Abstract

Due to the limitations of micro lens arrays and camera sensors, images on display devices through the integral imaging microscope systems have been suffering for a low-resolution. In this paper, a resolution-enhanced orthographic-view image display method for integral imaging microscopy is proposed and demonstrated. Iterative intermediate-view reconstructions are performed based on bilinear interpolation using neighborhood elemental image information, and a graphics processing unit parallel processing algorithm is applied for fast image processing. The proposed method is verified experimentally and the effective results are presented in this paper.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Real-time interactive display for integral imaging microscopy

Ki-Chul Kwon, Ji-Seong Jeong, Munkh-Uchral Erdenebat, Young-Tae Lim, Kwan-Hee Yoo, and Nam Kim
Appl. Opt. 53(20) 4450-4459 (2014)

Integral imaging microscopy with enhanced depth-of-field using a spatial multiplexing

Ki-Chul Kwon, Munkh-Uchral Erdenebat, Md. Ashraful Alam, Young-Tae Lim, Kwang Gi Kim, and Nam Kim
Opt. Express 24(3) 2072-2083 (2016)

Enhancement of the depth-of-field of integral imaging microscope by using switchable bifocal liquid-crystalline polymer micro lens array

Ki-Chul Kwon, Munkh-Uchral Erdenebat, Young-Tae Lim, Kyung-Il Joo, Min-Kyu Park, Heewon Park, Jong-Rae Jeong, Hak-Rin Kim, and Nam Kim
Opt. Express 25(24) 30503-30512 (2017)

References

  • View by:
  • |
  • |
  • |

  1. B. Herman and J. J. Lemasters, Optical microscopy: Emerging methods and applications (Academic, 1985).
  2. K.-C. Kwon, Y.-T. Lim, N. Kim, K.-H. Yoo, J.-M. Hong, and G.-C. Park, “High-definition 3D stereoscopic microscope display system for biomedical applications,” EURASIP J. Image Video Process. 2010, 1–8 (2010).
    [Crossref]
  3. M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM SIGGRAPH 25(3), 924–934 (2006).
    [Crossref]
  4. M. Levoy, Z. Zhang, and I. McDowall, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc. 235(2), 144–162 (2009).
    [Crossref] [PubMed]
  5. G. Lippmann, “La photographie integrale,” C. R. Acad. Sci. 146, 446–451 (1908).
  6. J.-H. Park, K. Hong, and B. Lee, “Recent progress in three-dimensional information processing based on integral imaging,” Appl. Opt. 48(34), H77–H94 (2009).
    [Crossref] [PubMed]
  7. N. Kim, A.-H. Phan, M.-U. Erdenebat, M. A. Alam, K.-C. Kwon, M.-L. Piao, and J.-H. Lee, “3D display technology,” Disp. Imag. 1, 73–95 (2014).
  8. N. Kim, M. A. Alam, L. T. Bang, A.-P. Phan, M.-L. Piao, and M.-U. Erdenebat, “Advances in the light field displays based on integral imaging and holographic techniques,” Chin. Opt. Lett. 12, 060005 (2014).
    [Crossref]
  9. J.-S. Jang and B. Javidi, “Three-dimensional integral imaging of micro-objects,” Opt. Lett. 29(11), 1230–1232 (2004).
    [Crossref] [PubMed]
  10. L. Erdmann and K. J. Gabriel, “High-resolution digital integral photography by use of a scanning microlens array,” Appl. Opt. 40(31), 5592–5599 (2001).
    [Crossref] [PubMed]
  11. J.-S. Jang and B. Javidi, “Improved viewing resolution of three-dimensional integral imaging by use of nonstationary micro-optics,” Opt. Lett. 27(5), 324–326 (2002).
    [Crossref] [PubMed]
  12. S. Kishk and B. Javidi, “Improved resolution 3D object sensing and recognition using time multiplexed computational integral imaging,” Opt. Express 11(26), 3528–3541 (2003).
    [Crossref] [PubMed]
  13. Y.-T. Lim, J.-H. Park, K.-C. Kwon, and N. Kim, “Resolution-enhanced integral imaging microscopy that uses lens array shifting,” Opt. Express 17(21), 19253–19263 (2009).
    [Crossref] [PubMed]
  14. K.-H. Bae and E.-S. Kim, “New disparity estimation scheme based on adaptive matching windows for intermediate view reconstruction,” Opt. Eng. 42(6), 1778–1786 (2003).
    [Crossref]
  15. D.-C. Hwang, J.-S. Park, S.-C. Kim, D.-H. Shin, and E.-S. Kim, “Magnification of 3D reconstructed images in integral imaging using an intermediate-view reconstruction technique,” Appl. Opt. 45(19), 4631–4637 (2006).
    [Crossref] [PubMed]
  16. S. Zhu and Y. Yu, “Intermediate view synthesis based on disparity estimation and image interpolation,” in Proceedings of IEEE International Conference on Computer Science and Information Processing (IEEE, 2012), pp. 1035–1038.
  17. K.-C. Kwon, J.-S. Jeong, M.-U. Erdenebat, Y.-T. Lim, K.-H. Yoo, and N. Kim, “Real-time interactive display for integral imaging microscopy,” Appl. Opt. 53(20), 4450–4459 (2014).
    [Crossref] [PubMed]
  18. K.-C. Kwon, C. Park, M.-U. Erdenebat, J.-S. Jeong, J.-H. Choi, N. Kim, J.-H. Park, Y.-T. Lim, and K.-H. Yoo, “High speed image space parallel processing for computer-generated integral imaging system,” Opt. Express 20(2), 732–740 (2012).
    [Crossref] [PubMed]
  19. D.-H. Kim, M.-U. Erdenebat, K.-C. Kwon, J.-S. Jeong, J.-W. Lee, K.-A. Kim, N. Kim, and K.-H. Yoo, “Real-time 3D display system based on computer-generated integral imaging technique using enhanced ISPP for hexagonal lens array,” Appl. Opt. 52(34), 8411–8418 (2013).
    [Crossref] [PubMed]
  20. J.-S. Jeong, K.-C. Kwon, M.-U. Erdenebat, Y. Piao, N. Kim, and K.-H. Yoo, “Development of a real-time integral imaging display system based on graphics processing unit parallel processing using a depth camera,” Opt. Eng. 53(1), 015103 (2014).
    [Crossref]
  21. A. M. Eskicioglu and P. S. Fisher, “Image quality measures and their performance,” IEEE Trans. Commun. 43(12), 2959–2965 (1995).
    [Crossref]

2014 (4)

N. Kim, A.-H. Phan, M.-U. Erdenebat, M. A. Alam, K.-C. Kwon, M.-L. Piao, and J.-H. Lee, “3D display technology,” Disp. Imag. 1, 73–95 (2014).

J.-S. Jeong, K.-C. Kwon, M.-U. Erdenebat, Y. Piao, N. Kim, and K.-H. Yoo, “Development of a real-time integral imaging display system based on graphics processing unit parallel processing using a depth camera,” Opt. Eng. 53(1), 015103 (2014).
[Crossref]

N. Kim, M. A. Alam, L. T. Bang, A.-P. Phan, M.-L. Piao, and M.-U. Erdenebat, “Advances in the light field displays based on integral imaging and holographic techniques,” Chin. Opt. Lett. 12, 060005 (2014).
[Crossref]

K.-C. Kwon, J.-S. Jeong, M.-U. Erdenebat, Y.-T. Lim, K.-H. Yoo, and N. Kim, “Real-time interactive display for integral imaging microscopy,” Appl. Opt. 53(20), 4450–4459 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (1)

2010 (1)

K.-C. Kwon, Y.-T. Lim, N. Kim, K.-H. Yoo, J.-M. Hong, and G.-C. Park, “High-definition 3D stereoscopic microscope display system for biomedical applications,” EURASIP J. Image Video Process. 2010, 1–8 (2010).
[Crossref]

2009 (3)

2006 (2)

2004 (1)

2003 (2)

S. Kishk and B. Javidi, “Improved resolution 3D object sensing and recognition using time multiplexed computational integral imaging,” Opt. Express 11(26), 3528–3541 (2003).
[Crossref] [PubMed]

K.-H. Bae and E.-S. Kim, “New disparity estimation scheme based on adaptive matching windows for intermediate view reconstruction,” Opt. Eng. 42(6), 1778–1786 (2003).
[Crossref]

2002 (1)

2001 (1)

1995 (1)

A. M. Eskicioglu and P. S. Fisher, “Image quality measures and their performance,” IEEE Trans. Commun. 43(12), 2959–2965 (1995).
[Crossref]

1908 (1)

G. Lippmann, “La photographie integrale,” C. R. Acad. Sci. 146, 446–451 (1908).

Adams, A.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM SIGGRAPH 25(3), 924–934 (2006).
[Crossref]

Alam, M. A.

N. Kim, A.-H. Phan, M.-U. Erdenebat, M. A. Alam, K.-C. Kwon, M.-L. Piao, and J.-H. Lee, “3D display technology,” Disp. Imag. 1, 73–95 (2014).

N. Kim, M. A. Alam, L. T. Bang, A.-P. Phan, M.-L. Piao, and M.-U. Erdenebat, “Advances in the light field displays based on integral imaging and holographic techniques,” Chin. Opt. Lett. 12, 060005 (2014).
[Crossref]

Bae, K.-H.

K.-H. Bae and E.-S. Kim, “New disparity estimation scheme based on adaptive matching windows for intermediate view reconstruction,” Opt. Eng. 42(6), 1778–1786 (2003).
[Crossref]

Bang, L. T.

Choi, J.-H.

Erdenebat, M.-U.

Erdmann, L.

Eskicioglu, A. M.

A. M. Eskicioglu and P. S. Fisher, “Image quality measures and their performance,” IEEE Trans. Commun. 43(12), 2959–2965 (1995).
[Crossref]

Fisher, P. S.

A. M. Eskicioglu and P. S. Fisher, “Image quality measures and their performance,” IEEE Trans. Commun. 43(12), 2959–2965 (1995).
[Crossref]

Footer, M.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM SIGGRAPH 25(3), 924–934 (2006).
[Crossref]

Gabriel, K. J.

Hong, J.-M.

K.-C. Kwon, Y.-T. Lim, N. Kim, K.-H. Yoo, J.-M. Hong, and G.-C. Park, “High-definition 3D stereoscopic microscope display system for biomedical applications,” EURASIP J. Image Video Process. 2010, 1–8 (2010).
[Crossref]

Hong, K.

Horowitz, M.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM SIGGRAPH 25(3), 924–934 (2006).
[Crossref]

Hwang, D.-C.

Jang, J.-S.

Javidi, B.

Jeong, J.-S.

Kim, D.-H.

Kim, E.-S.

D.-C. Hwang, J.-S. Park, S.-C. Kim, D.-H. Shin, and E.-S. Kim, “Magnification of 3D reconstructed images in integral imaging using an intermediate-view reconstruction technique,” Appl. Opt. 45(19), 4631–4637 (2006).
[Crossref] [PubMed]

K.-H. Bae and E.-S. Kim, “New disparity estimation scheme based on adaptive matching windows for intermediate view reconstruction,” Opt. Eng. 42(6), 1778–1786 (2003).
[Crossref]

Kim, K.-A.

Kim, N.

N. Kim, M. A. Alam, L. T. Bang, A.-P. Phan, M.-L. Piao, and M.-U. Erdenebat, “Advances in the light field displays based on integral imaging and holographic techniques,” Chin. Opt. Lett. 12, 060005 (2014).
[Crossref]

J.-S. Jeong, K.-C. Kwon, M.-U. Erdenebat, Y. Piao, N. Kim, and K.-H. Yoo, “Development of a real-time integral imaging display system based on graphics processing unit parallel processing using a depth camera,” Opt. Eng. 53(1), 015103 (2014).
[Crossref]

N. Kim, A.-H. Phan, M.-U. Erdenebat, M. A. Alam, K.-C. Kwon, M.-L. Piao, and J.-H. Lee, “3D display technology,” Disp. Imag. 1, 73–95 (2014).

K.-C. Kwon, J.-S. Jeong, M.-U. Erdenebat, Y.-T. Lim, K.-H. Yoo, and N. Kim, “Real-time interactive display for integral imaging microscopy,” Appl. Opt. 53(20), 4450–4459 (2014).
[Crossref] [PubMed]

D.-H. Kim, M.-U. Erdenebat, K.-C. Kwon, J.-S. Jeong, J.-W. Lee, K.-A. Kim, N. Kim, and K.-H. Yoo, “Real-time 3D display system based on computer-generated integral imaging technique using enhanced ISPP for hexagonal lens array,” Appl. Opt. 52(34), 8411–8418 (2013).
[Crossref] [PubMed]

K.-C. Kwon, C. Park, M.-U. Erdenebat, J.-S. Jeong, J.-H. Choi, N. Kim, J.-H. Park, Y.-T. Lim, and K.-H. Yoo, “High speed image space parallel processing for computer-generated integral imaging system,” Opt. Express 20(2), 732–740 (2012).
[Crossref] [PubMed]

K.-C. Kwon, Y.-T. Lim, N. Kim, K.-H. Yoo, J.-M. Hong, and G.-C. Park, “High-definition 3D stereoscopic microscope display system for biomedical applications,” EURASIP J. Image Video Process. 2010, 1–8 (2010).
[Crossref]

Y.-T. Lim, J.-H. Park, K.-C. Kwon, and N. Kim, “Resolution-enhanced integral imaging microscopy that uses lens array shifting,” Opt. Express 17(21), 19253–19263 (2009).
[Crossref] [PubMed]

Kim, S.-C.

Kishk, S.

Kwon, K.-C.

J.-S. Jeong, K.-C. Kwon, M.-U. Erdenebat, Y. Piao, N. Kim, and K.-H. Yoo, “Development of a real-time integral imaging display system based on graphics processing unit parallel processing using a depth camera,” Opt. Eng. 53(1), 015103 (2014).
[Crossref]

N. Kim, A.-H. Phan, M.-U. Erdenebat, M. A. Alam, K.-C. Kwon, M.-L. Piao, and J.-H. Lee, “3D display technology,” Disp. Imag. 1, 73–95 (2014).

K.-C. Kwon, J.-S. Jeong, M.-U. Erdenebat, Y.-T. Lim, K.-H. Yoo, and N. Kim, “Real-time interactive display for integral imaging microscopy,” Appl. Opt. 53(20), 4450–4459 (2014).
[Crossref] [PubMed]

D.-H. Kim, M.-U. Erdenebat, K.-C. Kwon, J.-S. Jeong, J.-W. Lee, K.-A. Kim, N. Kim, and K.-H. Yoo, “Real-time 3D display system based on computer-generated integral imaging technique using enhanced ISPP for hexagonal lens array,” Appl. Opt. 52(34), 8411–8418 (2013).
[Crossref] [PubMed]

K.-C. Kwon, C. Park, M.-U. Erdenebat, J.-S. Jeong, J.-H. Choi, N. Kim, J.-H. Park, Y.-T. Lim, and K.-H. Yoo, “High speed image space parallel processing for computer-generated integral imaging system,” Opt. Express 20(2), 732–740 (2012).
[Crossref] [PubMed]

K.-C. Kwon, Y.-T. Lim, N. Kim, K.-H. Yoo, J.-M. Hong, and G.-C. Park, “High-definition 3D stereoscopic microscope display system for biomedical applications,” EURASIP J. Image Video Process. 2010, 1–8 (2010).
[Crossref]

Y.-T. Lim, J.-H. Park, K.-C. Kwon, and N. Kim, “Resolution-enhanced integral imaging microscopy that uses lens array shifting,” Opt. Express 17(21), 19253–19263 (2009).
[Crossref] [PubMed]

Lee, B.

Lee, J.-H.

N. Kim, A.-H. Phan, M.-U. Erdenebat, M. A. Alam, K.-C. Kwon, M.-L. Piao, and J.-H. Lee, “3D display technology,” Disp. Imag. 1, 73–95 (2014).

Lee, J.-W.

Levoy, M.

M. Levoy, Z. Zhang, and I. McDowall, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc. 235(2), 144–162 (2009).
[Crossref] [PubMed]

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM SIGGRAPH 25(3), 924–934 (2006).
[Crossref]

Lim, Y.-T.

Lippmann, G.

G. Lippmann, “La photographie integrale,” C. R. Acad. Sci. 146, 446–451 (1908).

McDowall, I.

M. Levoy, Z. Zhang, and I. McDowall, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc. 235(2), 144–162 (2009).
[Crossref] [PubMed]

Ng, R.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM SIGGRAPH 25(3), 924–934 (2006).
[Crossref]

Park, C.

Park, G.-C.

K.-C. Kwon, Y.-T. Lim, N. Kim, K.-H. Yoo, J.-M. Hong, and G.-C. Park, “High-definition 3D stereoscopic microscope display system for biomedical applications,” EURASIP J. Image Video Process. 2010, 1–8 (2010).
[Crossref]

Park, J.-H.

Park, J.-S.

Phan, A.-H.

N. Kim, A.-H. Phan, M.-U. Erdenebat, M. A. Alam, K.-C. Kwon, M.-L. Piao, and J.-H. Lee, “3D display technology,” Disp. Imag. 1, 73–95 (2014).

Phan, A.-P.

Piao, M.-L.

N. Kim, M. A. Alam, L. T. Bang, A.-P. Phan, M.-L. Piao, and M.-U. Erdenebat, “Advances in the light field displays based on integral imaging and holographic techniques,” Chin. Opt. Lett. 12, 060005 (2014).
[Crossref]

N. Kim, A.-H. Phan, M.-U. Erdenebat, M. A. Alam, K.-C. Kwon, M.-L. Piao, and J.-H. Lee, “3D display technology,” Disp. Imag. 1, 73–95 (2014).

Piao, Y.

J.-S. Jeong, K.-C. Kwon, M.-U. Erdenebat, Y. Piao, N. Kim, and K.-H. Yoo, “Development of a real-time integral imaging display system based on graphics processing unit parallel processing using a depth camera,” Opt. Eng. 53(1), 015103 (2014).
[Crossref]

Shin, D.-H.

Yoo, K.-H.

Zhang, Z.

M. Levoy, Z. Zhang, and I. McDowall, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc. 235(2), 144–162 (2009).
[Crossref] [PubMed]

ACM SIGGRAPH (1)

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM SIGGRAPH 25(3), 924–934 (2006).
[Crossref]

Appl. Opt. (5)

C. R. Acad. Sci. (1)

G. Lippmann, “La photographie integrale,” C. R. Acad. Sci. 146, 446–451 (1908).

Chin. Opt. Lett. (1)

Disp. Imag. (1)

N. Kim, A.-H. Phan, M.-U. Erdenebat, M. A. Alam, K.-C. Kwon, M.-L. Piao, and J.-H. Lee, “3D display technology,” Disp. Imag. 1, 73–95 (2014).

EURASIP J. Image Video Process. (1)

K.-C. Kwon, Y.-T. Lim, N. Kim, K.-H. Yoo, J.-M. Hong, and G.-C. Park, “High-definition 3D stereoscopic microscope display system for biomedical applications,” EURASIP J. Image Video Process. 2010, 1–8 (2010).
[Crossref]

IEEE Trans. Commun. (1)

A. M. Eskicioglu and P. S. Fisher, “Image quality measures and their performance,” IEEE Trans. Commun. 43(12), 2959–2965 (1995).
[Crossref]

J. Microsc. (1)

M. Levoy, Z. Zhang, and I. McDowall, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc. 235(2), 144–162 (2009).
[Crossref] [PubMed]

Opt. Eng. (2)

K.-H. Bae and E.-S. Kim, “New disparity estimation scheme based on adaptive matching windows for intermediate view reconstruction,” Opt. Eng. 42(6), 1778–1786 (2003).
[Crossref]

J.-S. Jeong, K.-C. Kwon, M.-U. Erdenebat, Y. Piao, N. Kim, and K.-H. Yoo, “Development of a real-time integral imaging display system based on graphics processing unit parallel processing using a depth camera,” Opt. Eng. 53(1), 015103 (2014).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Other (2)

S. Zhu and Y. Yu, “Intermediate view synthesis based on disparity estimation and image interpolation,” in Proceedings of IEEE International Conference on Computer Science and Information Processing (IEEE, 2012), pp. 1035–1038.

B. Herman and J. J. Lemasters, Optical microscopy: Emerging methods and applications (Academic, 1985).

Supplementary Material (5)

» Media 1: MP4 (3917 KB)     
» Media 2: MP4 (4186 KB)     
» Media 3: MP4 (5085 KB)     
» Media 4: MP4 (4169 KB)     
» Media 5: MP4 (4794 KB)     

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

Schematic configuration for the optical structure of the integral imaging microscope.

Fig. 2
Fig. 2

Schematic diagram for the geometry of the integral imaging pickup system.

Fig. 3
Fig. 3

Flowchart of the proposed interpolation-based resolution-enhancing method for the IIM.

Fig. 4
Fig. 4

Schematic diagram of the IVR generation method based on bilinear interpolation.

Fig. 5
Fig. 5

The reconstruction process for each directional-view image based on the resolution-enhanced EIA.

Fig. 6
Fig. 6

Example of resolution enhancement in the IIM by the proposed method. (a) The skin of a bronchial tube imaged through a conventional microscope, (b) the original EIA captured by the IIM, (c) a resolution-enhanced EIA via three times of iterative IVR, (d) the orthographic-view image based on the initially captured EIA, and (e) the orthographic-view image based on the resolution-enhanced EIA. Note that the directional-view image at 65 × 65 pixels in the (d) and at 513 × 513 pixels in the (e).

Fig. 7
Fig. 7

(a) Prototype IIM for the proposed resolution-enhancing method consisting of the IIM and camera, a PC and an LCD. (b) The initially captured EIA (smallest image, bottom left) and resolution-enhanced EIAs after iterative interpolation processes, and (c) reconstructed orthographic-view images based on the corresponding EIAs.

Fig. 8
Fig. 8

Experimental results for evaluation of the IIM and the displayed directional-view images: (a) dayfly, (b) fruit fly, (c) the eye of a fruit fly, (d) the skin of a bronchial tube, and (e) an enlarged area of skin from the bronchial tube.

Fig. 9
Fig. 9

Graphs of processing time for resolution-enhanced II by using (a) CPU and (b) GPU.

Fig. 10
Fig. 10

The PSNR value for the objects listed in the Table 2 up to 5 iterations of the bilinear interpolation process.

Fig. 11
Fig. 11

The example of the comparison of the directional-view image display between the original and the proposed resolution-enhancing method (Media 1: Dayfly; Media 2: Fruit fly; Media 3: The eye of a fruit fly; Media 4: The skin of a bronchial tube: Media 5: An enlarged area of skin from the bronchial tube).

Tables (2)

Tables Icon

Table 1 Specifications for the proposed prototype IIM system.

Tables Icon

Table 2 PSNR and IF value for the proposed resolution-enhanced IIM.

Equations (4)

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

y q = g( qPy ) z
Δ y q = y q1 y q2 = gP( q 1 q 2 ) z
{ E I IVT =( 1α )×E I TL +α×E I TR ,( 0α1 ) E I IVB =( 1α )×E I BL +α×E I BR ,( 0α1 )
{ E I IVC =( 1β )×E I IVT +β×E I IVB ,( 0β1 ) E I IVL =( 1β )×E I TL +β×E I BL ,( 0β1 ) E I IVR =( 1β )×E I TR +β×E I BR ,( 0β1 )

Metrics