Abstract

Stereoscopic displays provide viewers with a truly fascinating viewing experience. However, current stereoscopic displays suffer from crosstalk that is detrimental to image quality, depth quality, and visual comfort. In order to reduce the perceived crosstalk in stereoscopic displays, this paper proposes a crosstalk reduction method that combines disparity adjustment and crosstalk cancellation. The main idea of the proposed method is to displace the visible crosstalk using the disparity adjustment in a way that less amounts of intensity leakage occur on perceptually important regions in a scene. To this purpose, we estimate a crosstalk visibility index map for the scene that represents pixel-by-pixel importance values associated with the amount of perceived crosstalk and negative-after-effects of the crosstalk cancellation. Based on the crosstalk visibility index, we introduce a new disparity adjustment method that reduces the annoying crosstalk in processed images, which is followed by the crosstalk cancellation. The effectiveness of the proposed method has been successfully evaluated by subjective assessments of image quality and viewing preference. Experimental results demonstrate that the proposed method effectively improves the image quality and overall viewing quality of stereoscopic videos.

© 2014 Optical Society of America

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  1. P. Benzie, J. Watson, P. Surman, I. Rakkolainen, K. Hopf, H. Urey, V. Sainov, and C. Kopylow, “A survey of 3DTV displays: techniques and technologies,” IEEE Trans. Circ. Syst. Video Tech. 17(11), 1647–1658 (2007).
    [Crossref]
  2. H. Sohn, Y. J. Jung, S.-i. Lee, F. Speranza, and Y. M. Ro, “Visual comfort amelioration technique for stereoscopic image: disparity remapping to mitigate global and local discomfort causes,” IEEE Trans. Circ. Syst. Video Tech. (to be published).
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  5. Y. J. Jung, H. Sohn, S. I. Lee, Y. M. Ro, and H. W. Park, “Quantitative measurement of binocular color fusion limit for non-spectral colors,” Opt. Express 19(8), 7325–7338 (2011).
    [Crossref] [PubMed]
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  8. F. L. Kooi and A. Toet, “Visual comfort of binocular and 3D displays,” Displays 25(2–3), 99–108 (2004).
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  11. M. Barkowsky, S. Tourancheau, K. Brunnström, K. Wang, and B. Andrén, “Crosstalk measurement of shutter glasses 3D displays,” in Proceedings of SID Symposium Dig. Tech. Pap. 42(1), 812–815 (2011).
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  22. S. L. Franconeri and D. J. Simons, “Moving and looming stimuli capture attention,” Percept. Psychophys. 65(7), 999–1010 (2003).
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  25. H. Sohn, Y. J. Jung, S. I. Lee, and Y. M. Ro, “Predicting visual discomfort using object size and disparity information in stereoscopic images,” IEEE Trans. Broadcast 59(1), 28–37 (2013).
  26. M. Lang, A. Hornung, O. Wang, S. Poulakos, A. Smolic, and M. Gross, “Nonlinear disparity mapping for stereoscopic 3D,” ACM Trans. Graph. 29(4), 1–10 (2010).
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    [Crossref] [PubMed]
  33. J.-C. Liou, K. Lee, and J.-F. Huang, “Low crosstalk multi-view tracking 3-D display of synchro-signal LED scanning backlight system,” J. Display Technol. 7(8), 411–419 (2011).
    [Crossref]
  34. L. Chen, Y. Tu, W. Liu, and Q. Li, “Investigation of crosstalk in a 2-view 3D display,” in Proceedings of SID Symposium Dig. Tech. Pap. 39(1), 1138–1141 (2008).
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    [Crossref] [PubMed]
  37. T. Shibata, J. Kim, D. M. Hoffman, and M. S. Banks, “The zone of comfort: Predicting visual discomfort with stereo displays,” J. Vis. 11(8), 11 (2011).
    [Crossref] [PubMed]
  38. Y. J. Jung, H. Sohn, S.-i. Lee, F. Speranza, and Y. M. Ro, “Visual importance- and discomfort region-selective low-pass filtering for reducing visual discomfort in stereoscopic displays,” IEEE Trans. Circ. Syst. Video Tech. 23(8), 1408–1421 (2013).
    [Crossref]
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2013 (2)

H. Sohn, Y. J. Jung, S. I. Lee, and Y. M. Ro, “Predicting visual discomfort using object size and disparity information in stereoscopic images,” IEEE Trans. Broadcast 59(1), 28–37 (2013).

Y. J. Jung, H. Sohn, S.-i. Lee, F. Speranza, and Y. M. Ro, “Visual importance- and discomfort region-selective low-pass filtering for reducing visual discomfort in stereoscopic displays,” IEEE Trans. Circ. Syst. Video Tech. 23(8), 1408–1421 (2013).
[Crossref]

2012 (3)

D.-H. Kang, E.-J. Lee, J.-H. Lee, and J.-K. Song, “Perceptual strength of 3-D crosstalk in both achromatic and color images in stereoscopic 3-D displays,” IEEE Trans. Image Process. 21(7), 3253–3261 (2012).
[Crossref] [PubMed]

A. J. Woods, “Crosstalk in stereoscopic displays: a review,” J. Electron. Imaging 21(4), 040902 (2012).
[Crossref]

L. Xing, J. You, T. Ebrahimi, and A. Perkis, “Assessment of stereoscopic crosstalk perception,” IEEE Trans. Multimed. 14(2), 326–337 (2012).
[Crossref]

2011 (6)

Y. J. Jung, H. Sohn, S. I. Lee, Y. M. Ro, and H. W. Park, “Quantitative measurement of binocular color fusion limit for non-spectral colors,” Opt. Express 19(8), 7325–7338 (2011).
[Crossref] [PubMed]

I. Tsirlin, L. M. Wilcox, and R. S. Allison, “The effect of crosstalk on the perceived depth from disparity and monocular occlusions,” IEEE Trans. Broadcast 57(2), 445–453 (2011).
[Crossref]

M. Barkowsky, S. Tourancheau, K. Brunnström, K. Wang, and B. Andrén, “Crosstalk measurement of shutter glasses 3D displays,” in Proceedings of SID Symposium Dig. Tech. Pap. 42(1), 812–815 (2011).
[Crossref]

C. Lee, G. Seo, J. Lee, T. H. Han, and J. G. Park, “Auto-stereoscopic 3D displays with reduced crosstalk,” Opt. Express 19(24), 24762–24774 (2011).
[Crossref] [PubMed]

J.-C. Liou, K. Lee, and J.-F. Huang, “Low crosstalk multi-view tracking 3-D display of synchro-signal LED scanning backlight system,” J. Display Technol. 7(8), 411–419 (2011).
[Crossref]

T. Shibata, J. Kim, D. M. Hoffman, and M. S. Banks, “The zone of comfort: Predicting visual discomfort with stereo displays,” J. Vis. 11(8), 11 (2011).
[Crossref] [PubMed]

2010 (2)

M. Lang, A. Hornung, O. Wang, S. Poulakos, A. Smolic, and M. Gross, “Nonlinear disparity mapping for stereoscopic 3D,” ACM Trans. Graph. 29(4), 1–10 (2010).
[Crossref]

S. Shestak, D.-S. Kim, and S.-D. Hwang, “Measuring of gray-to-gray crosstalk in a LCD based time-sequential stereoscopic displays,” in Proceedings of SID Symposium Dig. Tech. Pap. 41(1), 132–135 (2010).
[Crossref]

2009 (1)

M. Lambooij, W. A. IJsselsteijn, and I. Heynderickx, “Visual discomfort and visual fatigue of stereoscopic displays: a review,” J. Imaging Sci. Technol. 53(3), 030201 (2009).
[Crossref]

2008 (2)

L. Chen, Y. Tu, W. Liu, and Q. Li, “Investigation of crosstalk in a 2-view 3D display,” in Proceedings of SID Symposium Dig. Tech. Pap. 39(1), 1138–1141 (2008).
[Crossref]

A. M. Norcia, J. Hale, M. W. Pettet, S. P. McKee, and R. A. Harrad, “Disparity tuning of binocular facilitation and suppression after normal versus abnormal visual development,” Invest. Ophthalmol. Vis. Sci. 50(3), 1168–1175 (2008).
[Crossref] [PubMed]

2007 (1)

P. Benzie, J. Watson, P. Surman, I. Rakkolainen, K. Hopf, H. Urey, V. Sainov, and C. Kopylow, “A survey of 3DTV displays: techniques and technologies,” IEEE Trans. Circ. Syst. Video Tech. 17(11), 1647–1658 (2007).
[Crossref]

2005 (1)

P. J. H. Seuntiëns, L. M. J. Meesters, and W. A. IJsselsteijn, “Perceptual attributes of crosstalk in 3D images,” Displays 26(4–5), 177–183 (2005).
[Crossref]

2004 (2)

F. L. Kooi and A. Toet, “Visual comfort of binocular and 3D displays,” Displays 25(2–3), 99–108 (2004).
[Crossref]

L. Itti, “Automatic foveation for video compression using a neurobiological model of visual attention,” IEEE Trans. Image Process. 13(10), 1304–1318 (2004).
[Crossref] [PubMed]

2003 (1)

S. L. Franconeri and D. J. Simons, “Moving and looming stimuli capture attention,” Percept. Psychophys. 65(7), 999–1010 (2003).
[Crossref] [PubMed]

2000 (2)

J. Konrad, B. Lacotte, and E. Dubois, “Cancellation of image crosstalk in time-sequential displays of stereoscopic video,” IEEE Trans. Image Process. 9(5), 897–908 (2000).
[Crossref] [PubMed]

K.-C. Huang, C.-H. Tsai, K. Lee, and W.-J. Hsueh, “Measurement of contrast ratios for 3D display,” Proc. SPIE 4080, 78–86 (2000).
[Crossref]

1998 (1)

L. Itti, C. Koch, and E. Niebur, “A model of saliency-based visual attention for rapid scene analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 20(11), 1254–1259 (1998).
[Crossref]

1994 (1)

J. Lipscomb and W. Wooten, “Reducing crosstalk between stereoscopic views,” Proc. SPIE 2177, 92–96 (1994).
[Crossref]

1992 (1)

I. Pitas and A. N. Venetsanopoulos, “Order statistics in digital image processing,” Proc. IEEE 80(12), 1893–1921 (1992).
[Crossref]

1990 (1)

Y.-Y. Yeh and L. D. Silverstein, “Limits of fusion and depth judgment in stereoscopic color displays,” Hum. Factors 32(1), 45–60 (1990).
[Crossref] [PubMed]

1977 (1)

W. Frei, “Image enhancement by histogram hyperbolization,” Comput. Gr. Image Process. 6(3), 286–294 (1977).
[Crossref]

Allison, R. S.

I. Tsirlin, L. M. Wilcox, and R. S. Allison, “The effect of crosstalk on the perceived depth from disparity and monocular occlusions,” IEEE Trans. Broadcast 57(2), 445–453 (2011).
[Crossref]

Andrén, B.

M. Barkowsky, S. Tourancheau, K. Brunnström, K. Wang, and B. Andrén, “Crosstalk measurement of shutter glasses 3D displays,” in Proceedings of SID Symposium Dig. Tech. Pap. 42(1), 812–815 (2011).
[Crossref]

Banks, M. S.

T. Shibata, J. Kim, D. M. Hoffman, and M. S. Banks, “The zone of comfort: Predicting visual discomfort with stereo displays,” J. Vis. 11(8), 11 (2011).
[Crossref] [PubMed]

Barkowsky, M.

M. Barkowsky, S. Tourancheau, K. Brunnström, K. Wang, and B. Andrén, “Crosstalk measurement of shutter glasses 3D displays,” in Proceedings of SID Symposium Dig. Tech. Pap. 42(1), 812–815 (2011).
[Crossref]

Benzie, P.

P. Benzie, J. Watson, P. Surman, I. Rakkolainen, K. Hopf, H. Urey, V. Sainov, and C. Kopylow, “A survey of 3DTV displays: techniques and technologies,” IEEE Trans. Circ. Syst. Video Tech. 17(11), 1647–1658 (2007).
[Crossref]

Brunnström, K.

M. Barkowsky, S. Tourancheau, K. Brunnström, K. Wang, and B. Andrén, “Crosstalk measurement of shutter glasses 3D displays,” in Proceedings of SID Symposium Dig. Tech. Pap. 42(1), 812–815 (2011).
[Crossref]

Chen, L.

L. Chen, Y. Tu, W. Liu, and Q. Li, “Investigation of crosstalk in a 2-view 3D display,” in Proceedings of SID Symposium Dig. Tech. Pap. 39(1), 1138–1141 (2008).
[Crossref]

Dubois, E.

J. Konrad, B. Lacotte, and E. Dubois, “Cancellation of image crosstalk in time-sequential displays of stereoscopic video,” IEEE Trans. Image Process. 9(5), 897–908 (2000).
[Crossref] [PubMed]

Ebrahimi, T.

L. Xing, J. You, T. Ebrahimi, and A. Perkis, “Assessment of stereoscopic crosstalk perception,” IEEE Trans. Multimed. 14(2), 326–337 (2012).
[Crossref]

Franconeri, S. L.

S. L. Franconeri and D. J. Simons, “Moving and looming stimuli capture attention,” Percept. Psychophys. 65(7), 999–1010 (2003).
[Crossref] [PubMed]

Frei, W.

W. Frei, “Image enhancement by histogram hyperbolization,” Comput. Gr. Image Process. 6(3), 286–294 (1977).
[Crossref]

Gross, M.

M. Lang, A. Hornung, O. Wang, S. Poulakos, A. Smolic, and M. Gross, “Nonlinear disparity mapping for stereoscopic 3D,” ACM Trans. Graph. 29(4), 1–10 (2010).
[Crossref]

Hale, J.

A. M. Norcia, J. Hale, M. W. Pettet, S. P. McKee, and R. A. Harrad, “Disparity tuning of binocular facilitation and suppression after normal versus abnormal visual development,” Invest. Ophthalmol. Vis. Sci. 50(3), 1168–1175 (2008).
[Crossref] [PubMed]

Han, T. H.

Harrad, R. A.

A. M. Norcia, J. Hale, M. W. Pettet, S. P. McKee, and R. A. Harrad, “Disparity tuning of binocular facilitation and suppression after normal versus abnormal visual development,” Invest. Ophthalmol. Vis. Sci. 50(3), 1168–1175 (2008).
[Crossref] [PubMed]

Heynderickx, I.

M. Lambooij, W. A. IJsselsteijn, and I. Heynderickx, “Visual discomfort and visual fatigue of stereoscopic displays: a review,” J. Imaging Sci. Technol. 53(3), 030201 (2009).
[Crossref]

Hoffman, D. M.

T. Shibata, J. Kim, D. M. Hoffman, and M. S. Banks, “The zone of comfort: Predicting visual discomfort with stereo displays,” J. Vis. 11(8), 11 (2011).
[Crossref] [PubMed]

Hopf, K.

P. Benzie, J. Watson, P. Surman, I. Rakkolainen, K. Hopf, H. Urey, V. Sainov, and C. Kopylow, “A survey of 3DTV displays: techniques and technologies,” IEEE Trans. Circ. Syst. Video Tech. 17(11), 1647–1658 (2007).
[Crossref]

Hornung, A.

M. Lang, A. Hornung, O. Wang, S. Poulakos, A. Smolic, and M. Gross, “Nonlinear disparity mapping for stereoscopic 3D,” ACM Trans. Graph. 29(4), 1–10 (2010).
[Crossref]

Hsueh, W.-J.

K.-C. Huang, C.-H. Tsai, K. Lee, and W.-J. Hsueh, “Measurement of contrast ratios for 3D display,” Proc. SPIE 4080, 78–86 (2000).
[Crossref]

Huang, J.-F.

Huang, K.-C.

K.-C. Huang, C.-H. Tsai, K. Lee, and W.-J. Hsueh, “Measurement of contrast ratios for 3D display,” Proc. SPIE 4080, 78–86 (2000).
[Crossref]

Hwang, S.-D.

S. Shestak, D.-S. Kim, and S.-D. Hwang, “Measuring of gray-to-gray crosstalk in a LCD based time-sequential stereoscopic displays,” in Proceedings of SID Symposium Dig. Tech. Pap. 41(1), 132–135 (2010).
[Crossref]

IJsselsteijn, W. A.

M. Lambooij, W. A. IJsselsteijn, and I. Heynderickx, “Visual discomfort and visual fatigue of stereoscopic displays: a review,” J. Imaging Sci. Technol. 53(3), 030201 (2009).
[Crossref]

P. J. H. Seuntiëns, L. M. J. Meesters, and W. A. IJsselsteijn, “Perceptual attributes of crosstalk in 3D images,” Displays 26(4–5), 177–183 (2005).
[Crossref]

Itti, L.

L. Itti, “Automatic foveation for video compression using a neurobiological model of visual attention,” IEEE Trans. Image Process. 13(10), 1304–1318 (2004).
[Crossref] [PubMed]

L. Itti, C. Koch, and E. Niebur, “A model of saliency-based visual attention for rapid scene analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 20(11), 1254–1259 (1998).
[Crossref]

Jung, Y. J.

H. Sohn, Y. J. Jung, S. I. Lee, and Y. M. Ro, “Predicting visual discomfort using object size and disparity information in stereoscopic images,” IEEE Trans. Broadcast 59(1), 28–37 (2013).

Y. J. Jung, H. Sohn, S.-i. Lee, F. Speranza, and Y. M. Ro, “Visual importance- and discomfort region-selective low-pass filtering for reducing visual discomfort in stereoscopic displays,” IEEE Trans. Circ. Syst. Video Tech. 23(8), 1408–1421 (2013).
[Crossref]

Y. J. Jung, H. Sohn, S. I. Lee, Y. M. Ro, and H. W. Park, “Quantitative measurement of binocular color fusion limit for non-spectral colors,” Opt. Express 19(8), 7325–7338 (2011).
[Crossref] [PubMed]

Y. J. Jung, H. Sohn, S.-i. Lee, and Y. M. Ro, “Visual comfort improvement in stereoscopic 3-D displays using perceptually plausible assessment metric of visual comfort,” IEEE Trans. Consum. Electron.submitted.

H. Sohn, Y. J. Jung, S.-i. Lee, F. Speranza, and Y. M. Ro, “Visual comfort amelioration technique for stereoscopic image: disparity remapping to mitigate global and local discomfort causes,” IEEE Trans. Circ. Syst. Video Tech. (to be published).

Kang, D.-H.

D.-H. Kang, E.-J. Lee, J.-H. Lee, and J.-K. Song, “Perceptual strength of 3-D crosstalk in both achromatic and color images in stereoscopic 3-D displays,” IEEE Trans. Image Process. 21(7), 3253–3261 (2012).
[Crossref] [PubMed]

Kim, D.-S.

S. Shestak, D.-S. Kim, and S.-D. Hwang, “Measuring of gray-to-gray crosstalk in a LCD based time-sequential stereoscopic displays,” in Proceedings of SID Symposium Dig. Tech. Pap. 41(1), 132–135 (2010).
[Crossref]

Kim, J.

T. Shibata, J. Kim, D. M. Hoffman, and M. S. Banks, “The zone of comfort: Predicting visual discomfort with stereo displays,” J. Vis. 11(8), 11 (2011).
[Crossref] [PubMed]

Koch, C.

L. Itti, C. Koch, and E. Niebur, “A model of saliency-based visual attention for rapid scene analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 20(11), 1254–1259 (1998).
[Crossref]

Konrad, J.

J. Konrad, B. Lacotte, and E. Dubois, “Cancellation of image crosstalk in time-sequential displays of stereoscopic video,” IEEE Trans. Image Process. 9(5), 897–908 (2000).
[Crossref] [PubMed]

Kooi, F. L.

F. L. Kooi and A. Toet, “Visual comfort of binocular and 3D displays,” Displays 25(2–3), 99–108 (2004).
[Crossref]

Kopylow, C.

P. Benzie, J. Watson, P. Surman, I. Rakkolainen, K. Hopf, H. Urey, V. Sainov, and C. Kopylow, “A survey of 3DTV displays: techniques and technologies,” IEEE Trans. Circ. Syst. Video Tech. 17(11), 1647–1658 (2007).
[Crossref]

Lacotte, B.

J. Konrad, B. Lacotte, and E. Dubois, “Cancellation of image crosstalk in time-sequential displays of stereoscopic video,” IEEE Trans. Image Process. 9(5), 897–908 (2000).
[Crossref] [PubMed]

Lambooij, M.

M. Lambooij, W. A. IJsselsteijn, and I. Heynderickx, “Visual discomfort and visual fatigue of stereoscopic displays: a review,” J. Imaging Sci. Technol. 53(3), 030201 (2009).
[Crossref]

Lang, M.

M. Lang, A. Hornung, O. Wang, S. Poulakos, A. Smolic, and M. Gross, “Nonlinear disparity mapping for stereoscopic 3D,” ACM Trans. Graph. 29(4), 1–10 (2010).
[Crossref]

Lee, C.

Lee, E.-J.

D.-H. Kang, E.-J. Lee, J.-H. Lee, and J.-K. Song, “Perceptual strength of 3-D crosstalk in both achromatic and color images in stereoscopic 3-D displays,” IEEE Trans. Image Process. 21(7), 3253–3261 (2012).
[Crossref] [PubMed]

Lee, J.

Lee, J.-H.

D.-H. Kang, E.-J. Lee, J.-H. Lee, and J.-K. Song, “Perceptual strength of 3-D crosstalk in both achromatic and color images in stereoscopic 3-D displays,” IEEE Trans. Image Process. 21(7), 3253–3261 (2012).
[Crossref] [PubMed]

Lee, K.

J.-C. Liou, K. Lee, and J.-F. Huang, “Low crosstalk multi-view tracking 3-D display of synchro-signal LED scanning backlight system,” J. Display Technol. 7(8), 411–419 (2011).
[Crossref]

K.-C. Huang, C.-H. Tsai, K. Lee, and W.-J. Hsueh, “Measurement of contrast ratios for 3D display,” Proc. SPIE 4080, 78–86 (2000).
[Crossref]

Lee, S. I.

H. Sohn, Y. J. Jung, S. I. Lee, and Y. M. Ro, “Predicting visual discomfort using object size and disparity information in stereoscopic images,” IEEE Trans. Broadcast 59(1), 28–37 (2013).

Y. J. Jung, H. Sohn, S. I. Lee, Y. M. Ro, and H. W. Park, “Quantitative measurement of binocular color fusion limit for non-spectral colors,” Opt. Express 19(8), 7325–7338 (2011).
[Crossref] [PubMed]

Lee, S.-i.

Y. J. Jung, H. Sohn, S.-i. Lee, F. Speranza, and Y. M. Ro, “Visual importance- and discomfort region-selective low-pass filtering for reducing visual discomfort in stereoscopic displays,” IEEE Trans. Circ. Syst. Video Tech. 23(8), 1408–1421 (2013).
[Crossref]

Y. J. Jung, H. Sohn, S.-i. Lee, and Y. M. Ro, “Visual comfort improvement in stereoscopic 3-D displays using perceptually plausible assessment metric of visual comfort,” IEEE Trans. Consum. Electron.submitted.

H. Sohn, Y. J. Jung, S.-i. Lee, F. Speranza, and Y. M. Ro, “Visual comfort amelioration technique for stereoscopic image: disparity remapping to mitigate global and local discomfort causes,” IEEE Trans. Circ. Syst. Video Tech. (to be published).

Li, Q.

L. Chen, Y. Tu, W. Liu, and Q. Li, “Investigation of crosstalk in a 2-view 3D display,” in Proceedings of SID Symposium Dig. Tech. Pap. 39(1), 1138–1141 (2008).
[Crossref]

Liou, J.-C.

Lipscomb, J.

J. Lipscomb and W. Wooten, “Reducing crosstalk between stereoscopic views,” Proc. SPIE 2177, 92–96 (1994).
[Crossref]

Liu, W.

L. Chen, Y. Tu, W. Liu, and Q. Li, “Investigation of crosstalk in a 2-view 3D display,” in Proceedings of SID Symposium Dig. Tech. Pap. 39(1), 1138–1141 (2008).
[Crossref]

McKee, S. P.

A. M. Norcia, J. Hale, M. W. Pettet, S. P. McKee, and R. A. Harrad, “Disparity tuning of binocular facilitation and suppression after normal versus abnormal visual development,” Invest. Ophthalmol. Vis. Sci. 50(3), 1168–1175 (2008).
[Crossref] [PubMed]

Meesters, L. M. J.

P. J. H. Seuntiëns, L. M. J. Meesters, and W. A. IJsselsteijn, “Perceptual attributes of crosstalk in 3D images,” Displays 26(4–5), 177–183 (2005).
[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. Mach. Intell. 20(11), 1254–1259 (1998).
[Crossref]

Norcia, A. M.

A. M. Norcia, J. Hale, M. W. Pettet, S. P. McKee, and R. A. Harrad, “Disparity tuning of binocular facilitation and suppression after normal versus abnormal visual development,” Invest. Ophthalmol. Vis. Sci. 50(3), 1168–1175 (2008).
[Crossref] [PubMed]

Park, H. W.

Park, J. G.

Perkis, A.

L. Xing, J. You, T. Ebrahimi, and A. Perkis, “Assessment of stereoscopic crosstalk perception,” IEEE Trans. Multimed. 14(2), 326–337 (2012).
[Crossref]

Pettet, M. W.

A. M. Norcia, J. Hale, M. W. Pettet, S. P. McKee, and R. A. Harrad, “Disparity tuning of binocular facilitation and suppression after normal versus abnormal visual development,” Invest. Ophthalmol. Vis. Sci. 50(3), 1168–1175 (2008).
[Crossref] [PubMed]

Pitas, I.

I. Pitas and A. N. Venetsanopoulos, “Order statistics in digital image processing,” Proc. IEEE 80(12), 1893–1921 (1992).
[Crossref]

Poulakos, S.

M. Lang, A. Hornung, O. Wang, S. Poulakos, A. Smolic, and M. Gross, “Nonlinear disparity mapping for stereoscopic 3D,” ACM Trans. Graph. 29(4), 1–10 (2010).
[Crossref]

Rakkolainen, I.

P. Benzie, J. Watson, P. Surman, I. Rakkolainen, K. Hopf, H. Urey, V. Sainov, and C. Kopylow, “A survey of 3DTV displays: techniques and technologies,” IEEE Trans. Circ. Syst. Video Tech. 17(11), 1647–1658 (2007).
[Crossref]

Ro, Y. M.

H. Sohn, Y. J. Jung, S. I. Lee, and Y. M. Ro, “Predicting visual discomfort using object size and disparity information in stereoscopic images,” IEEE Trans. Broadcast 59(1), 28–37 (2013).

Y. J. Jung, H. Sohn, S.-i. Lee, F. Speranza, and Y. M. Ro, “Visual importance- and discomfort region-selective low-pass filtering for reducing visual discomfort in stereoscopic displays,” IEEE Trans. Circ. Syst. Video Tech. 23(8), 1408–1421 (2013).
[Crossref]

Y. J. Jung, H. Sohn, S. I. Lee, Y. M. Ro, and H. W. Park, “Quantitative measurement of binocular color fusion limit for non-spectral colors,” Opt. Express 19(8), 7325–7338 (2011).
[Crossref] [PubMed]

Y. J. Jung, H. Sohn, S.-i. Lee, and Y. M. Ro, “Visual comfort improvement in stereoscopic 3-D displays using perceptually plausible assessment metric of visual comfort,” IEEE Trans. Consum. Electron.submitted.

H. Sohn, Y. J. Jung, S.-i. Lee, F. Speranza, and Y. M. Ro, “Visual comfort amelioration technique for stereoscopic image: disparity remapping to mitigate global and local discomfort causes,” IEEE Trans. Circ. Syst. Video Tech. (to be published).

Sainov, V.

P. Benzie, J. Watson, P. Surman, I. Rakkolainen, K. Hopf, H. Urey, V. Sainov, and C. Kopylow, “A survey of 3DTV displays: techniques and technologies,” IEEE Trans. Circ. Syst. Video Tech. 17(11), 1647–1658 (2007).
[Crossref]

Seo, G.

Seuntiëns, P. J. H.

P. J. H. Seuntiëns, L. M. J. Meesters, and W. A. IJsselsteijn, “Perceptual attributes of crosstalk in 3D images,” Displays 26(4–5), 177–183 (2005).
[Crossref]

Shestak, S.

S. Shestak, D.-S. Kim, and S.-D. Hwang, “Measuring of gray-to-gray crosstalk in a LCD based time-sequential stereoscopic displays,” in Proceedings of SID Symposium Dig. Tech. Pap. 41(1), 132–135 (2010).
[Crossref]

Shibata, T.

T. Shibata, J. Kim, D. M. Hoffman, and M. S. Banks, “The zone of comfort: Predicting visual discomfort with stereo displays,” J. Vis. 11(8), 11 (2011).
[Crossref] [PubMed]

Silverstein, L. D.

Y.-Y. Yeh and L. D. Silverstein, “Limits of fusion and depth judgment in stereoscopic color displays,” Hum. Factors 32(1), 45–60 (1990).
[Crossref] [PubMed]

Simons, D. J.

S. L. Franconeri and D. J. Simons, “Moving and looming stimuli capture attention,” Percept. Psychophys. 65(7), 999–1010 (2003).
[Crossref] [PubMed]

Smolic, A.

M. Lang, A. Hornung, O. Wang, S. Poulakos, A. Smolic, and M. Gross, “Nonlinear disparity mapping for stereoscopic 3D,” ACM Trans. Graph. 29(4), 1–10 (2010).
[Crossref]

Sohn, H.

H. Sohn, Y. J. Jung, S. I. Lee, and Y. M. Ro, “Predicting visual discomfort using object size and disparity information in stereoscopic images,” IEEE Trans. Broadcast 59(1), 28–37 (2013).

Y. J. Jung, H. Sohn, S.-i. Lee, F. Speranza, and Y. M. Ro, “Visual importance- and discomfort region-selective low-pass filtering for reducing visual discomfort in stereoscopic displays,” IEEE Trans. Circ. Syst. Video Tech. 23(8), 1408–1421 (2013).
[Crossref]

Y. J. Jung, H. Sohn, S. I. Lee, Y. M. Ro, and H. W. Park, “Quantitative measurement of binocular color fusion limit for non-spectral colors,” Opt. Express 19(8), 7325–7338 (2011).
[Crossref] [PubMed]

Y. J. Jung, H. Sohn, S.-i. Lee, and Y. M. Ro, “Visual comfort improvement in stereoscopic 3-D displays using perceptually plausible assessment metric of visual comfort,” IEEE Trans. Consum. Electron.submitted.

H. Sohn, Y. J. Jung, S.-i. Lee, F. Speranza, and Y. M. Ro, “Visual comfort amelioration technique for stereoscopic image: disparity remapping to mitigate global and local discomfort causes,” IEEE Trans. Circ. Syst. Video Tech. (to be published).

Song, J.-K.

D.-H. Kang, E.-J. Lee, J.-H. Lee, and J.-K. Song, “Perceptual strength of 3-D crosstalk in both achromatic and color images in stereoscopic 3-D displays,” IEEE Trans. Image Process. 21(7), 3253–3261 (2012).
[Crossref] [PubMed]

Speranza, F.

Y. J. Jung, H. Sohn, S.-i. Lee, F. Speranza, and Y. M. Ro, “Visual importance- and discomfort region-selective low-pass filtering for reducing visual discomfort in stereoscopic displays,” IEEE Trans. Circ. Syst. Video Tech. 23(8), 1408–1421 (2013).
[Crossref]

H. Sohn, Y. J. Jung, S.-i. Lee, F. Speranza, and Y. M. Ro, “Visual comfort amelioration technique for stereoscopic image: disparity remapping to mitigate global and local discomfort causes,” IEEE Trans. Circ. Syst. Video Tech. (to be published).

Surman, P.

P. Benzie, J. Watson, P. Surman, I. Rakkolainen, K. Hopf, H. Urey, V. Sainov, and C. Kopylow, “A survey of 3DTV displays: techniques and technologies,” IEEE Trans. Circ. Syst. Video Tech. 17(11), 1647–1658 (2007).
[Crossref]

Toet, A.

F. L. Kooi and A. Toet, “Visual comfort of binocular and 3D displays,” Displays 25(2–3), 99–108 (2004).
[Crossref]

Tourancheau, S.

M. Barkowsky, S. Tourancheau, K. Brunnström, K. Wang, and B. Andrén, “Crosstalk measurement of shutter glasses 3D displays,” in Proceedings of SID Symposium Dig. Tech. Pap. 42(1), 812–815 (2011).
[Crossref]

Tsai, C.-H.

K.-C. Huang, C.-H. Tsai, K. Lee, and W.-J. Hsueh, “Measurement of contrast ratios for 3D display,” Proc. SPIE 4080, 78–86 (2000).
[Crossref]

Tsirlin, I.

I. Tsirlin, L. M. Wilcox, and R. S. Allison, “The effect of crosstalk on the perceived depth from disparity and monocular occlusions,” IEEE Trans. Broadcast 57(2), 445–453 (2011).
[Crossref]

Tu, Y.

L. Chen, Y. Tu, W. Liu, and Q. Li, “Investigation of crosstalk in a 2-view 3D display,” in Proceedings of SID Symposium Dig. Tech. Pap. 39(1), 1138–1141 (2008).
[Crossref]

Urey, H.

P. Benzie, J. Watson, P. Surman, I. Rakkolainen, K. Hopf, H. Urey, V. Sainov, and C. Kopylow, “A survey of 3DTV displays: techniques and technologies,” IEEE Trans. Circ. Syst. Video Tech. 17(11), 1647–1658 (2007).
[Crossref]

Venetsanopoulos, A. N.

I. Pitas and A. N. Venetsanopoulos, “Order statistics in digital image processing,” Proc. IEEE 80(12), 1893–1921 (1992).
[Crossref]

Wang, K.

M. Barkowsky, S. Tourancheau, K. Brunnström, K. Wang, and B. Andrén, “Crosstalk measurement of shutter glasses 3D displays,” in Proceedings of SID Symposium Dig. Tech. Pap. 42(1), 812–815 (2011).
[Crossref]

Wang, O.

M. Lang, A. Hornung, O. Wang, S. Poulakos, A. Smolic, and M. Gross, “Nonlinear disparity mapping for stereoscopic 3D,” ACM Trans. Graph. 29(4), 1–10 (2010).
[Crossref]

Watson, J.

P. Benzie, J. Watson, P. Surman, I. Rakkolainen, K. Hopf, H. Urey, V. Sainov, and C. Kopylow, “A survey of 3DTV displays: techniques and technologies,” IEEE Trans. Circ. Syst. Video Tech. 17(11), 1647–1658 (2007).
[Crossref]

Wilcox, L. M.

I. Tsirlin, L. M. Wilcox, and R. S. Allison, “The effect of crosstalk on the perceived depth from disparity and monocular occlusions,” IEEE Trans. Broadcast 57(2), 445–453 (2011).
[Crossref]

Woods, A. J.

A. J. Woods, “Crosstalk in stereoscopic displays: a review,” J. Electron. Imaging 21(4), 040902 (2012).
[Crossref]

Wooten, W.

J. Lipscomb and W. Wooten, “Reducing crosstalk between stereoscopic views,” Proc. SPIE 2177, 92–96 (1994).
[Crossref]

Xing, L.

L. Xing, J. You, T. Ebrahimi, and A. Perkis, “Assessment of stereoscopic crosstalk perception,” IEEE Trans. Multimed. 14(2), 326–337 (2012).
[Crossref]

Yeh, Y.-Y.

Y.-Y. Yeh and L. D. Silverstein, “Limits of fusion and depth judgment in stereoscopic color displays,” Hum. Factors 32(1), 45–60 (1990).
[Crossref] [PubMed]

You, J.

L. Xing, J. You, T. Ebrahimi, and A. Perkis, “Assessment of stereoscopic crosstalk perception,” IEEE Trans. Multimed. 14(2), 326–337 (2012).
[Crossref]

ACM Trans. Graph. (1)

M. Lang, A. Hornung, O. Wang, S. Poulakos, A. Smolic, and M. Gross, “Nonlinear disparity mapping for stereoscopic 3D,” ACM Trans. Graph. 29(4), 1–10 (2010).
[Crossref]

Comput. Gr. Image Process. (1)

W. Frei, “Image enhancement by histogram hyperbolization,” Comput. Gr. Image Process. 6(3), 286–294 (1977).
[Crossref]

Displays (2)

P. J. H. Seuntiëns, L. M. J. Meesters, and W. A. IJsselsteijn, “Perceptual attributes of crosstalk in 3D images,” Displays 26(4–5), 177–183 (2005).
[Crossref]

F. L. Kooi and A. Toet, “Visual comfort of binocular and 3D displays,” Displays 25(2–3), 99–108 (2004).
[Crossref]

Hum. Factors (1)

Y.-Y. Yeh and L. D. Silverstein, “Limits of fusion and depth judgment in stereoscopic color displays,” Hum. Factors 32(1), 45–60 (1990).
[Crossref] [PubMed]

IEEE Trans. Broadcast (2)

I. Tsirlin, L. M. Wilcox, and R. S. Allison, “The effect of crosstalk on the perceived depth from disparity and monocular occlusions,” IEEE Trans. Broadcast 57(2), 445–453 (2011).
[Crossref]

H. Sohn, Y. J. Jung, S. I. Lee, and Y. M. Ro, “Predicting visual discomfort using object size and disparity information in stereoscopic images,” IEEE Trans. Broadcast 59(1), 28–37 (2013).

IEEE Trans. Circ. Syst. Video Tech. (2)

P. Benzie, J. Watson, P. Surman, I. Rakkolainen, K. Hopf, H. Urey, V. Sainov, and C. Kopylow, “A survey of 3DTV displays: techniques and technologies,” IEEE Trans. Circ. Syst. Video Tech. 17(11), 1647–1658 (2007).
[Crossref]

Y. J. Jung, H. Sohn, S.-i. Lee, F. Speranza, and Y. M. Ro, “Visual importance- and discomfort region-selective low-pass filtering for reducing visual discomfort in stereoscopic displays,” IEEE Trans. Circ. Syst. Video Tech. 23(8), 1408–1421 (2013).
[Crossref]

IEEE Trans. Image Process. (3)

D.-H. Kang, E.-J. Lee, J.-H. Lee, and J.-K. Song, “Perceptual strength of 3-D crosstalk in both achromatic and color images in stereoscopic 3-D displays,” IEEE Trans. Image Process. 21(7), 3253–3261 (2012).
[Crossref] [PubMed]

L. Itti, “Automatic foveation for video compression using a neurobiological model of visual attention,” IEEE Trans. Image Process. 13(10), 1304–1318 (2004).
[Crossref] [PubMed]

J. Konrad, B. Lacotte, and E. Dubois, “Cancellation of image crosstalk in time-sequential displays of stereoscopic video,” IEEE Trans. Image Process. 9(5), 897–908 (2000).
[Crossref] [PubMed]

IEEE Trans. Multimed. (1)

L. Xing, J. You, T. Ebrahimi, and A. Perkis, “Assessment of stereoscopic crosstalk perception,” IEEE Trans. Multimed. 14(2), 326–337 (2012).
[Crossref]

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

L. Itti, C. Koch, and E. Niebur, “A model of saliency-based visual attention for rapid scene analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 20(11), 1254–1259 (1998).
[Crossref]

in Proceedings of SID Symposium Dig. Tech. Pap. (3)

S. Shestak, D.-S. Kim, and S.-D. Hwang, “Measuring of gray-to-gray crosstalk in a LCD based time-sequential stereoscopic displays,” in Proceedings of SID Symposium Dig. Tech. Pap. 41(1), 132–135 (2010).
[Crossref]

L. Chen, Y. Tu, W. Liu, and Q. Li, “Investigation of crosstalk in a 2-view 3D display,” in Proceedings of SID Symposium Dig. Tech. Pap. 39(1), 1138–1141 (2008).
[Crossref]

M. Barkowsky, S. Tourancheau, K. Brunnström, K. Wang, and B. Andrén, “Crosstalk measurement of shutter glasses 3D displays,” in Proceedings of SID Symposium Dig. Tech. Pap. 42(1), 812–815 (2011).
[Crossref]

Invest. Ophthalmol. Vis. Sci. (1)

A. M. Norcia, J. Hale, M. W. Pettet, S. P. McKee, and R. A. Harrad, “Disparity tuning of binocular facilitation and suppression after normal versus abnormal visual development,” Invest. Ophthalmol. Vis. Sci. 50(3), 1168–1175 (2008).
[Crossref] [PubMed]

J. Display Technol. (1)

J. Electron. Imaging (1)

A. J. Woods, “Crosstalk in stereoscopic displays: a review,” J. Electron. Imaging 21(4), 040902 (2012).
[Crossref]

J. Imaging Sci. Technol. (1)

M. Lambooij, W. A. IJsselsteijn, and I. Heynderickx, “Visual discomfort and visual fatigue of stereoscopic displays: a review,” J. Imaging Sci. Technol. 53(3), 030201 (2009).
[Crossref]

J. Vis. (1)

T. Shibata, J. Kim, D. M. Hoffman, and M. S. Banks, “The zone of comfort: Predicting visual discomfort with stereo displays,” J. Vis. 11(8), 11 (2011).
[Crossref] [PubMed]

Opt. Express (2)

Percept. Psychophys. (1)

S. L. Franconeri and D. J. Simons, “Moving and looming stimuli capture attention,” Percept. Psychophys. 65(7), 999–1010 (2003).
[Crossref] [PubMed]

Proc. IEEE (1)

I. Pitas and A. N. Venetsanopoulos, “Order statistics in digital image processing,” Proc. IEEE 80(12), 1893–1921 (1992).
[Crossref]

Proc. SPIE (2)

J. Lipscomb and W. Wooten, “Reducing crosstalk between stereoscopic views,” Proc. SPIE 2177, 92–96 (1994).
[Crossref]

K.-C. Huang, C.-H. Tsai, K. Lee, and W.-J. Hsueh, “Measurement of contrast ratios for 3D display,” Proc. SPIE 4080, 78–86 (2000).
[Crossref]

Other (11)

H. Sohn, Y. J. Jung, S.-i. Lee, F. Speranza, and Y. M. Ro, “Visual comfort amelioration technique for stereoscopic image: disparity remapping to mitigate global and local discomfort causes,” IEEE Trans. Circ. Syst. Video Tech. (to be published).

C. Doutre and P. Nasiopoulos, “Crosstalk cancellation in 3D video with local contrast reduction,” in Proceedings of European Signal Processing Conference (2011).

Y. C. Change, C. Y. M, and Y. P. Huang, “Crosstalk suppression by image processing in 3D display,” in Proceeding of SID Symposium.41(1), 124–127 (2010).
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J. V. Baar, S. Poulakos, W. Jarosz, D. Nowrouzezahrai, R. Tamstorf, and M. Gross, “Perceptually-based compensation of light pollution in display systems,” in Proceedings of ACM Symposium on Applied Perception in Graphics and Visualization (2011).

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Y. J. Jung, H. Sohn, S.-i. Lee, and Y. M. Ro, “Visual comfort improvement in stereoscopic 3-D displays using perceptually plausible assessment metric of visual comfort,” IEEE Trans. Consum. Electron.submitted.

ISO/IEC JTC1/SC29/WG11, “Description of exploration experiments in 3D video coding,” Doc. N9991 (2008).

Tanimoto Laboratory FTV test sequences, available: http://www.tanimoto.nuee.nagoya-u.ac.jp .

PanC.-C. et al, “Cross-talk evaluation of shutter-type stereoscopic 3D display,” in Proceedings of SID Symposium Dig. Tech. Pap.41(1), 128–131 (2010).
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Supplementary Material (10)

» Media 1: MOV (895 KB)     
» Media 2: MOV (885 KB)     
» Media 3: MOV (265 KB)     
» Media 4: MOV (246 KB)     
» Media 5: MOV (284 KB)     
» Media 6: MOV (313 KB)     
» Media 7: MOV (1241 KB)     
» Media 8: MOV (957 KB)     
» Media 9: MOV (1121 KB)     
» Media 10: MOV (1171 KB)     

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Figures (14)

Fig. 1
Fig. 1

Crosstalk cancellation with intensity mapping methods: (a) the original image with crosstalk, (b) uncorrectable regions (red color) by the crosstalk cancellation [3,14–16], (c) crosstalk cancellation without an intensity mapping, (d) crosstalk cancellation with the global intensity mapping [14,15], and (e) crosstalk cancellation with the local intensity mapping [15].

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Fig. 2
Fig. 2

The effect of disparity magnitude on the extent of uncorrectable regions. Note that the uncorrectable regions are marked in red color. In these examples, disparity magnitude of the lamp decreases from the left to right figures.

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Fig. 3
Fig. 3

Different visibility of system crosstalk: (a) high intensity object, (b) lower intensity object than (a), and (c) object with brighter background than (a). Note the objects in (a) and (c) have the same intensity, but the system crosstalk in (a) is more visible that that in (c).

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Fig. 4
Fig. 4

The effect of temporal changes of leakage image: (a) change of leakage image on a moving object (see the tire) and (b) change of the extent of crosstalk regions.

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Fig. 5
Fig. 5

Crosstalk visibility weight map: (a) image with system crosstalk, (b) zoomed-in images of (a), (c) original zoomed-in images corresponding to (b), (d) crosstalk visibility weight map, and (e) crosstalk visibility index map. Note that, in the visibility weight map, the larger values (i.e., white) represent higher visibility weights. In addition, in the visibility index map, the larger values (i.e., white) represent that the system crosstalk is more visible around those regions. In this figure, the dashed-line rectangles have larger visibility weights than that of the solid-line rectangle. As shown in (b), the crosstalk is more visible around larger visibility weights (see the short pants), which is also indicated in (e).

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Fig. 6
Fig. 6

Change of uncorrectable regions with varying amounts of disparity shifting: (a) original image (left-view), (b) the image shifted by 0.2 degrees towards the uncrossed disparity direction, and (c) the image shifted by 0.4 degrees towards the uncrossed disparity direction. Note that the uncorrectable regions are marked in light red color. The horizontal boundaries of the images in (b) and (c) were cropped due to the disparity shifting.

Download Full Size | PPT Slide | PDF

Fig. 7
Fig. 7

Examples of the processed image (left-view): (a) the original image with perceived crosstalk (Media 1) and (b) processed image using the proposed disparity adjustment (Media 2), (c) disparity range of the original stereo video, (d) disparity range of the processed stereo video, and (e) comparison of the crosstalk visibility index between the original and processed stereo video. Note that, in (c) and (d), red vertical line represents the frame index where (a) and (b) were captured. Also, note that the disparity shifting in the proposed method displaces the perceived crosstalk occurred on perceptually important regions (see dashed-line rectangles in the figures) to less important regions (see solid-line rectangles in the figures). As shown in (b), the perceived crosstalk occurred on the less important region (i.e., balloon) is less visible and thus less annoying. Note that horizontal boundaries of the image in (b) were cropped due to the disparity shifting.

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Fig. 8
Fig. 8

Examples of the processed image: (a) crosstalk cancellation with the global intensity mapping [14], (b) crosstalk cancellation with the local intensity mapping [15], and (c) the proposed method that combines the disparity adjustment and crosstalk cancellation with the local intensity mapping. Note that horizontal boundaries of the image in (c) were cropped due to the disparity shifting.

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Fig. 9
Fig. 9

Stereoscopic 3D videos used in our experiments.

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Fig. 10
Fig. 10

Measured DMOS of image quality: (a) the proposed method vs. crosstalk cancellation with the global intensity mapping and (b) the proposed method vs. crosstalk cancellation with the local intensity mapping. Note that higher DMOS values represent that the proposed method provides higher image quality.

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Fig. 11
Fig. 11

Comparison of the assessment results for viewing preference: (a) the proposed method vs. crosstalk cancellation with the global intensity mapping and (b) the proposed method vs. crosstalk cancellation with the local intensity mapping.

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Fig. 12
Fig. 12

Examples of the processed videos (left-view): (a) original video (Eiffel tower) (Media 3), (b) crosstalk cancellation with the global intensity mapping (Media 4), (c) crosstalk cancellation with the local intensity mapping (Media 5), and (d) the proposed method (Media 6). Note that horizontal boundaries of the images in (d) were cropped due to the disparity shifting.

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Fig. 13
Fig. 13

Additional examples of the processed videos (left-view): (a) original video (Pantomime) (Media 7), (b) crosstalk cancellation with the global intensity mapping (Media 8), (c) crosstalk cancellation with the local intensity mapping (Media 9), and (d) the proposed method (Media 10).

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Fig. 14
Fig. 14

Crosstalk visibility index of the processed stereo videos: (a) Eiffel tower and (b) Pantomime.

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Tables (1)

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Table 1 Statistical results of subjective assessment for image quality.

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Equations (6)

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

Q(n)= 1 | R | ∑ x,y∈R L(x,y,n)⋅V(x,y,n),
V S (x,y,n)=−log( M I (x,y,n)+γ),
V T ( x , y , n ) = | M U ( x , y , n ) − M U ( x , y , n − 1 ) | ,
V= w S ⋅ V ′ S + w T ⋅ V ′ T , where w S + w T =1,
H(n)= argmin h Q h (n), for h min <h< h max ,
Q h (n)= 1 | R h | ∑ x,y∈ R h α M ′ U h (x,y,n)⋅ V h (x,y,n),

Metrics