Abstract

A method to sharpen digital color images that takes viewing conditions and human vision models into consideration is described. The method combines the Laplacian of Gaussian (LoG) operator with spatial filters that approximate the contrast sensitivity functions of human visual systems. The sharpening operation is introduced in the opponent color space, following the scheme proposed in the spatial extension of CIELAB (S-CIELAB). We deduce the modification of the original image necessary to obtain the spatially filtered image that approaches the perceived LoG-sharpened image for given viewing conditions. At short viewing distances, for which the spatial blurring is small, most fine edges and object contours are sharpened. At long distances, for which the spatial blurring is greater, only large figures are sharpened. Because of the smoothing Gaussian functions involved in the LoG operator, the proposed image sharpening does not tend to increase noise. When the sharpening operation is limited to the achromatic channel, the results are good. This is consistent with the high importance attached to the luminance channel in the spatial content of color images. Image sharpening based on only the Laplacian of the original is not sensitive to variations of viewing conditions, tends to increase noise, and suffers from its appearance deteriorating rather quickly with the depth of the sharpening operation.

© 2006 Optical Society of America

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References

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  1. R. C. González, R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLAB (Prentice-Hall, 2004).
  2. S. Di Zenzo, "A note on the gradient of a multi-image," Comput. Vis. Graph. Image Process. 33, 116-125 (1986).
  3. J. Weickert, "Coherence-enhancing diffusion of colour images," Image Vis. Comput. 17, 201-212 (1999).
    [CrossRef]
  4. N. Sochen, R. Kimmel, and R. Malladi, "A general framework for low level vision," IEEE Trans. Image Process. 7, 310-318 (1998).
    [CrossRef]
  5. R. Kimmel, R. Malladi, and N. Sochen, "Images as embedded maps and minimal surfaces: movies, color, texture, and volumetric medical images," Int. J. Comput. Vis. 39, 111-129 (2000).
    [CrossRef]
  6. C.-K. Yang, T.-C. Wu, J.-C. Lin, and W.-H. Tsai, "Color image sharpening by moment-preserving technique," Signal Process. 45, 397-403 (1995).
    [CrossRef]
  7. M. Vanrell, R. Baldrich, A. Salvatella, R. Benavente, and F. Tous, "Induction operators for a computational colour-texture representation," Comput. Vis. Image Underst. 94, 92-114 (2004).
    [CrossRef]
  8. J. C. Russ, The Image Processing Handbook, 4th ed. (CRC, 2002).
  9. M. S. Millán and E. Valencia, "Colour image sharpening using color difference based operators," in Proceedings of the Tenth Congress of the International Colour Association (Granada, 2005), pp. 1055-1058.
  10. X. Zhang and B. A. Wandell, "A spatial extension of CIELAB for digital color image reproduction," SID Int. Digest Tech. Papers 27, 731-734 (1996).
  11. X. Zhang, D. A. Silverstein, J. E. Farrell, and B. A. Wandell, "Color image quality metric S-CIELAB and its application on halftone texture visibility," in Proceedings of IEEE COMPCON (IEEE, 1997), Vol. 97, pp. 44-51.
  12. M. Mirmehdi and M. Petrou, "Segmentation of color textures," IEEE Trans. Pattern Anal. Mach. Intell. 22, 142-159 (2000).
    [CrossRef]
  13. G. M. Johnson and M. D. Fairchild, "A top down description of S-CIELAB and CIEDE2000," Color Res. Appl. 28, 425-435 (2003).
    [CrossRef]
  14. M. R. Luo, G. Cui, and B. Rigg, "The development of the CIE 2000 colour-difference formula: CIEDE2000," Color Res. Appl. 26, 340-350 (2001).
    [CrossRef]
  15. S. Westland, "Models of the visual system and their application to image-quality assessment," in Proceedings of the Tenth Congress of the International Colour Association (Granada, 2005), pp. 309-312.
  16. B. A. Wandell, Foundations of Vision (Sinauer, 1995).
  17. P. Kruizinga and N. Petkov, "Computational model of dot-pattern selective cells," Biological Cybern. 83, 313-325 (2000).
    [CrossRef]
  18. T. T. Norton, D. A. Corliss, and J. E. Bailey, The Psychophysical Measurement of Visual Function (Butterworth-Heinemann, 2002).
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    [CrossRef]
  20. IEC 61966-2-1 and Basic sRGB Math are available at http://www.srgb.com/basicsofsrgb.htm.
  21. R. Berns, Billmeyer and Saltzman's Principles of Color Technology (Wiley, 2000).
  22. A. B. Poirson and B. A. Wandell, "The appearance of colored patterns: pattern-color separability," J. Opt. Soc. A 10, 2458-2470 (1993).
    [CrossRef]
  23. A. Huertas and G. Medioni, "Detection of intensity changes with subpixel accuracy using Laplacian-Gaussian masks," IEEE Trans. Pattern Anal. Mach. Intell. 8, 651-664 (1986).
    [CrossRef] [PubMed]
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    [CrossRef]
  25. http://white.stanford.edu/∼brian/scielab/scielab.html.

2004

M. Vanrell, R. Baldrich, A. Salvatella, R. Benavente, and F. Tous, "Induction operators for a computational colour-texture representation," Comput. Vis. Image Underst. 94, 92-114 (2004).
[CrossRef]

2003

G. M. Johnson and M. D. Fairchild, "A top down description of S-CIELAB and CIEDE2000," Color Res. Appl. 28, 425-435 (2003).
[CrossRef]

2001

M. R. Luo, G. Cui, and B. Rigg, "The development of the CIE 2000 colour-difference formula: CIEDE2000," Color Res. Appl. 26, 340-350 (2001).
[CrossRef]

2000

P. Kruizinga and N. Petkov, "Computational model of dot-pattern selective cells," Biological Cybern. 83, 313-325 (2000).
[CrossRef]

M. Mirmehdi and M. Petrou, "Segmentation of color textures," IEEE Trans. Pattern Anal. Mach. Intell. 22, 142-159 (2000).
[CrossRef]

R. Kimmel, R. Malladi, and N. Sochen, "Images as embedded maps and minimal surfaces: movies, color, texture, and volumetric medical images," Int. J. Comput. Vis. 39, 111-129 (2000).
[CrossRef]

1999

J. Weickert, "Coherence-enhancing diffusion of colour images," Image Vis. Comput. 17, 201-212 (1999).
[CrossRef]

S. R. Gunn, "On the discrete representation of the Laplacian of Gaussian," Pattern Recogn. 32, 1463-1472 (1999).
[CrossRef]

1998

N. Sochen, R. Kimmel, and R. Malladi, "A general framework for low level vision," IEEE Trans. Image Process. 7, 310-318 (1998).
[CrossRef]

1996

X. Zhang and B. A. Wandell, "A spatial extension of CIELAB for digital color image reproduction," SID Int. Digest Tech. Papers 27, 731-734 (1996).

1995

C.-K. Yang, T.-C. Wu, J.-C. Lin, and W.-H. Tsai, "Color image sharpening by moment-preserving technique," Signal Process. 45, 397-403 (1995).
[CrossRef]

1993

A. B. Poirson and B. A. Wandell, "The appearance of colored patterns: pattern-color separability," J. Opt. Soc. A 10, 2458-2470 (1993).
[CrossRef]

1986

A. Huertas and G. Medioni, "Detection of intensity changes with subpixel accuracy using Laplacian-Gaussian masks," IEEE Trans. Pattern Anal. Mach. Intell. 8, 651-664 (1986).
[CrossRef] [PubMed]

S. Di Zenzo, "A note on the gradient of a multi-image," Comput. Vis. Graph. Image Process. 33, 116-125 (1986).

1980

D. Marr and E. Hildreth, "Theory of edge detection," Proc. R. Soc. London , Ser. B 207, 187-217 (1980).
[CrossRef]

Bailey, J. E.

T. T. Norton, D. A. Corliss, and J. E. Bailey, The Psychophysical Measurement of Visual Function (Butterworth-Heinemann, 2002).

Baldrich, R.

M. Vanrell, R. Baldrich, A. Salvatella, R. Benavente, and F. Tous, "Induction operators for a computational colour-texture representation," Comput. Vis. Image Underst. 94, 92-114 (2004).
[CrossRef]

Benavente, R.

M. Vanrell, R. Baldrich, A. Salvatella, R. Benavente, and F. Tous, "Induction operators for a computational colour-texture representation," Comput. Vis. Image Underst. 94, 92-114 (2004).
[CrossRef]

Berns, R.

R. Berns, Billmeyer and Saltzman's Principles of Color Technology (Wiley, 2000).

Corliss, D. A.

T. T. Norton, D. A. Corliss, and J. E. Bailey, The Psychophysical Measurement of Visual Function (Butterworth-Heinemann, 2002).

Cui, G.

M. R. Luo, G. Cui, and B. Rigg, "The development of the CIE 2000 colour-difference formula: CIEDE2000," Color Res. Appl. 26, 340-350 (2001).
[CrossRef]

Di Zenzo, S.

S. Di Zenzo, "A note on the gradient of a multi-image," Comput. Vis. Graph. Image Process. 33, 116-125 (1986).

Eddins, S. L.

R. C. González, R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLAB (Prentice-Hall, 2004).

Fairchild, M. D.

G. M. Johnson and M. D. Fairchild, "A top down description of S-CIELAB and CIEDE2000," Color Res. Appl. 28, 425-435 (2003).
[CrossRef]

Farrell, J. E.

X. Zhang, D. A. Silverstein, J. E. Farrell, and B. A. Wandell, "Color image quality metric S-CIELAB and its application on halftone texture visibility," in Proceedings of IEEE COMPCON (IEEE, 1997), Vol. 97, pp. 44-51.

González, R. C.

R. C. González, R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLAB (Prentice-Hall, 2004).

Gunn, S. R.

S. R. Gunn, "On the discrete representation of the Laplacian of Gaussian," Pattern Recogn. 32, 1463-1472 (1999).
[CrossRef]

Hildreth, E.

D. Marr and E. Hildreth, "Theory of edge detection," Proc. R. Soc. London , Ser. B 207, 187-217 (1980).
[CrossRef]

Huertas, A.

A. Huertas and G. Medioni, "Detection of intensity changes with subpixel accuracy using Laplacian-Gaussian masks," IEEE Trans. Pattern Anal. Mach. Intell. 8, 651-664 (1986).
[CrossRef] [PubMed]

Johnson, G. M.

G. M. Johnson and M. D. Fairchild, "A top down description of S-CIELAB and CIEDE2000," Color Res. Appl. 28, 425-435 (2003).
[CrossRef]

Kimmel, R.

R. Kimmel, R. Malladi, and N. Sochen, "Images as embedded maps and minimal surfaces: movies, color, texture, and volumetric medical images," Int. J. Comput. Vis. 39, 111-129 (2000).
[CrossRef]

N. Sochen, R. Kimmel, and R. Malladi, "A general framework for low level vision," IEEE Trans. Image Process. 7, 310-318 (1998).
[CrossRef]

Kruizinga, P.

P. Kruizinga and N. Petkov, "Computational model of dot-pattern selective cells," Biological Cybern. 83, 313-325 (2000).
[CrossRef]

Lin, J.-C.

C.-K. Yang, T.-C. Wu, J.-C. Lin, and W.-H. Tsai, "Color image sharpening by moment-preserving technique," Signal Process. 45, 397-403 (1995).
[CrossRef]

Luo, M. R.

M. R. Luo, G. Cui, and B. Rigg, "The development of the CIE 2000 colour-difference formula: CIEDE2000," Color Res. Appl. 26, 340-350 (2001).
[CrossRef]

Malladi, R.

R. Kimmel, R. Malladi, and N. Sochen, "Images as embedded maps and minimal surfaces: movies, color, texture, and volumetric medical images," Int. J. Comput. Vis. 39, 111-129 (2000).
[CrossRef]

N. Sochen, R. Kimmel, and R. Malladi, "A general framework for low level vision," IEEE Trans. Image Process. 7, 310-318 (1998).
[CrossRef]

Marr, D.

D. Marr and E. Hildreth, "Theory of edge detection," Proc. R. Soc. London , Ser. B 207, 187-217 (1980).
[CrossRef]

Medioni, G.

A. Huertas and G. Medioni, "Detection of intensity changes with subpixel accuracy using Laplacian-Gaussian masks," IEEE Trans. Pattern Anal. Mach. Intell. 8, 651-664 (1986).
[CrossRef] [PubMed]

Millán, M. S.

M. S. Millán and E. Valencia, "Colour image sharpening using color difference based operators," in Proceedings of the Tenth Congress of the International Colour Association (Granada, 2005), pp. 1055-1058.

Mirmehdi, M.

M. Mirmehdi and M. Petrou, "Segmentation of color textures," IEEE Trans. Pattern Anal. Mach. Intell. 22, 142-159 (2000).
[CrossRef]

Norton, T. T.

T. T. Norton, D. A. Corliss, and J. E. Bailey, The Psychophysical Measurement of Visual Function (Butterworth-Heinemann, 2002).

Petkov, N.

P. Kruizinga and N. Petkov, "Computational model of dot-pattern selective cells," Biological Cybern. 83, 313-325 (2000).
[CrossRef]

Petrou, M.

M. Mirmehdi and M. Petrou, "Segmentation of color textures," IEEE Trans. Pattern Anal. Mach. Intell. 22, 142-159 (2000).
[CrossRef]

Poirson, A. B.

A. B. Poirson and B. A. Wandell, "The appearance of colored patterns: pattern-color separability," J. Opt. Soc. A 10, 2458-2470 (1993).
[CrossRef]

Rigg, B.

M. R. Luo, G. Cui, and B. Rigg, "The development of the CIE 2000 colour-difference formula: CIEDE2000," Color Res. Appl. 26, 340-350 (2001).
[CrossRef]

Russ, J. C.

J. C. Russ, The Image Processing Handbook, 4th ed. (CRC, 2002).

Salvatella, A.

M. Vanrell, R. Baldrich, A. Salvatella, R. Benavente, and F. Tous, "Induction operators for a computational colour-texture representation," Comput. Vis. Image Underst. 94, 92-114 (2004).
[CrossRef]

Silverstein, D. A.

X. Zhang, D. A. Silverstein, J. E. Farrell, and B. A. Wandell, "Color image quality metric S-CIELAB and its application on halftone texture visibility," in Proceedings of IEEE COMPCON (IEEE, 1997), Vol. 97, pp. 44-51.

Sochen, N.

R. Kimmel, R. Malladi, and N. Sochen, "Images as embedded maps and minimal surfaces: movies, color, texture, and volumetric medical images," Int. J. Comput. Vis. 39, 111-129 (2000).
[CrossRef]

N. Sochen, R. Kimmel, and R. Malladi, "A general framework for low level vision," IEEE Trans. Image Process. 7, 310-318 (1998).
[CrossRef]

Tous, F.

M. Vanrell, R. Baldrich, A. Salvatella, R. Benavente, and F. Tous, "Induction operators for a computational colour-texture representation," Comput. Vis. Image Underst. 94, 92-114 (2004).
[CrossRef]

Tsai, W.-H.

C.-K. Yang, T.-C. Wu, J.-C. Lin, and W.-H. Tsai, "Color image sharpening by moment-preserving technique," Signal Process. 45, 397-403 (1995).
[CrossRef]

Valencia, E.

M. S. Millán and E. Valencia, "Colour image sharpening using color difference based operators," in Proceedings of the Tenth Congress of the International Colour Association (Granada, 2005), pp. 1055-1058.

Vanrell, M.

M. Vanrell, R. Baldrich, A. Salvatella, R. Benavente, and F. Tous, "Induction operators for a computational colour-texture representation," Comput. Vis. Image Underst. 94, 92-114 (2004).
[CrossRef]

Wandell, B. A.

X. Zhang and B. A. Wandell, "A spatial extension of CIELAB for digital color image reproduction," SID Int. Digest Tech. Papers 27, 731-734 (1996).

A. B. Poirson and B. A. Wandell, "The appearance of colored patterns: pattern-color separability," J. Opt. Soc. A 10, 2458-2470 (1993).
[CrossRef]

X. Zhang, D. A. Silverstein, J. E. Farrell, and B. A. Wandell, "Color image quality metric S-CIELAB and its application on halftone texture visibility," in Proceedings of IEEE COMPCON (IEEE, 1997), Vol. 97, pp. 44-51.

B. A. Wandell, Foundations of Vision (Sinauer, 1995).

Weickert, J.

J. Weickert, "Coherence-enhancing diffusion of colour images," Image Vis. Comput. 17, 201-212 (1999).
[CrossRef]

Westland, S.

S. Westland, "Models of the visual system and their application to image-quality assessment," in Proceedings of the Tenth Congress of the International Colour Association (Granada, 2005), pp. 309-312.

Woods, R. E.

R. C. González, R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLAB (Prentice-Hall, 2004).

Wu, T.-C.

C.-K. Yang, T.-C. Wu, J.-C. Lin, and W.-H. Tsai, "Color image sharpening by moment-preserving technique," Signal Process. 45, 397-403 (1995).
[CrossRef]

Yang, C.-K.

C.-K. Yang, T.-C. Wu, J.-C. Lin, and W.-H. Tsai, "Color image sharpening by moment-preserving technique," Signal Process. 45, 397-403 (1995).
[CrossRef]

Zhang, X.

X. Zhang and B. A. Wandell, "A spatial extension of CIELAB for digital color image reproduction," SID Int. Digest Tech. Papers 27, 731-734 (1996).

X. Zhang, D. A. Silverstein, J. E. Farrell, and B. A. Wandell, "Color image quality metric S-CIELAB and its application on halftone texture visibility," in Proceedings of IEEE COMPCON (IEEE, 1997), Vol. 97, pp. 44-51.

Biological Cybern.

P. Kruizinga and N. Petkov, "Computational model of dot-pattern selective cells," Biological Cybern. 83, 313-325 (2000).
[CrossRef]

Color Res. Appl.

G. M. Johnson and M. D. Fairchild, "A top down description of S-CIELAB and CIEDE2000," Color Res. Appl. 28, 425-435 (2003).
[CrossRef]

M. R. Luo, G. Cui, and B. Rigg, "The development of the CIE 2000 colour-difference formula: CIEDE2000," Color Res. Appl. 26, 340-350 (2001).
[CrossRef]

Comput. Vis.

S. Di Zenzo, "A note on the gradient of a multi-image," Comput. Vis. Graph. Image Process. 33, 116-125 (1986).

Comput. Vis. Image Underst.

M. Vanrell, R. Baldrich, A. Salvatella, R. Benavente, and F. Tous, "Induction operators for a computational colour-texture representation," Comput. Vis. Image Underst. 94, 92-114 (2004).
[CrossRef]

IEEE Trans. Image Process.

N. Sochen, R. Kimmel, and R. Malladi, "A general framework for low level vision," IEEE Trans. Image Process. 7, 310-318 (1998).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell.

M. Mirmehdi and M. Petrou, "Segmentation of color textures," IEEE Trans. Pattern Anal. Mach. Intell. 22, 142-159 (2000).
[CrossRef]

A. Huertas and G. Medioni, "Detection of intensity changes with subpixel accuracy using Laplacian-Gaussian masks," IEEE Trans. Pattern Anal. Mach. Intell. 8, 651-664 (1986).
[CrossRef] [PubMed]

Image Vis. Comput.

J. Weickert, "Coherence-enhancing diffusion of colour images," Image Vis. Comput. 17, 201-212 (1999).
[CrossRef]

Int. J. Comput. Vis.

R. Kimmel, R. Malladi, and N. Sochen, "Images as embedded maps and minimal surfaces: movies, color, texture, and volumetric medical images," Int. J. Comput. Vis. 39, 111-129 (2000).
[CrossRef]

J. Opt. Soc. A

A. B. Poirson and B. A. Wandell, "The appearance of colored patterns: pattern-color separability," J. Opt. Soc. A 10, 2458-2470 (1993).
[CrossRef]

Pattern Recogn.

S. R. Gunn, "On the discrete representation of the Laplacian of Gaussian," Pattern Recogn. 32, 1463-1472 (1999).
[CrossRef]

Proc. R. Soc. London

D. Marr and E. Hildreth, "Theory of edge detection," Proc. R. Soc. London , Ser. B 207, 187-217 (1980).
[CrossRef]

SID Int. Digest Tech. Papers

X. Zhang and B. A. Wandell, "A spatial extension of CIELAB for digital color image reproduction," SID Int. Digest Tech. Papers 27, 731-734 (1996).

Signal Process.

C.-K. Yang, T.-C. Wu, J.-C. Lin, and W.-H. Tsai, "Color image sharpening by moment-preserving technique," Signal Process. 45, 397-403 (1995).
[CrossRef]

Other

X. Zhang, D. A. Silverstein, J. E. Farrell, and B. A. Wandell, "Color image quality metric S-CIELAB and its application on halftone texture visibility," in Proceedings of IEEE COMPCON (IEEE, 1997), Vol. 97, pp. 44-51.

J. C. Russ, The Image Processing Handbook, 4th ed. (CRC, 2002).

M. S. Millán and E. Valencia, "Colour image sharpening using color difference based operators," in Proceedings of the Tenth Congress of the International Colour Association (Granada, 2005), pp. 1055-1058.

R. C. González, R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLAB (Prentice-Hall, 2004).

T. T. Norton, D. A. Corliss, and J. E. Bailey, The Psychophysical Measurement of Visual Function (Butterworth-Heinemann, 2002).

S. Westland, "Models of the visual system and their application to image-quality assessment," in Proceedings of the Tenth Congress of the International Colour Association (Granada, 2005), pp. 309-312.

B. A. Wandell, Foundations of Vision (Sinauer, 1995).

IEC 61966-2-1 and Basic sRGB Math are available at http://www.srgb.com/basicsofsrgb.htm.

R. Berns, Billmeyer and Saltzman's Principles of Color Technology (Wiley, 2000).

http://white.stanford.edu/∼brian/scielab/scielab.html.

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Figures (11)

Fig. 1
Fig. 1

Profile of the (negative) LoG function (solid curve). The Gaussian considered was G(x, y, s = 5) [Eq. (3)]. The LoG profile can be approximated by a DoG function (dashed curve) G(x, y, s 1) − G(x, y, s 2), with s 2s 1 = 1.6 and s 1 = s (Ref. 19). The DoG function has been plotted normalized to the LoG maximum for comparison.

Fig. 2
Fig. 2

(Color online) (a) Test, original image of 385 × 289 pixel size. (b) Set of ten regions of interest of nearly uniform colors that are defined to analyze noise and color variations due to the processes.

Fig. 3
Fig. 3

Sharpening operation in the A channel (i = 0) for d = 50 pixels∕degree and k = 5: (a) original image component I 0 ( x , y ) , (b) spatially filtered image I d 0 ( x , y ) shown with the same scale as in (a), (c) LoG term k LoG { F d 0 } I 0 ( x , y ) , (d) sharpened image component ShI 0 ( x , y ) , (e) spatially filtered sharpened image component ShI d 0 ( x , y ) shown with the same scale as in (d), (f) scaled versions of I d 0 ( x , y ) and ShI d 0 ( x , y ) as they would be seen at d = 50 pixels∕degree.

Fig. 4
Fig. 4

(Color online) (a) Original image (I); (b) A component ( I 0 ); (c) C1 component ( I 1 ); (d) C 2 component ( I 2 ); LoG-sharpened images obtained by using Eq. (10) with k = 5 and d = 50 pixels∕degree: (e) limited to the A channel, and (f) in the A, C1, and C2 channels. (g) CIEDE2000 color difference between the (e) and (a) image pair based on the S-CIELAB metric. (h) CIEDE2000 color difference between the (f) and (a) image pair based on the S-CIELAB metric.

Fig. 5
Fig. 5

(Color online) LoG-sharpened images obtained by using Eq. 10 with k = 5 and d = 50 pixels∕degree: (a) limited to the A channel, and (b) in the A, C1, and C2 channels. (c) CIEDE2000 color difference between the (a) and (b) images based on the S-CIELAB metric. The data corresponding to the CIEDE2000 color differences of the processed whole images (of 385 × 289 pixels) are mean = 2.7197, std = 4.7788, max = 54.9434, min = 0.0036.

Fig. 6
Fig. 6

(Color online) (a)–(d) Zone of the image of Fig. 2(a), displayed on the monitor with p = 57 ppc: (a) original, (b) sharpened image using the Laplacian [Eq. (13)], (c) sharpened image using the proposed LoG method [Eq. (10)] to be seen at d = 25 pixels∕degree; (d) same as (c) but to be seen at d = 50 pixels∕degree; (e)–(g) spatially filtered images of (a)–(c) for the viewing conditions of d = 25 pixels∕degree; (h) and (i): color differences Δ E 00 SCIELAB ( I , ShI 2 ) and Δ E 00 SCIELAB ( I , ShI ) for the viewing condition of d = 25 pixels∕degree; (j), (k), (l) spatially filtered images of (a), (b), (d), respectively, for the viewing condition of d = 50 pixels∕degree; (m), (n) color differences Δ E 00 SCIELAB ( I , ShI 2 ) and Δ E 00 SCIELAB ( I , ShI ) for the viewing condition of d = 50 pixels∕degree.

Fig. 7
Fig. 7

(Color online) (a) Area of the original image (Fig. 2). Sharpened images obtained by using (b) the LoG operator [Eq. (10)], (c) the DoG [Eq. (14)] instead of LoG in Eq. (10). Values of k = 5 and d = 50 pixels∕degree were used to compute (b) and (c). (d) Color difference between (b) and (c) image pair based on the S-CIELAB metric. Statistics of Δ E 00 SCIELAB ( ShI LoG , ShI DoG ) in CIEDE2000 units: mean = 6.3, std = 8.6, max = 112, min = 0.01.

Fig. 8
Fig. 8

(Color online) (a) Achromatic test with three gray levels: light (triangle), medium (background), dark (star). The column of pixels marked with arrows is analyzed in (c)–(f); (b) sharpened image with (k = 5, d = 50); (c)–(e) CIELAB coordinates of the pixels of the column in the original I (thick black curve) and the sharpened ShI (red line) images; (f) distortions [Eq. (19)].

Fig. 9
Fig. 9

(Color online) Butterfly, original image 300 × 197 pixels, displayed with 57 ppc to be seen at L = 25 cm (d = 25 pixels∕degree). Artifacts appear when the sharpening LoG operator of Eq. (10) is used with high values of k. For instance in this figure halos in antennas and wings and pseudotexture in the background. Note that these artifacts are clearly visible for k = 5 not only in the displayed image (left column) but also in the spatially filtered image (right column).

Fig. 10
Fig. 10

(Color online) Dependence on k = {2.5, 5, 7.5} and d = {25, 50} pixels∕degree. (a) Original image I and sharpened ShI images as they would be displayed. On the left, the A component of the original image and LoG terms in channel A. (b) Spatially filtered (original and sharpened) images as they would be perceived.

Fig. 11
Fig. 11

(Color online) Original and sharpened images for d = {25, 50} pixels∕degree. First row, images as they are displayed with p = 57 ppc. Second row, spatially filtered images as they would be seen at distances L = {25, 50} cm from the display. Note that (e) sharpening with low values of k is preferable when the image is to be seen at short viewing distances, whereas (f) higher values of k must be used to produce similar effects at longer viewing distances.

Tables (2)

Tables Icon

Table 1 Weight and Spread of Gaussian Kernels Used to Build the Spatial Filters for Image Convolution in the Opponent Channels

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Table 2 Average Metrics of the ROIs in the SCIELAB ΔE00 Color Differences Computed between the Sharpened and Original Images a

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AC 1 C 2
( C 1 , C 2 )
Δ E 00
C 1
C 2
( 2 )
( C 1 , C 2 )
AC 1 C 2
[ A C 1 C 2 ] = [ 0.297 0.72 0.107 0.449 0.29 0.077 0.086 0.59 0.501 ] [ X Y Z ] .
F d i
F d i ( x , y ) = j w i j G i j ( x , y , d σ i j 2 ) ,
i = { 0 , 1 , 2 }
{ A , C 1 , C 2 }
w i j
G i j
G ( x , y , s ) = 1 S exp [ ( x 2 + y 2 ) 2 s 2 ] .
s i j = d σ i j / 2
( σ i j )
w i j
I d i
I d i
F d i
I i  and 
I i
I d i ( x , y ) = F d i ( x , y ) I i ( x , y ) ,
I di ( x , y ) = F d i ( x , y ) I i ( x , y ) ,
I d i
I d i
[ X Y Z ] = [ 0.979 1.535 0.445 1.189 0.764 0.135 1.232 1.163 2.079 ] [ A C 1 C 2 ] ,
I d ( X Y Z )
I d ( X Y Z )
X n
Y n
Z n
I d ( CIELAB )
I d ( CIELAB )
Δ E a b *
( Δ E a b *
Δ E 94 *
Δ E 00 )
( Δ E 00 )
2 [ G ( x , y , s ) I ( x , y ) ] =
2 G ( x , y , s ) I ( x , y )
2 G ( x , y , s )
W × W
W = 3 c 8.5 s
c = 2 2 s
2 G ( x , y , s )
ShI ( x , y ) = I ( x , y ) LoG I ( x , y ) .
F d i
ShI d i ( x , y ) = I d i ( x , y ) k LoG { F d i } I d i ( x , y ) ,
LoG { F d i ( x , y ) } = j w i j LoG d i j = j w i j 2 G i j ( x , y , d σ i j 2 ) .
ShI d i
ShI i
F d i ( x , y ) ShI i ( x , y ) = ShI d i ( x , y ) .
ShI i ( x , y ) = I i ( x , y ) k LoG { F d i } I i ( x , y ) .
ShI i ( x , y )
ShI d i ( x , y )
N × M
LoG { F d i }
ShI i
ShI RGB
C 1
C 2
ShI d i ( x , y ) = I d i ( x , y ) k LoG { F d i } I i ( x , y ) .
ShI d i ( x , y ) = I d i ( x , y ) k 2 I d i ( x , y )
= F di ( x , y ) [ I i ( x , y ) k 2 I i ( x , y ) ] ,
ShI i ( x , y ) = I i ( x , y ) k 2 I i ( x , y ) .
DoG ( x , y , s 1 , s 2 ) = G ( x , y , s 1 ) G ( x , y , s 2 ) ,
s 2 / s 1 = 1.6
I ( x , y )
385 × 289   pixel
[ X Y Z ] = [ 0.4124 0.3576 0.1805 0.2126 0.7152 0.0722 0.0193 0.1192 0.9505 ] [ R G B ] ,
[ R G B ] = [ 3.2406 1.5372 0.4986 0.9689 1.8758 0.0415 0.0557 0.2040 1.0570 ] [ X Y Z ] .
d = pL   tan ( π 180 ) = 0.0175 pL .
p = 57   ppc
L = { 25 , 50 }   cm
d = 50
k = 5
F d i ( x , y )
d = 50
i = 0
k Log { F d 0 } I 0 ( x , y )
ShI 0 ( x , y )
d = 50
I d 0 ( x , y )
ShI d 0 ( x , y )
d = 50
ShI d 0 ( x , y )
I d 0 ( x , y )
C 1
C 2
ShI 2
[ Δ E 00 SCIELAB ( I , ShI )
Δ E 00 SCIELAB ( I , ShI 2 ) ]
6 × 6
4 × 9
[ Δ E 00 SCIELAB ( I , ShI )
Δ E 00 SCIELAB ( I , ShI 2 ) ]
( V max V min )
SNR = ( 20 N ROI ) i ROI log 10 ( V max V min s i ) ,
V max
V min
N ROI
s i
Δ E 00 SCIELAB ( I , ShI )
Δ E 00 SCIELAB ( I , ShI 2 ) ]
s 2 / s 1 = 1.6
AC 1 C 2
C 1  and  C 2
C 1
C 2
k = 5
d = 50
C 1
C 2
C 1
C 2
ShI A   only
385 × 289
ShI 2
d = { 25 , 50 }
k = 7.5
p = 57   ppc
L = { 25 , 50 }   cm
d = { 25 , 50 }
ShI 2
ShI 2
I d i ( x , y ) k 2 I d i ( x , y ) F d i ( x , y ) [ I i ( x , y ) k 2 I i ( x , y ) ] .
F d i ( x , y ) [ I i ( x , y ) k 2 I i ( x , y ) ]
( Δ E 00 )
Δ E 00 SCIELAB ( I , ShI )
Δ E 00 SCIELAB ( I , ShI 2 )
ShI 2
Δ E 00 SCIELAB ( I , ShI 2 )
Δ E 00 SCIELAB ( I , ShI )
ShI LoG
ShI DoG
k = 5
d = 50
Δ E 00 SCIELAB
( ShI LoG , ShI DoG )
Δ E 00 SCIELAB ( ShI LoG , ShI DoG )
mean = 0.99
std = 0.29
max = 1.70
min = 0.58
AC 1 C 2
( k = 5 , d = 50 )
L *
a *
b *
a *
b *
a *
b *
a *
I d i
ShI d i
Δ L , Δ a , and  Δ b
( j , j + 1 )
{ Δ L ( j , j + 1 ) ,
Δ a ( j , j + 1 ) ,
Δ b ( j , j + 1 ) }
Δ L , Δ a , and  Δ b
ShI d i
I d i
D L * = | Δ L ( j , j + 1 ) ShI d i Δ L ( j , j + 1 ) I d i | , D a * = | Δ a ( j , j + 1 ) ShI d i Δ a ( j , j + 1 ) I d i | , D b * = | Δ b ( j , j + 1 ) ShI d i Δ b ( j , j + 1 ) I d i | .
D L * , D a * , and  D b *
L *
a *
b *
d = 25
d = 50
k = 2.5
( d = 25 )
( d = 50 )
LoG { F d i }
d = 25 , 50
( k = 2.5 , 5 , 7.5 )
Δ E 00 SCIELAB ( I , S h I )
Δ E 00 SCIELAB ( I , S h I 2 )
Δ E 00 SCIELAB ( I , S h I )
Δ E 00 SCIELAB ( I , S h I 2 )
I 0 ( x , y )
I d 0 ( x , y )
k LoG { F d 0 } I 0 ( x , y )
ShI 0 ( x , y )
ShI d 0 ( x , y )
I d 0 ( x , y )
ShI d 0 ( x , y )
I 0
I 1
I 2
Δ E 00 SCIELAB ( I , ShI 2 )
Δ E 00 SCIELAB ( I , ShI )
Δ E 00 SCIELAB ( I , ShI 2 )
Δ E 00 SCIELAB ( I , ShI )
Δ E 00 SCIELAB ( ShI LoG , ShI DoG )

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