Abstract

For images, stochastic resonance or useful-noise effects have previously been assessed with low-level pixel-based information measures. Such measures are not sensitive to coherent spatial structures usually existing in images. As a result, we show that such measures are not sufficient to properly account for stochastic resonance occurring in visual perception. We introduce higher-level similarity measures, inspired from visual perception, and based on local feature descriptors of scale invariant feature transform (SIFT) type. We demonstrate that such SIFT-based measures allow for an assessment of stochastic resonance that matches the visual perception of images with spatial structures. Constructive action of noise is registered in this way with both additive noise and multiplicative speckle noise. Speckle noise, with its grainy appearance, is particularly prone to introducing spurious spatial structures in images, and the stochastic resonance visually perceived and quantitatively assessed with SIFT-based measures is specially examined in this context.

© 2012 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  4. K. P. Singh, G. Ropars, M. Brunel, and A. Le Floch, “Stochastic resonance in an optical two-order parameter vectorial system,” Phys. Rev. Lett. 87, 213901 (2001).
    [CrossRef]
  5. F. Marino, M. Giudici, S. Barland, and S. Balle, “Experimental evidence of stochastic resonance in an excitable optical system,” Phys. Rev. Lett. 88, 040601 (2002).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  8. F. Chapeau-Blondeau, D. Rousseau, S. Blanchard, and D. Gindre, “Optimizing the speckle noise for maximum efficacy of data acquisition in coherent imaging,” J. Opt. Soc. Am. A 25, 1287–1292 (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  11. Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9, 81–84 (2002).
    [CrossRef]
  12. L. Itti, C. Koch, and E. Niebur, “A model of saliency-based visual attention for rapid scene analysis,” IEEE Trans. Pattern Anal. Machine Intell. 20, 1254–1259 (1998).
    [CrossRef]
  13. J. Li and N. M. Allison, “A comprehensive review of current local features for computer vision,” Neurocomputing 71, 1771–1787 (2008).
    [CrossRef]
  14. D. G. Lowe, “Distinctive image features from scale-invariant keypoints,” Int. J. Comput. Vis. 60, 91–110 (2004).
    [CrossRef]
  15. http://www.vlfeat.org/∼vedaldi/code/sift.html .
  16. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts & Company, 2006).
  17. F. Moss, L. M. Ward, and W. G. Sannita, “Stochastic resonance and sensory information processing: a tutorial and review of application,” Clin. Neurophysiol. 115, 267–281 (2004).
    [CrossRef]
  18. A. T. Duchowski, Eye Tracking Methodology: Theory and Practice (Springer, 2007).
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    [CrossRef]
  20. A. Delahaies, D. Rousseau, D. Gindre, and F. Chapeau-Blondeau, “Exploiting the speckle noise for compressive sensing,” Opt. Commun. 284, 3939–3945 (2011).
    [CrossRef]
  21. D. Ruderman and W. Bialek, “Statistics of natural images: scaling in the woods,” Phys. Rev. Lett. 73, 814–817 (1994).
    [CrossRef]
  22. P. Isola, J. Xiao, A. Torralba, and A. Oliva, “What makes an image memorable?” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2011), pp. 145–156.

2011 (2)

A. Delahaies, D. Rousseau, and F. Chapeau-Blondeau, “Joint acquisition-processing approach to optimize observation scales in noisy imaging,” Opt. Lett. 36, 972–974 (2011).
[CrossRef]

A. Delahaies, D. Rousseau, D. Gindre, and F. Chapeau-Blondeau, “Exploiting the speckle noise for compressive sensing,” Opt. Commun. 284, 3939–3945 (2011).
[CrossRef]

2010 (2)

D. Rousseau, A. Delahaies, and F. Chapeau-Blondeau, “Structural similarity measure to assess improvement by noise in nonlinear image transmission,” IEEE Signal Process. Lett. 17, 36–39 (2010).
[CrossRef]

D. V. Dylov and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nat. Photon. 4, 323–328 (2010).
[CrossRef]

2008 (2)

2007 (1)

2004 (2)

D. G. Lowe, “Distinctive image features from scale-invariant keypoints,” Int. J. Comput. Vis. 60, 91–110 (2004).
[CrossRef]

F. Moss, L. M. Ward, and W. G. Sannita, “Stochastic resonance and sensory information processing: a tutorial and review of application,” Clin. Neurophysiol. 115, 267–281 (2004).
[CrossRef]

2002 (2)

Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9, 81–84 (2002).
[CrossRef]

F. Marino, M. Giudici, S. Barland, and S. Balle, “Experimental evidence of stochastic resonance in an excitable optical system,” Phys. Rev. Lett. 88, 040601 (2002).
[CrossRef]

2001 (1)

K. P. Singh, G. Ropars, M. Brunel, and A. Le Floch, “Stochastic resonance in an optical two-order parameter vectorial system,” Phys. Rev. Lett. 87, 213901 (2001).
[CrossRef]

1998 (2)

F. Vaudelle, J. Gazengel, G. Rivoire, X. Godivier, and F. Chapeau-Blondeau, “Stochastic resonance and noise-enhanced transmission of spatial signals in optics: the case of scattering,” J. Opt. Soc. Am. B 15, 2674–2680 (1998).
[CrossRef]

L. Itti, C. Koch, and E. Niebur, “A model of saliency-based visual attention for rapid scene analysis,” IEEE Trans. Pattern Anal. Machine Intell. 20, 1254–1259 (1998).
[CrossRef]

1997 (1)

E. Simonotto, M. Riani, C. Seife, M. Roberts, J. Twitty, and F. Moss, “Visual perception of stochastic resonance,” Phys. Rev. Lett. 78, 1186–1189 (1997).
[CrossRef]

1996 (1)

1994 (1)

D. Ruderman and W. Bialek, “Statistics of natural images: scaling in the woods,” Phys. Rev. Lett. 73, 814–817 (1994).
[CrossRef]

Abbott, D.

M. D. McDonnell, N. G. Stocks, C. E. M. Pearce, and D. Abbott, Stochastic Resonance: From Suprathreshold Stochastic Resonance to Stochastic Signal Quantization (Cambridge University, 2008).

Allison, N. M.

J. Li and N. M. Allison, “A comprehensive review of current local features for computer vision,” Neurocomputing 71, 1771–1787 (2008).
[CrossRef]

Balle, S.

F. Marino, M. Giudici, S. Barland, and S. Balle, “Experimental evidence of stochastic resonance in an excitable optical system,” Phys. Rev. Lett. 88, 040601 (2002).
[CrossRef]

Barland, S.

F. Marino, M. Giudici, S. Barland, and S. Balle, “Experimental evidence of stochastic resonance in an excitable optical system,” Phys. Rev. Lett. 88, 040601 (2002).
[CrossRef]

Bialek, W.

D. Ruderman and W. Bialek, “Statistics of natural images: scaling in the woods,” Phys. Rev. Lett. 73, 814–817 (1994).
[CrossRef]

Blanchard, S.

Bovik, A. C.

Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9, 81–84 (2002).
[CrossRef]

Brunel, M.

K. P. Singh, G. Ropars, M. Brunel, and A. Le Floch, “Stochastic resonance in an optical two-order parameter vectorial system,” Phys. Rev. Lett. 87, 213901 (2001).
[CrossRef]

Chapeau-Blondeau, F.

Delahaies, A.

A. Delahaies, D. Rousseau, D. Gindre, and F. Chapeau-Blondeau, “Exploiting the speckle noise for compressive sensing,” Opt. Commun. 284, 3939–3945 (2011).
[CrossRef]

A. Delahaies, D. Rousseau, and F. Chapeau-Blondeau, “Joint acquisition-processing approach to optimize observation scales in noisy imaging,” Opt. Lett. 36, 972–974 (2011).
[CrossRef]

D. Rousseau, A. Delahaies, and F. Chapeau-Blondeau, “Structural similarity measure to assess improvement by noise in nonlinear image transmission,” IEEE Signal Process. Lett. 17, 36–39 (2010).
[CrossRef]

Duchowski, A. T.

A. T. Duchowski, Eye Tracking Methodology: Theory and Practice (Springer, 2007).

Dylov, D. V.

D. V. Dylov and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nat. Photon. 4, 323–328 (2010).
[CrossRef]

Fleischer, J. W.

D. V. Dylov and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nat. Photon. 4, 323–328 (2010).
[CrossRef]

Gazengel, J.

Gindre, D.

Giudici, M.

F. Marino, M. Giudici, S. Barland, and S. Balle, “Experimental evidence of stochastic resonance in an excitable optical system,” Phys. Rev. Lett. 88, 040601 (2002).
[CrossRef]

Godivier, X.

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts & Company, 2006).

Isola, P.

P. Isola, J. Xiao, A. Torralba, and A. Oliva, “What makes an image memorable?” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2011), pp. 145–156.

Itti, L.

L. Itti, C. Koch, and E. Niebur, “A model of saliency-based visual attention for rapid scene analysis,” IEEE Trans. Pattern Anal. Machine Intell. 20, 1254–1259 (1998).
[CrossRef]

Jost, B. M.

Koch, C.

L. Itti, C. Koch, and E. Niebur, “A model of saliency-based visual attention for rapid scene analysis,” IEEE Trans. Pattern Anal. Machine Intell. 20, 1254–1259 (1998).
[CrossRef]

Le Floch, A.

K. P. Singh, G. Ropars, M. Brunel, and A. Le Floch, “Stochastic resonance in an optical two-order parameter vectorial system,” Phys. Rev. Lett. 87, 213901 (2001).
[CrossRef]

Li, J.

J. Li and N. M. Allison, “A comprehensive review of current local features for computer vision,” Neurocomputing 71, 1771–1787 (2008).
[CrossRef]

Lowe, D. G.

D. G. Lowe, “Distinctive image features from scale-invariant keypoints,” Int. J. Comput. Vis. 60, 91–110 (2004).
[CrossRef]

Marino, F.

F. Marino, M. Giudici, S. Barland, and S. Balle, “Experimental evidence of stochastic resonance in an excitable optical system,” Phys. Rev. Lett. 88, 040601 (2002).
[CrossRef]

McDonnell, M. D.

M. D. McDonnell, N. G. Stocks, C. E. M. Pearce, and D. Abbott, Stochastic Resonance: From Suprathreshold Stochastic Resonance to Stochastic Signal Quantization (Cambridge University, 2008).

Moss, F.

F. Moss, L. M. Ward, and W. G. Sannita, “Stochastic resonance and sensory information processing: a tutorial and review of application,” Clin. Neurophysiol. 115, 267–281 (2004).
[CrossRef]

E. Simonotto, M. Riani, C. Seife, M. Roberts, J. Twitty, and F. Moss, “Visual perception of stochastic resonance,” Phys. Rev. Lett. 78, 1186–1189 (1997).
[CrossRef]

Niebur, E.

L. Itti, C. Koch, and E. Niebur, “A model of saliency-based visual attention for rapid scene analysis,” IEEE Trans. Pattern Anal. Machine Intell. 20, 1254–1259 (1998).
[CrossRef]

Oliva, A.

P. Isola, J. Xiao, A. Torralba, and A. Oliva, “What makes an image memorable?” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2011), pp. 145–156.

Pearce, C. E. M.

M. D. McDonnell, N. G. Stocks, C. E. M. Pearce, and D. Abbott, Stochastic Resonance: From Suprathreshold Stochastic Resonance to Stochastic Signal Quantization (Cambridge University, 2008).

Riani, M.

E. Simonotto, M. Riani, C. Seife, M. Roberts, J. Twitty, and F. Moss, “Visual perception of stochastic resonance,” Phys. Rev. Lett. 78, 1186–1189 (1997).
[CrossRef]

Rivoire, G.

Roberts, M.

E. Simonotto, M. Riani, C. Seife, M. Roberts, J. Twitty, and F. Moss, “Visual perception of stochastic resonance,” Phys. Rev. Lett. 78, 1186–1189 (1997).
[CrossRef]

Ropars, G.

K. P. Singh, G. Ropars, M. Brunel, and A. Le Floch, “Stochastic resonance in an optical two-order parameter vectorial system,” Phys. Rev. Lett. 87, 213901 (2001).
[CrossRef]

Rousseau, D.

Ruderman, D.

D. Ruderman and W. Bialek, “Statistics of natural images: scaling in the woods,” Phys. Rev. Lett. 73, 814–817 (1994).
[CrossRef]

Saleh, B. E. A.

Sannita, W. G.

F. Moss, L. M. Ward, and W. G. Sannita, “Stochastic resonance and sensory information processing: a tutorial and review of application,” Clin. Neurophysiol. 115, 267–281 (2004).
[CrossRef]

Seife, C.

E. Simonotto, M. Riani, C. Seife, M. Roberts, J. Twitty, and F. Moss, “Visual perception of stochastic resonance,” Phys. Rev. Lett. 78, 1186–1189 (1997).
[CrossRef]

Simonotto, E.

E. Simonotto, M. Riani, C. Seife, M. Roberts, J. Twitty, and F. Moss, “Visual perception of stochastic resonance,” Phys. Rev. Lett. 78, 1186–1189 (1997).
[CrossRef]

Singh, K. P.

K. P. Singh, G. Ropars, M. Brunel, and A. Le Floch, “Stochastic resonance in an optical two-order parameter vectorial system,” Phys. Rev. Lett. 87, 213901 (2001).
[CrossRef]

Stocks, N. G.

M. D. McDonnell, N. G. Stocks, C. E. M. Pearce, and D. Abbott, Stochastic Resonance: From Suprathreshold Stochastic Resonance to Stochastic Signal Quantization (Cambridge University, 2008).

Torralba, A.

P. Isola, J. Xiao, A. Torralba, and A. Oliva, “What makes an image memorable?” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2011), pp. 145–156.

Twitty, J.

E. Simonotto, M. Riani, C. Seife, M. Roberts, J. Twitty, and F. Moss, “Visual perception of stochastic resonance,” Phys. Rev. Lett. 78, 1186–1189 (1997).
[CrossRef]

Vaudelle, F.

Wang, Z.

Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9, 81–84 (2002).
[CrossRef]

Ward, L. M.

F. Moss, L. M. Ward, and W. G. Sannita, “Stochastic resonance and sensory information processing: a tutorial and review of application,” Clin. Neurophysiol. 115, 267–281 (2004).
[CrossRef]

Xiao, J.

P. Isola, J. Xiao, A. Torralba, and A. Oliva, “What makes an image memorable?” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2011), pp. 145–156.

Clin. Neurophysiol. (1)

F. Moss, L. M. Ward, and W. G. Sannita, “Stochastic resonance and sensory information processing: a tutorial and review of application,” Clin. Neurophysiol. 115, 267–281 (2004).
[CrossRef]

IEEE Signal Process. Lett. (2)

D. Rousseau, A. Delahaies, and F. Chapeau-Blondeau, “Structural similarity measure to assess improvement by noise in nonlinear image transmission,” IEEE Signal Process. Lett. 17, 36–39 (2010).
[CrossRef]

Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9, 81–84 (2002).
[CrossRef]

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

L. Itti, C. Koch, and E. Niebur, “A model of saliency-based visual attention for rapid scene analysis,” IEEE Trans. Pattern Anal. Machine Intell. 20, 1254–1259 (1998).
[CrossRef]

Int. J. Comput. Vis. (1)

D. G. Lowe, “Distinctive image features from scale-invariant keypoints,” Int. J. Comput. Vis. 60, 91–110 (2004).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Nat. Photon. (1)

D. V. Dylov and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nat. Photon. 4, 323–328 (2010).
[CrossRef]

Neurocomputing (1)

J. Li and N. M. Allison, “A comprehensive review of current local features for computer vision,” Neurocomputing 71, 1771–1787 (2008).
[CrossRef]

Opt. Commun. (1)

A. Delahaies, D. Rousseau, D. Gindre, and F. Chapeau-Blondeau, “Exploiting the speckle noise for compressive sensing,” Opt. Commun. 284, 3939–3945 (2011).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. Lett. (4)

K. P. Singh, G. Ropars, M. Brunel, and A. Le Floch, “Stochastic resonance in an optical two-order parameter vectorial system,” Phys. Rev. Lett. 87, 213901 (2001).
[CrossRef]

F. Marino, M. Giudici, S. Barland, and S. Balle, “Experimental evidence of stochastic resonance in an excitable optical system,” Phys. Rev. Lett. 88, 040601 (2002).
[CrossRef]

E. Simonotto, M. Riani, C. Seife, M. Roberts, J. Twitty, and F. Moss, “Visual perception of stochastic resonance,” Phys. Rev. Lett. 78, 1186–1189 (1997).
[CrossRef]

D. Ruderman and W. Bialek, “Statistics of natural images: scaling in the woods,” Phys. Rev. Lett. 73, 814–817 (1994).
[CrossRef]

Other (5)

P. Isola, J. Xiao, A. Torralba, and A. Oliva, “What makes an image memorable?” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2011), pp. 145–156.

M. D. McDonnell, N. G. Stocks, C. E. M. Pearce, and D. Abbott, Stochastic Resonance: From Suprathreshold Stochastic Resonance to Stochastic Signal Quantization (Cambridge University, 2008).

http://www.vlfeat.org/∼vedaldi/code/sift.html .

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts & Company, 2006).

A. T. Duchowski, Eye Tracking Methodology: Theory and Practice (Springer, 2007).

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Figures (7)

Fig. 1.
Fig. 1.

(a) Initial binary input image x with gray levels x 0 = 0 and x 1 = 1 . (b)–(d) Binary images y at the output of the two-level quantizer of Eqs. (1) and (2) with threshold θ = 1.1 , with the additive white noise n taken centered with a Gaussian distribution with standard deviation σ n = 0.07 (b), σ n = 0.49 (c), and σ n = 1.5 (d). (f)–(h) are identical to (b)–(d) with the input binary image (e) having the same proportions of black and white pixels as (a).

Fig. 2.
Fig. 2.

Similarity measure between the input binary image x of Fig. 1(a) or Fig. 1(e) and the binary output image y as a function of the rms amplitude σ n of the noise n taken zero-mean Gaussian. The normalized cross-covariance C ( x , y ) of Eq. (3), the SSIM index S ( x , y ) of Eq. (4), and the Shannon mutual information I ( x , y ) of Eq. (5) are identical for Figs. 1(a) and 1(e).

Fig. 3.
Fig. 3.

Input–output similarity based on the number of colocalized SIFT matches counted in the images of Fig. 1. Lines materialize the keypoints detected as matching in the input and in the output image. Dashed horizontal lines are for colocalized SIFT matches associating pairs of keypoints with same spatial location in input and output images. Solid lines, mainly oblique, are for SIFT matches with wrong locations. The left column corresponds to the structured image of Fig. 1(a), and the right column to the unstructured image of Fig. 1(e).

Fig. 4.
Fig. 4.

Average number of colocalized SIFT matches found over 100 realizations between initial input binary images x [Fig. 1(a) or Fig. 1(e)] and the output binary image y , as a function of the noise level. By contrast with the similarity measures of Fig. 2, the number of colocalized SIFT matches differs for the structured image of Fig. 1(a) and the unstructured image Fig. 1(e), for which the number of colocalized SIFT matches detected is artifactually low and constant.

Fig. 5.
Fig. 5.

Same input binary images as in Fig. 1 with gray levels x 0 = 0.5 , x 1 = 1 and threshold θ = 1 . The multiplicative speckle noise n is exponentially distributed as in Eq. (11) with rms amplitude 2 σ n . Solid lines stand for the normalized cross-covariance C ( x , y ) of Eq. (3), and the SSIM index S ( x , y ) of Eq. (4) and the Shannon mutual information I ( x , y ) of Eq. (5) are identical for Figs. 1(a) and 1(e). The discrete set of points stands for the numerical average over 100 realizations with the speckle grain size of Fig. 6(b)—circles and Fig. 6(d)—crosses.

Fig. 6.
Fig. 6.

Output images with the same speckle noise rms amplitude taken at 2 σ n = 1.5 . Input image is the binary image of Fig. 1(a) with gray levels x 0 = 0.5 , x 1 = 1 , threshold θ = 1 . From left to right, the size of the speckle grain is increased.

Fig. 7.
Fig. 7.

Average number of colocalized SIFT matches found over 100 realizations between the initial input binary image x [Fig. 1(a)] and the output binary image y , as a function of the speckle noise level. Gray levels x 0 = 0.5 , x 1 = 1 , threshold θ = 1 . Plots (a), (b), (c), and (d) are obtained with grain sizes increasing for the speckle as in Fig. 6.

Equations (13)

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

y = g ( x + n ) ,
g ( x ) = { 0 for x θ 1 for x > θ .
C ( x , y ) = x y x y x 2 x 2 y 2 y 2 ,
S ( x , y ) = 4 ( x y x y ) x y ( x 2 x 2 + y 2 y 2 ) ( x 2 + y 2 ) ,
I ( x , y ) = H ( y ) H ( y | x ) ,
H ( y ) = y d y p y ( y ) log 2 [ p y ( y ) ] ,
H ( y | x ) = x d x p x ( x ) y d y p y | x ( y ) log 2 [ p y | x ( y ) ]
C ( x , y ) = p 1 ( p 11 q 1 ) p 1 ( 1 p 1 ) q 1 ( 1 q 1 ) ,
S ( x , y ) = 4 ( p 1 p 11 p 1 q 1 ) p 1 q 1 ( p 1 p 1 2 + q 1 q 1 2 ) ( p 1 2 + q 1 2 ) ,
I ( x , y ) = h [ p 11 p 1 + ( 1 p 00 ) ( 1 p 1 ) ] + h [ ( 1 p 11 ) p 1 + p 00 ( 1 p 1 ) ] ( 1 p 1 ) [ h ( p 00 ) + h ( 1 p 00 ) ] + p 1 [ h ( p 11 ) + h ( 1 p 11 ) ] ,
p n ( j ) = 1 σ n exp ( j σ n ) , j 0
F n ( j ) = 1 exp ( j σ n ) , j 0 .
y = g ( x × n ) ,

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