos and C. Balas, “Hyperspectral imaging: potential in nondestructive analysis of paintings,” in Proceedings of the IEEE International Conference on Image Processing (IEEE, 2005), pp. 618–621.
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    [CrossRef]
  5. C. Fisher and I. Kakoulli, “Multispectral and hyperspectral imaging technologies in conservation: current research and potential applications,” Rev. Conserv. 7, 3–16 (2006).
  6. S. Baronti, A. Casini, F. Lotti, and S. Porcinai, “Multispectral imaging system for the mapping of pigments in works of art by use of principal component analysis,” Appl. Opt. 37, 1299–1309 (1998).
    [CrossRef]
  7. G. A. Ware, D. M. Chabries, R. W. Christiansen, J. E. Brady, and C. E. Martin, “Multispectral analysis of ancient Maya pigments: implications for the Naj Tunich corpus,” in Proceedings of the IEEE 2000 International Geoscience and Remote Sensing Symposium (IEEE, 2000), pp. 2489–2491.
  8. M. Attas, E. Cloutis, C. Collins, D. Goltz, C. Majzels, J. R. Mansfield, and H. H. Mantsch, “Near-infrared spectroscopy imaging in art conservation: investigation of drawing constituents,” J. Cult. Herit. 4, 127–136 (2003).
    [CrossRef]
  9. K. Knox, R. Johnston, and R. L. Easton, “Imaging the Dead Sea Scrolls,” Opt. Photonics News 8(8), 30–34 (1997).
  10. R. L. Easton, K. T. Knox, and W. A. Christens-Barry, “Multispectral imaging of the Archimedes Palimpsest,” in Proceedings of the 32nd Applied Imagery Pattern Recognition Workshop (IEEE, 2003), pp. 111–116.
  11. E. Salerno, A. Tonazzini, and L. Bedini, “Digital image analysis to enhance underwritten text in the Archimedes Palimpsest,” Int. J. Document Anal. 9, 79–87 (2007).
    [CrossRef]
  12. M. Lettner and R. Sablatnig, “Spatial and spectral based segmentation of text in multispectral images of ancient documents,” in Proceedings of the 10th International Conference on Document Analysis and Recognition (IEEE, 2009), pp. 813–817.
  13. M. Barni, A. Pelagotti, and A. Piva, “Image processing for the analysis and conservation of paintings: opportunities and challenges,” IEEE Signal Process. Mag. 22(5), 141–144 (2005).
    [CrossRef]
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  15. “Archimedes Palimpsest project,” http://archimedespalimpsest.net/Data/0000-100v/ .
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  18. M. Yamaguchi, H. Haneishi, H. Fukuda, J. Kishimoto, H. Kanazawa, M. Tsuchida, R. Iwama, and N. Ohyama, “High-fidelity video and still-image communication based on spectral information: natural vision system and its applications,” Proc. SPIE 6062, 60620G (2006).
    [CrossRef]
  19. M. Yamaguchi, T. Teraji, K. Ohsawa, T. Uchiyama, H. Motomura, Y. Murakami, and N. Ohyama, “Color image reproduction based on the multispectral and multiprimary imaging: experimental evaluation,” Proc. SPIE 4663, 15–26 (2002).
    [CrossRef]
  20. W. Pratt and C. E. Mancill, “Spectral estimation techniques for the spectral calibration of a color image scanner,” Appl. Opt. 15, 73–75 (1976).
    [CrossRef]
  21. S. K. Park and F. O. Huck, “Estimation of spectral reflectance curves from multispectral image data,” Appl. Opt. 16, 3107–3114 (1977).
    [CrossRef]
  22. N. Keshava and J. F. Mustard, “Spectral unmixing,” IEEE Signal Process. Mag. 19(1), 44–57 (2002).
    [CrossRef]
  23. G. X. Ritter, P. Sussner, and J. L. Díaz de León, “Morphological associative memories,” IEEE Trans. Neural Netw. 9, 281–293 (1998).
    [CrossRef]
  24. G. X. Ritter, G. Urcid, and L. Iancu, “Reconstruction of patterns from noisy inputs using morphological associative memories,” J. Math. Imaging Vision 19, 95–111 (2003).
    [CrossRef]
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  26. G. X. Ritter and P. Gader, “Fixed point of lattice transforms and lattice associative memories,” in Advances in Imaging and Electron Physics, P. Hawkes, ed., Vol. 144 (Elsevier, 2006), pp. 165–242.
  27. G. Urcid and J. C. Valdiviezo-N, “Generation of lattice independent vector sets for pattern recognition applications,” Proc. SPIE 6700, 67000C (2007).
    [CrossRef]
  28. R. Cuninghame-Green, “Minimax algebra and applications,” in Advances in Imaging and Electron Physics, P. Hawkes, ed., Vol. 90 (Academic, 1995), pp. 1–121.
  29. G. Urcid and J. C. Valdiviezo-N, “Lattice algebra approach to color image segmentation,” J. Math. Imaging Vision 42, 150–162 (2012).
    [CrossRef]
  30. G. X. Ritter, G. Urcid, and M. S. Schmalz, “Autonomous single-pass endmember approximation using lattice auto-associative memories,” Neurocomputing 72, 2101–2110 (2009).
    [CrossRef]
  31. G. X. Ritter and G. Urcid, “Lattice algebra approach to endmember determination in hyperspectral imagery,” in Advances in Imaging and Electron Physics, P. W. Hawkes, ed., Vol. 160 (Academic, 2010), pp. 113–169.
  32. S. Hordley, G. Finlayson, and P. Morovic, “A multi-spectral image database and an application to image rendering across illumination,” in Proceedings of the IEEE Third International Conference on Image and Graphics (IEEE, 2004), pp. 394–397.
  33. C. L. Lawson and R. J. Hanson, Solving Least Squares Problems (Prentice-Hall, 1974).
  34. J. C. Valdiviezo-N and G. Urcid, “Multispectral images segmentation of ancient documents with lattice memories,” in Digital Image Processing and Analysis Conference, OSA Technical Digest Series (Optical Society of America, 2010), paper DMD6.
  35. Y.-Q. Zhao, L. Zhang, and S. G. Kong, “Band-subset-based clustering and fusion for hyperspectral imagery classification,” IEEE Trans. Geosci. Remote Sens. 49, 747–756 (2011).
    [CrossRef]

2012 (1)

G. Urcid and J. C. Valdiviezo-N, “Lattice algebra approach to color image segmentation,” J. Math. Imaging Vision 42, 150–162 (2012).
[CrossRef]

2011 (1)

Y.-Q. Zhao, L. Zhang, and S. G. Kong, “Band-subset-based clustering and fusion for hyperspectral imagery classification,” IEEE Trans. Geosci. Remote Sens. 49, 747–756 (2011).
[CrossRef]

2010 (1)

R. L. Easton and W. Noel, “Infinite possibilities: ten years of study of the Archimedes Palimpsest,” in Proc. Am. Philos. Soc. 154, 50–76 (2010).

2009 (1)

G. X. Ritter, G. Urcid, and M. S. Schmalz, “Autonomous single-pass endmember approximation using lattice auto-associative memories,” Neurocomputing 72, 2101–2110 (2009).
[CrossRef]

2008 (1)

S. Tominaga and N. Tanaka, “Spectral image acquisition, analysis, and rendering for art paintings,” J. Electron. Imaging 17, 043022 (2008).
[CrossRef]

2007 (2)

E. Salerno, A. Tonazzini, and L. Bedini, “Digital image analysis to enhance underwritten text in the Archimedes Palimpsest,” Int. J. Document Anal. 9, 79–87 (2007).
[CrossRef]

G. Urcid and J. C. Valdiviezo-N, “Generation of lattice independent vector sets for pattern recognition applications,” Proc. SPIE 6700, 67000C (2007).
[CrossRef]

2006 (2)

M. Yamaguchi, H. Haneishi, H. Fukuda, J. Kishimoto, H. Kanazawa, M. Tsuchida, R. Iwama, and N. Ohyama, “High-fidelity video and still-image communication based on spectral information: natural vision system and its applications,” Proc. SPIE 6062, 60620G (2006).
[CrossRef]

C. Fisher and I. Kakoulli, “Multispectral and hyperspectral imaging technologies in conservation: current research and potential applications,” Rev. Conserv. 7, 3–16 (2006).

2005 (1)

M. Barni, A. Pelagotti, and A. Piva, “Image processing for the analysis and conservation of paintings: opportunities and challenges,” IEEE Signal Process. Mag. 22(5), 141–144 (2005).
[CrossRef]

2004 (1)

J. Conde, H. Haneishi, M. Yamaguchi, N. Ohyama, and J. Baez, “Spectral reflectance estimation of ancient Mexican codices, multispectral images approach,” Rev. Mexicana Fís. 50, 484–489 (2004).

2003 (2)

G. X. Ritter, G. Urcid, and L. Iancu, “Reconstruction of patterns from noisy inputs using morphological associative memories,” J. Math. Imaging Vision 19, 95–111 (2003).
[CrossRef]

M. Attas, E. Cloutis, C. Collins, D. Goltz, C. Majzels, J. R. Mansfield, and H. H. Mantsch, “Near-infrared spectroscopy imaging in art conservation: investigation of drawing constituents,” J. Cult. Herit. 4, 127–136 (2003).
[CrossRef]

2002 (2)

N. Keshava and J. F. Mustard, “Spectral unmixing,” IEEE Signal Process. Mag. 19(1), 44–57 (2002).
[CrossRef]

M. Yamaguchi, T. Teraji, K. Ohsawa, T. Uchiyama, H. Motomura, Y. Murakami, and N. Ohyama, “Color image reproduction based on the multispectral and multiprimary imaging: experimental evaluation,” Proc. SPIE 4663, 15–26 (2002).
[CrossRef]

1998 (2)

G. X. Ritter, P. Sussner, and J. L. Díaz de León, “Morphological associative memories,” IEEE Trans. Neural Netw. 9, 281–293 (1998).
[CrossRef]

S. Baronti, A. Casini, F. Lotti, and S. Porcinai, “Multispectral imaging system for the mapping of pigments in works of art by use of principal component analysis,” Appl. Opt. 37, 1299–1309 (1998).
[CrossRef]

1997 (1)

K. Knox, R. Johnston, and R. L. Easton, “Imaging the Dead Sea Scrolls,” Opt. Photonics News 8(8), 30–34 (1997).

1977 (1)

S. K. Park and F. O. Huck, “Estimation of spectral reflectance curves from multispectral image data,” Appl. Opt. 16, 3107–3114 (1977).
[CrossRef]

1976 (1)

W. Pratt and C. E. Mancill, “Spectral estimation techniques for the spectral calibration of a color image scanner,” Appl. Opt. 15, 73–75 (1976).
[CrossRef]

1969 (1)

J. R. J. Van Asperen de Boer, “Reflectography of paintings using an infrared vidicon television system,” Stud. Conserv. 14, 96–118 (1969).
[CrossRef]

Attas, M.

M. Attas, E. Cloutis, C. Collins, D. Goltz, C. Majzels, J. R. Mansfield, and H. H. Mantsch, “Near-infrared spectroscopy imaging in art conservation: investigation of drawing constituents,” J. Cult. Herit. 4, 127–136 (2003).
[CrossRef]

Baez, J.

J. Conde, H. Haneishi, M. Yamaguchi, N. Ohyama, and J. Baez, “Spectral reflectance estimation of ancient Mexican codices, multispectral images approach,” Rev. Mexicana Fís. 50, 484–489 (2004).

Balas, C.

K. Rapantzikos and C. Balas, “Hyperspectral imaging: potential in nondestructive analysis of paintings,” in Proceedings of the IEEE International Conference on Image Processing (IEEE, 2005), pp. 618–621.

Barni, M.

M. Barni, A. Pelagotti, and A. Piva, “Image processing for the analysis and conservation of paintings: opportunities and challenges,” IEEE Signal Process. Mag. 22(5), 141–144 (2005).
[CrossRef]

Baronti, S.

S. Baronti, A. Casini, F. Lotti, and S. Porcinai, “Multispectral imaging system for the mapping of pigments in works of art by use of principal component analysis,” Appl. Opt. 37, 1299–1309 (1998).
[CrossRef]

Bedini, L.

E. Salerno, A. Tonazzini, and L. Bedini, “Digital image analysis to enhance underwritten text in the Archimedes Palimpsest,” Int. J. Document Anal. 9, 79–87 (2007).
[CrossRef]

Brady, J. E.

G. A. Ware, D. M. Chabries, R. W. Christiansen, J. E. Brady, and C. E. Martin, “Multispectral analysis of ancient Maya pigments: implications for the Naj Tunich corpus,” in Proceedings of the IEEE 2000 International Geoscience and Remote Sensing Symposium (IEEE, 2000), pp. 2489–2491.

Casini, A.

S. Baronti, A. Casini, F. Lotti, and S. Porcinai, “Multispectral imaging system for the mapping of pigments in works of art by use of principal component analysis,” Appl. Opt. 37, 1299–1309 (1998).
[CrossRef]

Chabries, D. M.

G. A. Ware, D. M. Chabries, R. W. Christiansen, J. E. Brady, and C. E. Martin, “Multispectral analysis of ancient Maya pigments: implications for the Naj Tunich corpus,” in Proceedings of the IEEE 2000 International Geoscience and Remote Sensing Symposium (IEEE, 2000), pp. 2489–2491.

Christens-Barry, W. A.

R. L. Easton, K. T. Knox, and W. A. Christens-Barry, “Multispectral imaging of the Archimedes Palimpsest,” in Proceedings of the 32nd Applied Imagery Pattern Recognition Workshop (IEEE, 2003), pp. 111–116.

Christiansen, R. W.

G. A. Ware, D. M. Chabries, R. W. Christiansen, J. E. Brady, and C. E. Martin, “Multispectral analysis of ancient Maya pigments: implications for the Naj Tunich corpus,” in Proceedings of the IEEE 2000 International Geoscience and Remote Sensing Symposium (IEEE, 2000), pp. 2489–2491.

Cloutis, E.

M. Attas, E. Cloutis, C. Collins, D. Goltz, C. Majzels, J. R. Mansfield, and H. H. Mantsch, “Near-infrared spectroscopy imaging in art conservation: investigation of drawing constituents,” J. Cult. Herit. 4, 127–136 (2003).
[CrossRef]

Collins, C.

M. Attas, E. Cloutis, C. Collins, D. Goltz, C. Majzels, J. R. Mansfield, and H. H. Mantsch, “Near-infrared spectroscopy imaging in art conservation: investigation of drawing constituents,” J. Cult. Herit. 4, 127–136 (2003).
[CrossRef]

Conde, J.

J. Conde, H. Haneishi, M. Yamaguchi, N. Ohyama, and J. Baez, “Spectral reflectance estimation of ancient Mexican codices, multispectral images approach,” Rev. Mexicana Fís. 50, 484–489 (2004).

Cuninghame-Green, R.

R. Cuninghame-Green, “Minimax algebra and applications,” in Advances in Imaging and Electron Physics, P. Hawkes, ed., Vol. 90 (Academic, 1995), pp. 1–121.

Díaz de León, J. L.

G. X. Ritter, P. Sussner, and J. L. Díaz de León, “Morphological associative memories,” IEEE Trans. Neural Netw. 9, 281–293 (1998).
[CrossRef]

Easton, R. L.

R. L. Easton and W. Noel, “Infinite possibilities: ten years of study of the Archimedes Palimpsest,” in Proc. Am. Philos. Soc. 154, 50–76 (2010).

K. Knox, R. Johnston, and R. L. Easton, “Imaging the Dead Sea Scrolls,” Opt. Photonics News 8(8), 30–34 (1997).

R. L. Easton, K. T. Knox, and W. A. Christens-Barry, “Multispectral imaging of the Archimedes Palimpsest,” in Proceedings of the 32nd Applied Imagery Pattern Recognition Workshop (IEEE, 2003), pp. 111–116.

Finlayson, G.

S. Hordley, G. Finlayson, and P. Morovic, “A multi-spectral image database and an application to image rendering across illumination,” in Proceedings of the IEEE Third International Conference on Image and Graphics (IEEE, 2004), pp. 394–397.

Fisher, C.

C. Fisher and I. Kakoulli, “Multispectral and hyperspectral imaging technologies in conservation: current research and potential applications,” Rev. Conserv. 7, 3–16 (2006).

Fukuda, H.

M. Yamaguchi, H. Haneishi, H. Fukuda, J. Kishimoto, H. Kanazawa, M. Tsuchida, R. Iwama, and N. Ohyama, “High-fidelity video and still-image communication based on spectral information: natural vision system and its applications,” Proc. SPIE 6062, 60620G (2006).
[CrossRef]

Gader, P.

G. X. Ritter and P. Gader, “Fixed point of lattice transforms and lattice associative memories,” in Advances in Imaging and Electron Physics, P. Hawkes, ed., Vol. 144 (Elsevier, 2006), pp. 165–242.

Goltz, D.

M. Attas, E. Cloutis, C. Collins, D. Goltz, C. Majzels, J. R. Mansfield, and H. H. Mantsch, “Near-infrared spectroscopy imaging in art conservation: investigation of drawing constituents,” J. Cult. Herit. 4, 127–136 (2003).
[CrossRef]

Haneishi, H.

M. Yamaguchi, H. Haneishi, H. Fukuda, J. Kishimoto, H. Kanazawa, M. Tsuchida, R. Iwama, and N. Ohyama, “High-fidelity video and still-image communication based on spectral information: natural vision system and its applications,” Proc. SPIE 6062, 60620G (2006).
[CrossRef]

J. Conde, H. Haneishi, M. Yamaguchi, N. Ohyama, and J. Baez, “Spectral reflectance estimation of ancient Mexican codices, multispectral images approach,” Rev. Mexicana Fís. 50, 484–489 (2004).

Hanson, R. J.

C. L. Lawson and R. J. Hanson, Solving Least Squares Problems (Prentice-Hall, 1974).

Hordley, S.

S. Hordley, G. Finlayson, and P. Morovic, “A multi-spectral image database and an application to image rendering across illumination,” in Proceedings of the IEEE Third International Conference on Image and Graphics (IEEE, 2004), pp. 394–397.

Huck, F. O.

S. K. Park and F. O. Huck, “Estimation of spectral reflectance curves from multispectral image data,” Appl. Opt. 16, 3107–3114 (1977).
[CrossRef]

Iancu, L.

G. X. Ritter, G. Urcid, and L. Iancu, “Reconstruction of patterns from noisy inputs using morphological associative memories,” J. Math. Imaging Vision 19, 95–111 (2003).
[CrossRef]

Iwama, R.

M. Yamaguchi, H. Haneishi, H. Fukuda, J. Kishimoto, H. Kanazawa, M. Tsuchida, R. Iwama, and N. Ohyama, “High-fidelity video and still-image communication based on spectral information: natural vision system and its applications,” Proc. SPIE 6062, 60620G (2006).
[CrossRef]

Johnston, R.

K. Knox, R. Johnston, and R. L. Easton, “Imaging the Dead Sea Scrolls,” Opt. Photonics News 8(8), 30–34 (1997).

Kakoulli, I.

C. Fisher and I. Kakoulli, “Multispectral and hyperspectral imaging technologies in conservation: current research and potential applications,” Rev. Conserv. 7, 3–16 (2006).

Kanazawa, H.

M. Yamaguchi, H. Haneishi, H. Fukuda, J. Kishimoto, H. Kanazawa, M. Tsuchida, R. Iwama, and N. Ohyama, “High-fidelity video and still-image communication based on spectral information: natural vision system and its applications,” Proc. SPIE 6062, 60620G (2006).
[CrossRef]

Keshava, N.

N. Keshava and J. F. Mustard, “Spectral unmixing,” IEEE Signal Process. Mag. 19(1), 44–57 (2002).
[CrossRef]

Kishimoto, J.

M. Yamaguchi, H. Haneishi, H. Fukuda, J. Kishimoto, H. Kanazawa, M. Tsuchida, R. Iwama, and N. Ohyama, “High-fidelity video and still-image communication based on spectral information: natural vision system and its applications,” Proc. SPIE 6062, 60620G (2006).
[CrossRef]

Knox, K.

K. Knox, R. Johnston, and R. L. Easton, “Imaging the Dead Sea Scrolls,” Opt. Photonics News 8(8), 30–34 (1997).

Knox, K. T.

R. L. Easton, K. T. Knox, and W. A. Christens-Barry, “Multispectral imaging of the Archimedes Palimpsest,” in Proceedings of the 32nd Applied Imagery Pattern Recognition Workshop (IEEE, 2003), pp. 111–116.

Kong, S. G.

Y.-Q. Zhao, L. Zhang, and S. G. Kong, “Band-subset-based clustering and fusion for hyperspectral imagery classification,” IEEE Trans. Geosci. Remote Sens. 49, 747–756 (2011).
[CrossRef]

Lawson, C. L.

C. L. Lawson and R. J. Hanson, Solving Least Squares Problems (Prentice-Hall, 1974).

Lettner, M.

M. Lettner and R. Sablatnig, “Spatial and spectral based segmentation of text in multispectral images of ancient documents,” in Proceedings of the 10th International Conference on Document Analysis and Recognition (IEEE, 2009), pp. 813–817.

M. Lettner and R. Sablatnig, “Multispectral imaging for analyzing ancient manuscripts,” in Proceedings of the 17th European Signal Processing Conference (EURASIP, 2009), pp. 1200–1204.

Lotti, F.

S. Baronti, A. Casini, F. Lotti, and S. Porcinai, “Multispectral imaging system for the mapping of pigments in works of art by use of principal component analysis,” Appl. Opt. 37, 1299–1309 (1998).
[CrossRef]

Majzels, C.

M. Attas, E. Cloutis, C. Collins, D. Goltz, C. Majzels, J. R. Mansfield, and H. H. Mantsch, “Near-infrared spectroscopy imaging in art conservation: investigation of drawing constituents,” J. Cult. Herit. 4, 127–136 (2003).
[CrossRef]

Mancill, C. E.

W. Pratt and C. E. Mancill, “Spectral estimation techniques for the spectral calibration of a color image scanner,” Appl. Opt. 15, 73–75 (1976).
[CrossRef]

Mansfield, J. R.

M. Attas, E. Cloutis, C. Collins, D. Goltz, C. Majzels, J. R. Mansfield, and H. H. Mantsch, “Near-infrared spectroscopy imaging in art conservation: investigation of drawing constituents,” J. Cult. Herit. 4, 127–136 (2003).
[CrossRef]

Mantsch, H. H.

M. Attas, E. Cloutis, C. Collins, D. Goltz, C. Majzels, J. R. Mansfield, and H. H. Mantsch, “Near-infrared spectroscopy imaging in art conservation: investigation of drawing constituents,” J. Cult. Herit. 4, 127–136 (2003).
[CrossRef]

Martin, C. E.

G. A. Ware, D. M. Chabries, R. W. Christiansen, J. E. Brady, and C. E. Martin, “Multispectral analysis of ancient Maya pigments: implications for the Naj Tunich corpus,” in Proceedings of the IEEE 2000 International Geoscience and Remote Sensing Symposium (IEEE, 2000), pp. 2489–2491.

Morovic, P.

S. Hordley, G. Finlayson, and P. Morovic, “A multi-spectral image database and an application to image rendering across illumination,” in Proceedings of the IEEE Third International Conference on Image and Graphics (IEEE, 2004), pp. 394–397.

Motomura, H.

M. Yamaguchi, T. Teraji, K. Ohsawa, T. Uchiyama, H. Motomura, Y. Murakami, and N. Ohyama, “Color image reproduction based on the multispectral and multiprimary imaging: experimental evaluation,” Proc. SPIE 4663, 15–26 (2002).
[CrossRef]

Murakami, Y.

M. Yamaguchi, T. Teraji, K. Ohsawa, T. Uchiyama, H. Motomura, Y. Murakami, and N. Ohyama, “Color image reproduction based on the multispectral and multiprimary imaging: experimental evaluation,” Proc. SPIE 4663, 15–26 (2002).
[CrossRef]

Mustard, J. F.

N. Keshava and J. F. Mustard, “Spectral unmixing,” IEEE Signal Process. Mag. 19(1), 44–57 (2002).
[CrossRef]

Noel, W.

R. L. Easton and W. Noel, “Infinite possibilities: ten years of study of the Archimedes Palimpsest,” in Proc. Am. Philos. Soc. 154, 50–76 (2010).

Ohsawa, K.

M. Yamaguchi, T. Teraji, K. Ohsawa, T. Uchiyama, H. Motomura, Y. Murakami, and N. Ohyama, “Color image reproduction based on the multispectral and multiprimary imaging: experimental evaluation,” Proc. SPIE 4663, 15–26 (2002).
[CrossRef]

Ohyama, N.

M. Yamaguchi, H. Haneishi, H. Fukuda, J. Kishimoto, H. Kanazawa, M. Tsuchida, R. Iwama, and N. Ohyama, “High-fidelity video and still-image communication based on spectral information: natural vision system and its applications,” Proc. SPIE 6062, 60620G (2006).
[CrossRef]

J. Conde, H. Haneishi, M. Yamaguchi, N. Ohyama, and J. Baez, “Spectral reflectance estimation of ancient Mexican codices, multispectral images approach,” Rev. Mexicana Fís. 50, 484–489 (2004).

M. Yamaguchi, T. Teraji, K. Ohsawa, T. Uchiyama, H. Motomura, Y. Murakami, and N. Ohyama, “Color image reproduction based on the multispectral and multiprimary imaging: experimental evaluation,” Proc. SPIE 4663, 15–26 (2002).
[CrossRef]

Park, S. K.

S. K. Park and F. O. Huck, “Estimation of spectral reflectance curves from multispectral image data,” Appl. Opt. 16, 3107–3114 (1977).
[CrossRef]

Pelagotti, A.

M. Barni, A. Pelagotti, and A. Piva, “Image processing for the analysis and conservation of paintings: opportunities and challenges,” IEEE Signal Process. Mag. 22(5), 141–144 (2005).
[CrossRef]

Piva, A.

M. Barni, A. Pelagotti, and A. Piva, “Image processing for the analysis and conservation of paintings: opportunities and challenges,” IEEE Signal Process. Mag. 22(5), 141–144 (2005).
[CrossRef]

Porcinai, S.

S. Baronti, A. Casini, F. Lotti, and S. Porcinai, “Multispectral imaging system for the mapping of pigments in works of art by use of principal component analysis,” Appl. Opt. 37, 1299–1309 (1998).
[CrossRef]

Pratt, W.

W. Pratt and C. E. Mancill, “Spectral estimation techniques for the spectral calibration of a color image scanner,” Appl. Opt. 15, 73–75 (1976).
[CrossRef]

Rapantzikos, K.

K. Rapantzikos and C. Balas, “Hyperspectral imaging: potential in nondestructive analysis of paintings,” in Proceedings of the IEEE International Conference on Image Processing (IEEE, 2005), pp. 618–621.

Ritter, G. X.

G. X. Ritter, G. Urcid, and M. S. Schmalz, “Autonomous single-pass endmember approximation using lattice auto-associative memories,” Neurocomputing 72, 2101–2110 (2009).
[CrossRef]

G. X. Ritter, G. Urcid, and L. Iancu, “Reconstruction of patterns from noisy inputs using morphological associative memories,” J. Math. Imaging Vision 19, 95–111 (2003).
[CrossRef]

G. X. Ritter, P. Sussner, and J. L. Díaz de León, “Morphological associative memories,” IEEE Trans. Neural Netw. 9, 281–293 (1998).
[CrossRef]

G. X. Ritter and P. Gader, “Fixed point of lattice transforms and lattice associative memories,” in Advances in Imaging and Electron Physics, P. Hawkes, ed., Vol. 144 (Elsevier, 2006), pp. 165–242.

G. X. Ritter and G. Urcid, “Lattice algebra approach to endmember determination in hyperspectral imagery,” in Advances in Imaging and Electron Physics, P. W. Hawkes, ed., Vol. 160 (Academic, 2010), pp. 113–169.

Sablatnig, R.

M. Lettner and R. Sablatnig, “Spatial and spectral based segmentation of text in multispectral images of ancient documents,” in Proceedings of the 10th International Conference on Document Analysis and Recognition (IEEE, 2009), pp. 813–817.

M. Lettner and R. Sablatnig, “Multispectral imaging for analyzing ancient manuscripts,” in Proceedings of the 17th European Signal Processing Conference (EURASIP, 2009), pp. 1200–1204.

Salerno, E.

E. Salerno, A. Tonazzini, and L. Bedini, “Digital image analysis to enhance underwritten text in the Archimedes Palimpsest,” Int. J. Document Anal. 9, 79–87 (2007).
[CrossRef]

Schmalz, M. S.

G. X. Ritter, G. Urcid, and M. S. Schmalz, “Autonomous single-pass endmember approximation using lattice auto-associative memories,” Neurocomputing 72, 2101–2110 (2009).
[CrossRef]

Sussner, P.

G. X. Ritter, P. Sussner, and J. L. Díaz de León, “Morphological associative memories,” IEEE Trans. Neural Netw. 9, 281–293 (1998).
[CrossRef]

Tanaka, N.

S. Tominaga and N. Tanaka, “Spectral image acquisition, analysis, and rendering for art paintings,” J. Electron. Imaging 17, 043022 (2008).
[CrossRef]

Teraji, T.

M. Yamaguchi, T. Teraji, K. Ohsawa, T. Uchiyama, H. Motomura, Y. Murakami, and N. Ohyama, “Color image reproduction based on the multispectral and multiprimary imaging: experimental evaluation,” Proc. SPIE 4663, 15–26 (2002).
[CrossRef]

Tominaga, S.

S. Tominaga and N. Tanaka, “Spectral image acquisition, analysis, and rendering for art paintings,” J. Electron. Imaging 17, 043022 (2008).
[CrossRef]

Tonazzini, A.

E. Salerno, A. Tonazzini, and L. Bedini, “Digital image analysis to enhance underwritten text in the Archimedes Palimpsest,” Int. J. Document Anal. 9, 79–87 (2007).
[CrossRef]

Tsuchida, M.

M. Yamaguchi, H. Haneishi, H. Fukuda, J. Kishimoto, H. Kanazawa, M. Tsuchida, R. Iwama, and N. Ohyama, “High-fidelity video and still-image communication based on spectral information: natural vision system and its applications,” Proc. SPIE 6062, 60620G (2006).
[CrossRef]

Uchiyama, T.

M. Yamaguchi, T. Teraji, K. Ohsawa, T. Uchiyama, H. Motomura, Y. Murakami, and N. Ohyama, “Color image reproduction based on the multispectral and multiprimary imaging: experimental evaluation,” Proc. SPIE 4663, 15–26 (2002).
[CrossRef]

Urcid, G.

G. Urcid and J. C. Valdiviezo-N, “Lattice algebra approach to color image segmentation,” J. Math. Imaging Vision 42, 150–162 (2012).
[CrossRef]

G. X. Ritter, G. Urcid, and M. S. Schmalz, “Autonomous single-pass endmember approximation using lattice auto-associative memories,” Neurocomputing 72, 2101–2110 (2009).
[CrossRef]

G. Urcid and J. C. Valdiviezo-N, “Generation of lattice independent vector sets for pattern recognition applications,” Proc. SPIE 6700, 67000C (2007).
[CrossRef]

G. X. Ritter, G. Urcid, and L. Iancu, “Reconstruction of patterns from noisy inputs using morphological associative memories,” J. Math. Imaging Vision 19, 95–111 (2003).
[CrossRef]

G. X. Ritter and G. Urcid, “Lattice algebra approach to endmember determination in hyperspectral imagery,” in Advances in Imaging and Electron Physics, P. W. Hawkes, ed., Vol. 160 (Academic, 2010), pp. 113–169.

J. C. Valdiviezo-N and G. Urcid, “Multispectral images segmentation of ancient documents with lattice memories,” in Digital Image Processing and Analysis Conference, OSA Technical Digest Series (Optical Society of America, 2010), paper DMD6.

Valdiviezo-N, J. C.

G. Urcid and J. C. Valdiviezo-N, “Lattice algebra approach to color image segmentation,” J. Math. Imaging Vision 42, 150–162 (2012).
[CrossRef]

G. Urcid and J. C. Valdiviezo-N, “Generation of lattice independent vector sets for pattern recognition applications,” Proc. SPIE 6700, 67000C (2007).
[CrossRef]

J. C. Valdiviezo-N and G. Urcid, “Multispectral images segmentation of ancient documents with lattice memories,” in Digital Image Processing and Analysis Conference, OSA Technical Digest Series (Optical Society of America, 2010), paper DMD6.

Van Asperen de Boer, J. R. J.

J. R. J. Van Asperen de Boer, “Reflectography of paintings using an infrared vidicon television system,” Stud. Conserv. 14, 96–118 (1969).
[CrossRef]

Ware, G. A.

G. A. Ware, D. M. Chabries, R. W. Christiansen, J. E. Brady, and C. E. Martin, “Multispectral analysis of ancient Maya pigments: implications for the Naj Tunich corpus,” in Proceedings of the IEEE 2000 International Geoscience and Remote Sensing Symposium (IEEE, 2000), pp. 2489–2491.

Yamaguchi, M.

M. Yamaguchi, H. Haneishi, H. Fukuda, J. Kishimoto, H. Kanazawa, M. Tsuchida, R. Iwama, and N. Ohyama, “High-fidelity video and still-image communication based on spectral information: natural vision system and its applications,” Proc. SPIE 6062, 60620G (2006).
[CrossRef]

J. Conde, H. Haneishi, M. Yamaguchi, N. Ohyama, and J. Baez, “Spectral reflectance estimation of ancient Mexican codices, multispectral images approach,” Rev. Mexicana Fís. 50, 484–489 (2004).

M. Yamaguchi, T. Teraji, K. Ohsawa, T. Uchiyama, H. Motomura, Y. Murakami, and N. Ohyama, “Color image reproduction based on the multispectral and multiprimary imaging: experimental evaluation,” Proc. SPIE 4663, 15–26 (2002).
[CrossRef]

Zhang, L.

Y.-Q. Zhao, L. Zhang, and S. G. Kong, “Band-subset-based clustering and fusion for hyperspectral imagery classification,” IEEE Trans. Geosci. Remote Sens. 49, 747–756 (2011).
[CrossRef]

Zhao, Y.-Q.

Y.-Q. Zhao, L. Zhang, and S. G. Kong, “Band-subset-based clustering and fusion for hyperspectral imagery classification,” IEEE Trans. Geosci. Remote Sens. 49, 747–756 (2011).
[CrossRef]

Appl. Opt. (3)

S. Baronti, A. Casini, F. Lotti, and S. Porcinai, “Multispectral imaging system for the mapping of pigments in works of art by use of principal component analysis,” Appl. Opt. 37, 1299–1309 (1998).
[CrossRef]

W. Pratt and C. E. Mancill, “Spectral estimation techniques for the spectral calibration of a color image scanner,” Appl. Opt. 15, 73–75 (1976).
[CrossRef]

S. K. Park and F. O. Huck, “Estimation of spectral reflectance curves from multispectral image data,” Appl. Opt. 16, 3107–3114 (1977).
[CrossRef]

IEEE Signal Process. Mag. (2)

N. Keshava and J. F. Mustard, “Spectral unmixing,” IEEE Signal Process. Mag. 19(1), 44–57 (2002).
[CrossRef]

M. Barni, A. Pelagotti, and A. Piva, “Image processing for the analysis and conservation of paintings: opportunities and challenges,” IEEE Signal Process. Mag. 22(5), 141–144 (2005).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (1)

Y.-Q. Zhao, L. Zhang, and S. G. Kong, “Band-subset-based clustering and fusion for hyperspectral imagery classification,” IEEE Trans. Geosci. Remote Sens. 49, 747–756 (2011).
[CrossRef]

IEEE Trans. Neural Netw. (1)

G. X. Ritter, P. Sussner, and J. L. Díaz de León, “Morphological associative memories,” IEEE Trans. Neural Netw. 9, 281–293 (1998).
[CrossRef]

Int. J. Document Anal. (1)

E. Salerno, A. Tonazzini, and L. Bedini, “Digital image analysis to enhance underwritten text in the Archimedes Palimpsest,” Int. J. Document Anal. 9, 79–87 (2007).
[CrossRef]

J. Cult. Herit. (1)

M. Attas, E. Cloutis, C. Collins, D. Goltz, C. Majzels, J. R. Mansfield, and H. H. Mantsch, “Near-infrared spectroscopy imaging in art conservation: investigation of drawing constituents,” J. Cult. Herit. 4, 127–136 (2003).
[CrossRef]

J. Electron. Imaging (1)

S. Tominaga and N. Tanaka, “Spectral image acquisition, analysis, and rendering for art paintings,” J. Electron. Imaging 17, 043022 (2008).
[CrossRef]

J. Math. Imaging Vision (2)

G. X. Ritter, G. Urcid, and L. Iancu, “Reconstruction of patterns from noisy inputs using morphological associative memories,” J. Math. Imaging Vision 19, 95–111 (2003).
[CrossRef]

G. Urcid and J. C. Valdiviezo-N, “Lattice algebra approach to color image segmentation,” J. Math. Imaging Vision 42, 150–162 (2012).
[CrossRef]

Neurocomputing (1)

G. X. Ritter, G. Urcid, and M. S. Schmalz, “Autonomous single-pass endmember approximation using lattice auto-associative memories,” Neurocomputing 72, 2101–2110 (2009).
[CrossRef]

Opt. Photonics News (1)

K. Knox, R. Johnston, and R. L. Easton, “Imaging the Dead Sea Scrolls,” Opt. Photonics News 8(8), 30–34 (1997).

Proc. Am. Philos. Soc. (1)

R. L. Easton and W. Noel, “Infinite possibilities: ten years of study of the Archimedes Palimpsest,” in Proc. Am. Philos. Soc. 154, 50–76 (2010).

Proc. SPIE (3)

M. Yamaguchi, H. Haneishi, H. Fukuda, J. Kishimoto, H. Kanazawa, M. Tsuchida, R. Iwama, and N. Ohyama, “High-fidelity video and still-image communication based on spectral information: natural vision system and its applications,” Proc. SPIE 6062, 60620G (2006).
[CrossRef]

M. Yamaguchi, T. Teraji, K. Ohsawa, T. Uchiyama, H. Motomura, Y. Murakami, and N. Ohyama, “Color image reproduction based on the multispectral and multiprimary imaging: experimental evaluation,” Proc. SPIE 4663, 15–26 (2002).
[CrossRef]

G. Urcid and J. C. Valdiviezo-N, “Generation of lattice independent vector sets for pattern recognition applications,” Proc. SPIE 6700, 67000C (2007).
[CrossRef]

Rev. Conserv. (1)

C. Fisher and I. Kakoulli, “Multispectral and hyperspectral imaging technologies in conservation: current research and potential applications,” Rev. Conserv. 7, 3–16 (2006).

Rev. Mexicana Fís. (1)

J. Conde, H. Haneishi, M. Yamaguchi, N. Ohyama, and J. Baez, “Spectral reflectance estimation of ancient Mexican codices, multispectral images approach,” Rev. Mexicana Fís. 50, 484–489 (2004).

Stud. Conserv. (1)

J. R. J. Van Asperen de Boer, “Reflectography of paintings using an infrared vidicon television system,” Stud. Conserv. 14, 96–118 (1969).
[CrossRef]

Other (14)

“Archimedes Palimpsest project,” http://archimedespalimpsest.net/Data/0000-100v/ .

“Biblioteca Digital Mexicana,” http://bdmx.mx .

M. Lettner and R. Sablatnig, “Spatial and spectral based segmentation of text in multispectral images of ancient documents,” in Proceedings of the 10th International Conference on Document Analysis and Recognition (IEEE, 2009), pp. 813–817.

M. Lettner and R. Sablatnig, “Multispectral imaging for analyzing ancient manuscripts,” in Proceedings of the 17th European Signal Processing Conference (EURASIP, 2009), pp. 1200–1204.

K. Rapantzikos and C. Balas, “Hyperspectral imaging: potential in nondestructive analysis of paintings,” in Proceedings of the IEEE International Conference on Image Processing (IEEE, 2005), pp. 618–621.

R. L. Easton, K. T. Knox, and W. A. Christens-Barry, “Multispectral imaging of the Archimedes Palimpsest,” in Proceedings of the 32nd Applied Imagery Pattern Recognition Workshop (IEEE, 2003), pp. 111–116.

G. A. Ware, D. M. Chabries, R. W. Christiansen, J. E. Brady, and C. E. Martin, “Multispectral analysis of ancient Maya pigments: implications for the Naj Tunich corpus,” in Proceedings of the IEEE 2000 International Geoscience and Remote Sensing Symposium (IEEE, 2000), pp. 2489–2491.

R. Cuninghame-Green, “Minimax algebra and applications,” in Advances in Imaging and Electron Physics, P. Hawkes, ed., Vol. 90 (Academic, 1995), pp. 1–121.

G. X. Ritter and G. Urcid, “Lattice algebra approach to endmember determination in hyperspectral imagery,” in Advances in Imaging and Electron Physics, P. W. Hawkes, ed., Vol. 160 (Academic, 2010), pp. 113–169.

S. Hordley, G. Finlayson, and P. Morovic, “A multi-spectral image database and an application to image rendering across illumination,” in Proceedings of the IEEE Third International Conference on Image and Graphics (IEEE, 2004), pp. 394–397.

C. L. Lawson and R. J. Hanson, Solving Least Squares Problems (Prentice-Hall, 1974).

J. C. Valdiviezo-N and G. Urcid, “Multispectral images segmentation of ancient documents with lattice memories,” in Digital Image Processing and Analysis Conference, OSA Technical Digest Series (Optical Society of America, 2010), paper DMD6.

V. G. Kaburlasos and G. X. Ritter, eds., Computational Intelligence based on Lattice Theory, Vol. 67 (Springer-Verlag, 2007).

G. X. Ritter and P. Gader, “Fixed point of lattice transforms and lattice associative memories,” in Advances in Imaging and Electron Physics, P. Hawkes, ed., Vol. 144 (Elsevier, 2006), pp. 165–242.

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Figures (6)

Fig. 1.
Fig. 1.

Spectral sensitivity of the 16 CCD multispectral camera used to collect the multispectral image of the pre-Hispanic codices.

Fig. 2.
Fig. 2.

Reflectance estimation realized with the generalized inversion (dashed curve) and the Wiener estimate (solid curve) with ρ=0.94, for a red pigment taken from the Matrícula de Tributos codex.

Fig. 3.
Fig. 3.

Left: three spectral pixels selected from the Macbeth chart multispectral image. Right: spectral curves associated with these selected pixels (solid curves) and corresponding spectral curves approximated by w¯31, w¯14, w¯6 (dashed-dotted curves).

Fig. 4.
Fig. 4.

Different scripts extracted from the Archimedes Palimpsest using the lattice-based method and linear unmixing. From left to right: Medieval twelfth century overlaid text (vertical), ancient Greek original text (horizontal), and background parchment. Brighter areas correspond to maximum percentage of the corresponding material.

Fig. 5.
Fig. 5.

Pigment distribution in the Matrícula de Tributos codex determined from the lattice-based method and linear unmixing. Blue color (dark gray in print version) represents red pigment, pink color (light gray) represents yellow pigment, and gray area (background) represents the amate paper.

Fig. 6.
Fig. 6.

Digital restoration of the Matrícula de Tributos codex achieved by means of the pigment distribution maps. Top: RGB color image representing true color. Bottom: digitally restored image.

Tables (2)

Tables Icon

Table 1. Techniques Used for Endmember Selection from the Set W¯{u}a

Tables Icon

Table 2. Techniques Used for Endmember Selection from the Set M¯{v}a

Equations (13)

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

ci=λminλmaxsi(λ)r(λ)dλ+ni,
ci=siTr+ni,
c=Sr+n.
r^=S+c=ST(SST)1c.
r^=M1ST(SM1ST)1c,
r^=CST(SCST)1c.
Cij=ρ(ij)sgn(ij),
x=i=1kaipi+n=Pa+n,
ai0iandi=1kai=1,
(AB)ij=k=1p(aik+bkj);(AB)ij=k=1p(aik+bkj).
(WXX)ij=wij=ξ=1k(xiξxjξ);(MXX)ij=mij=ξ=1k(xiξxjξ).
u=(ui)=ξ=1kxiξ;v=(vi)=ξ=1kxiξ.
w¯i=wi+ui;m¯i=mi+vi.

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