Abstract

In this paper, we proposed a new method for analyzing the image formation of a prism. The prism was considered as a single optical system composed of some planes. By analyzing each plane individually and then combining them together, we derived a transformation matrix which can express the relationship between an object point and its image by the refraction of a prism. We also explained how to use this matrix for epipolar geometry and three-dimensional point reconstruction. Our method is based on optical geometry and could be used in a multiocular prism. Experimentation results are presented to prove the accuracy of our method is better than former researchers’ and is comparable with that of the multicamera stereovision system.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. Wheatstone, “Contributions to the physiology of vision-part the first. On some remarkable, and hitherto unobserved, phenomena of binocular vision,” Philos. Trans. R. Soc. London 128, 371–394 (1838).
    [CrossRef]
  2. J. A. Kalomiros and J. Lygouras, “Design and hardware implementation of a stereo-matching system based on dynamic programming,” Microprocess. Microsyst. 35, 496–509 (2011).
    [CrossRef]
  3. L. Cai, L. He, Y. Xu, Y. Zhao, and X. Yang, “Multi-object detection and tracking by stereo vision,” Pattern Recogn. 43, 4028–4041 (2010).
    [CrossRef]
  4. J. Swgen and S. Kumar, “Shadow gestures: 3D hand poses estimation using a single camera,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1999), pp. 479–485.
  5. X. Cao and H. Foroosh, “Camera calibration and light source orientation from solar shadows,” Comput. Vis. Image Underst. 105, 60–72 (2007).
    [CrossRef]
  6. Q. Z. Ye, S. H. Ong, and X. Han, “A stereovision system for the inspection of IC bonding wires,” Int. J. Imaging Syst. Technol. 11, 254–262 (2000).
    [CrossRef]
  7. Y. Nishimoto and Y. Shirai, “A feature-based stereo model using small disparities histograms of multi-resolution channels,” Adv. Robot. 3, 17–33 (1988).
    [CrossRef]
  8. W. Teoh and X. D. Zhang, “An inexpensive stereoscopic vision system for robots,” in Proceedings of IEEE International Conference on Robotics and Automation (IEEE, 1984), pp. 186–189.
  9. A. Goshtasby and W. A. Gruver, “Design of a single-lens stereo camera system,” Pattern Recogn. 26, 923–937 (1993).
    [CrossRef]
  10. D. H. Lee, I. Kweon, and R. Cipolla, “Single lens stereo with a biprism,” in Proceedings of IAPR Workshop on Machine Vision Applications (1998), pp. 17–19.
  11. D. H. Lee, I. Kweon, and R. Cipolla, “A biprism-stereo camera system,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1999), pp. 82–87.
  12. D. H. Lee and I. Kweon, “A novel stereo camera system by a biprism,” IEEE Trans. Robot. Autom. 16, 528–541 (2000).
    [CrossRef]
  13. K. B. Lim and Y. Xiao, “Virtual stereovision system: new understanding on single-lens stereovision using a biprism,” J. Electron. Imaging 14, 043020 (2005).
    [CrossRef]
  14. C. Y. Chen, T.-T. Yang, and W. S. Sun, “Optics system design applying a micro-prism array of a single lens stereo image pair,” Opt. Express 16, 15495–15505 (2008).
    [CrossRef]
  15. F. A. Hankins and H. E. White, Fundamentals of Optics (McGraw-Hill, 1976), pp. 30–31.
  16. Y. Xiao and K. B. Lim, “A prism-based single-lens stereovision system: from trinocular to multi-ocular,” Image Vis. Comput. 25, 1725–1736 (2007).
    [CrossRef]
  17. R. Wang, X. Li, and Y. Zhang, “Analysis and optimization of the stereo system with a four-mirror adapter,” J. Eur. Opt. Soc. 3, 1–7 (2008).
  18. M. Bass and W. V. Stryland, Handbook of Optics II (McGraw-Hill, 1995).
  19. E. Hecht, Theory and Problems of Optics, Schaum’s Outline Series (McGraw-Hill, 1975), pp. 142–143.
  20. M. J. Zhao and K. B. Lim, “Stereo matching of single-lens bi-prism based stereovision system,” in Proceedings of the 2010 International Conference on Future Information Technology (2010), pp. 179–183.
  21. Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334(2000).
    [CrossRef]

2011

J. A. Kalomiros and J. Lygouras, “Design and hardware implementation of a stereo-matching system based on dynamic programming,” Microprocess. Microsyst. 35, 496–509 (2011).
[CrossRef]

2010

L. Cai, L. He, Y. Xu, Y. Zhao, and X. Yang, “Multi-object detection and tracking by stereo vision,” Pattern Recogn. 43, 4028–4041 (2010).
[CrossRef]

2008

C. Y. Chen, T.-T. Yang, and W. S. Sun, “Optics system design applying a micro-prism array of a single lens stereo image pair,” Opt. Express 16, 15495–15505 (2008).
[CrossRef]

R. Wang, X. Li, and Y. Zhang, “Analysis and optimization of the stereo system with a four-mirror adapter,” J. Eur. Opt. Soc. 3, 1–7 (2008).

2007

Y. Xiao and K. B. Lim, “A prism-based single-lens stereovision system: from trinocular to multi-ocular,” Image Vis. Comput. 25, 1725–1736 (2007).
[CrossRef]

X. Cao and H. Foroosh, “Camera calibration and light source orientation from solar shadows,” Comput. Vis. Image Underst. 105, 60–72 (2007).
[CrossRef]

2005

K. B. Lim and Y. Xiao, “Virtual stereovision system: new understanding on single-lens stereovision using a biprism,” J. Electron. Imaging 14, 043020 (2005).
[CrossRef]

2000

D. H. Lee and I. Kweon, “A novel stereo camera system by a biprism,” IEEE Trans. Robot. Autom. 16, 528–541 (2000).
[CrossRef]

Q. Z. Ye, S. H. Ong, and X. Han, “A stereovision system for the inspection of IC bonding wires,” Int. J. Imaging Syst. Technol. 11, 254–262 (2000).
[CrossRef]

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334(2000).
[CrossRef]

1993

A. Goshtasby and W. A. Gruver, “Design of a single-lens stereo camera system,” Pattern Recogn. 26, 923–937 (1993).
[CrossRef]

1988

Y. Nishimoto and Y. Shirai, “A feature-based stereo model using small disparities histograms of multi-resolution channels,” Adv. Robot. 3, 17–33 (1988).
[CrossRef]

1838

C. Wheatstone, “Contributions to the physiology of vision-part the first. On some remarkable, and hitherto unobserved, phenomena of binocular vision,” Philos. Trans. R. Soc. London 128, 371–394 (1838).
[CrossRef]

Bass, M.

M. Bass and W. V. Stryland, Handbook of Optics II (McGraw-Hill, 1995).

Cai, L.

L. Cai, L. He, Y. Xu, Y. Zhao, and X. Yang, “Multi-object detection and tracking by stereo vision,” Pattern Recogn. 43, 4028–4041 (2010).
[CrossRef]

Cao, X.

X. Cao and H. Foroosh, “Camera calibration and light source orientation from solar shadows,” Comput. Vis. Image Underst. 105, 60–72 (2007).
[CrossRef]

Chen, C. Y.

Cipolla, R.

D. H. Lee, I. Kweon, and R. Cipolla, “Single lens stereo with a biprism,” in Proceedings of IAPR Workshop on Machine Vision Applications (1998), pp. 17–19.

D. H. Lee, I. Kweon, and R. Cipolla, “A biprism-stereo camera system,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1999), pp. 82–87.

Foroosh, H.

X. Cao and H. Foroosh, “Camera calibration and light source orientation from solar shadows,” Comput. Vis. Image Underst. 105, 60–72 (2007).
[CrossRef]

Goshtasby, A.

A. Goshtasby and W. A. Gruver, “Design of a single-lens stereo camera system,” Pattern Recogn. 26, 923–937 (1993).
[CrossRef]

Gruver, W. A.

A. Goshtasby and W. A. Gruver, “Design of a single-lens stereo camera system,” Pattern Recogn. 26, 923–937 (1993).
[CrossRef]

Han, X.

Q. Z. Ye, S. H. Ong, and X. Han, “A stereovision system for the inspection of IC bonding wires,” Int. J. Imaging Syst. Technol. 11, 254–262 (2000).
[CrossRef]

Hankins, F. A.

F. A. Hankins and H. E. White, Fundamentals of Optics (McGraw-Hill, 1976), pp. 30–31.

He, L.

L. Cai, L. He, Y. Xu, Y. Zhao, and X. Yang, “Multi-object detection and tracking by stereo vision,” Pattern Recogn. 43, 4028–4041 (2010).
[CrossRef]

Hecht, E.

E. Hecht, Theory and Problems of Optics, Schaum’s Outline Series (McGraw-Hill, 1975), pp. 142–143.

Kalomiros, J. A.

J. A. Kalomiros and J. Lygouras, “Design and hardware implementation of a stereo-matching system based on dynamic programming,” Microprocess. Microsyst. 35, 496–509 (2011).
[CrossRef]

Kumar, S.

J. Swgen and S. Kumar, “Shadow gestures: 3D hand poses estimation using a single camera,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1999), pp. 479–485.

Kweon, I.

D. H. Lee and I. Kweon, “A novel stereo camera system by a biprism,” IEEE Trans. Robot. Autom. 16, 528–541 (2000).
[CrossRef]

D. H. Lee, I. Kweon, and R. Cipolla, “A biprism-stereo camera system,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1999), pp. 82–87.

D. H. Lee, I. Kweon, and R. Cipolla, “Single lens stereo with a biprism,” in Proceedings of IAPR Workshop on Machine Vision Applications (1998), pp. 17–19.

Lee, D. H.

D. H. Lee and I. Kweon, “A novel stereo camera system by a biprism,” IEEE Trans. Robot. Autom. 16, 528–541 (2000).
[CrossRef]

D. H. Lee, I. Kweon, and R. Cipolla, “A biprism-stereo camera system,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1999), pp. 82–87.

D. H. Lee, I. Kweon, and R. Cipolla, “Single lens stereo with a biprism,” in Proceedings of IAPR Workshop on Machine Vision Applications (1998), pp. 17–19.

Li, X.

R. Wang, X. Li, and Y. Zhang, “Analysis and optimization of the stereo system with a four-mirror adapter,” J. Eur. Opt. Soc. 3, 1–7 (2008).

Lim, K. B.

Y. Xiao and K. B. Lim, “A prism-based single-lens stereovision system: from trinocular to multi-ocular,” Image Vis. Comput. 25, 1725–1736 (2007).
[CrossRef]

K. B. Lim and Y. Xiao, “Virtual stereovision system: new understanding on single-lens stereovision using a biprism,” J. Electron. Imaging 14, 043020 (2005).
[CrossRef]

M. J. Zhao and K. B. Lim, “Stereo matching of single-lens bi-prism based stereovision system,” in Proceedings of the 2010 International Conference on Future Information Technology (2010), pp. 179–183.

Lygouras, J.

J. A. Kalomiros and J. Lygouras, “Design and hardware implementation of a stereo-matching system based on dynamic programming,” Microprocess. Microsyst. 35, 496–509 (2011).
[CrossRef]

Nishimoto, Y.

Y. Nishimoto and Y. Shirai, “A feature-based stereo model using small disparities histograms of multi-resolution channels,” Adv. Robot. 3, 17–33 (1988).
[CrossRef]

Ong, S. H.

Q. Z. Ye, S. H. Ong, and X. Han, “A stereovision system for the inspection of IC bonding wires,” Int. J. Imaging Syst. Technol. 11, 254–262 (2000).
[CrossRef]

Shirai, Y.

Y. Nishimoto and Y. Shirai, “A feature-based stereo model using small disparities histograms of multi-resolution channels,” Adv. Robot. 3, 17–33 (1988).
[CrossRef]

Stryland, W. V.

M. Bass and W. V. Stryland, Handbook of Optics II (McGraw-Hill, 1995).

Sun, W. S.

Swgen, J.

J. Swgen and S. Kumar, “Shadow gestures: 3D hand poses estimation using a single camera,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1999), pp. 479–485.

Teoh, W.

W. Teoh and X. D. Zhang, “An inexpensive stereoscopic vision system for robots,” in Proceedings of IEEE International Conference on Robotics and Automation (IEEE, 1984), pp. 186–189.

Wang, R.

R. Wang, X. Li, and Y. Zhang, “Analysis and optimization of the stereo system with a four-mirror adapter,” J. Eur. Opt. Soc. 3, 1–7 (2008).

Wheatstone, C.

C. Wheatstone, “Contributions to the physiology of vision-part the first. On some remarkable, and hitherto unobserved, phenomena of binocular vision,” Philos. Trans. R. Soc. London 128, 371–394 (1838).
[CrossRef]

White, H. E.

F. A. Hankins and H. E. White, Fundamentals of Optics (McGraw-Hill, 1976), pp. 30–31.

Xiao, Y.

Y. Xiao and K. B. Lim, “A prism-based single-lens stereovision system: from trinocular to multi-ocular,” Image Vis. Comput. 25, 1725–1736 (2007).
[CrossRef]

K. B. Lim and Y. Xiao, “Virtual stereovision system: new understanding on single-lens stereovision using a biprism,” J. Electron. Imaging 14, 043020 (2005).
[CrossRef]

Xu, Y.

L. Cai, L. He, Y. Xu, Y. Zhao, and X. Yang, “Multi-object detection and tracking by stereo vision,” Pattern Recogn. 43, 4028–4041 (2010).
[CrossRef]

Yang, T.-T.

Yang, X.

L. Cai, L. He, Y. Xu, Y. Zhao, and X. Yang, “Multi-object detection and tracking by stereo vision,” Pattern Recogn. 43, 4028–4041 (2010).
[CrossRef]

Ye, Q. Z.

Q. Z. Ye, S. H. Ong, and X. Han, “A stereovision system for the inspection of IC bonding wires,” Int. J. Imaging Syst. Technol. 11, 254–262 (2000).
[CrossRef]

Zhang, X. D.

W. Teoh and X. D. Zhang, “An inexpensive stereoscopic vision system for robots,” in Proceedings of IEEE International Conference on Robotics and Automation (IEEE, 1984), pp. 186–189.

Zhang, Y.

R. Wang, X. Li, and Y. Zhang, “Analysis and optimization of the stereo system with a four-mirror adapter,” J. Eur. Opt. Soc. 3, 1–7 (2008).

Zhang, Z.

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334(2000).
[CrossRef]

Zhao, M. J.

M. J. Zhao and K. B. Lim, “Stereo matching of single-lens bi-prism based stereovision system,” in Proceedings of the 2010 International Conference on Future Information Technology (2010), pp. 179–183.

Zhao, Y.

L. Cai, L. He, Y. Xu, Y. Zhao, and X. Yang, “Multi-object detection and tracking by stereo vision,” Pattern Recogn. 43, 4028–4041 (2010).
[CrossRef]

Adv. Robot.

Y. Nishimoto and Y. Shirai, “A feature-based stereo model using small disparities histograms of multi-resolution channels,” Adv. Robot. 3, 17–33 (1988).
[CrossRef]

Comput. Vis. Image Underst.

X. Cao and H. Foroosh, “Camera calibration and light source orientation from solar shadows,” Comput. Vis. Image Underst. 105, 60–72 (2007).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell.

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334(2000).
[CrossRef]

IEEE Trans. Robot. Autom.

D. H. Lee and I. Kweon, “A novel stereo camera system by a biprism,” IEEE Trans. Robot. Autom. 16, 528–541 (2000).
[CrossRef]

Image Vis. Comput.

Y. Xiao and K. B. Lim, “A prism-based single-lens stereovision system: from trinocular to multi-ocular,” Image Vis. Comput. 25, 1725–1736 (2007).
[CrossRef]

Int. J. Imaging Syst. Technol.

Q. Z. Ye, S. H. Ong, and X. Han, “A stereovision system for the inspection of IC bonding wires,” Int. J. Imaging Syst. Technol. 11, 254–262 (2000).
[CrossRef]

J. Electron. Imaging

K. B. Lim and Y. Xiao, “Virtual stereovision system: new understanding on single-lens stereovision using a biprism,” J. Electron. Imaging 14, 043020 (2005).
[CrossRef]

J. Eur. Opt. Soc.

R. Wang, X. Li, and Y. Zhang, “Analysis and optimization of the stereo system with a four-mirror adapter,” J. Eur. Opt. Soc. 3, 1–7 (2008).

Microprocess. Microsyst.

J. A. Kalomiros and J. Lygouras, “Design and hardware implementation of a stereo-matching system based on dynamic programming,” Microprocess. Microsyst. 35, 496–509 (2011).
[CrossRef]

Opt. Express

Pattern Recogn.

L. Cai, L. He, Y. Xu, Y. Zhao, and X. Yang, “Multi-object detection and tracking by stereo vision,” Pattern Recogn. 43, 4028–4041 (2010).
[CrossRef]

A. Goshtasby and W. A. Gruver, “Design of a single-lens stereo camera system,” Pattern Recogn. 26, 923–937 (1993).
[CrossRef]

Philos. Trans. R. Soc. London

C. Wheatstone, “Contributions to the physiology of vision-part the first. On some remarkable, and hitherto unobserved, phenomena of binocular vision,” Philos. Trans. R. Soc. London 128, 371–394 (1838).
[CrossRef]

Other

D. H. Lee, I. Kweon, and R. Cipolla, “Single lens stereo with a biprism,” in Proceedings of IAPR Workshop on Machine Vision Applications (1998), pp. 17–19.

D. H. Lee, I. Kweon, and R. Cipolla, “A biprism-stereo camera system,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1999), pp. 82–87.

W. Teoh and X. D. Zhang, “An inexpensive stereoscopic vision system for robots,” in Proceedings of IEEE International Conference on Robotics and Automation (IEEE, 1984), pp. 186–189.

J. Swgen and S. Kumar, “Shadow gestures: 3D hand poses estimation using a single camera,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1999), pp. 479–485.

F. A. Hankins and H. E. White, Fundamentals of Optics (McGraw-Hill, 1976), pp. 30–31.

M. Bass and W. V. Stryland, Handbook of Optics II (McGraw-Hill, 1995).

E. Hecht, Theory and Problems of Optics, Schaum’s Outline Series (McGraw-Hill, 1975), pp. 142–143.

M. J. Zhao and K. B. Lim, “Stereo matching of single-lens bi-prism based stereovision system,” in Proceedings of the 2010 International Conference on Future Information Technology (2010), pp. 179–183.

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 (15)

Fig. 1.
Fig. 1.

Geometry of virtual points.

Fig. 2.
Fig. 2.

Geometry of ray refraction in prism.

Fig. 3.
Fig. 3.

Geometry of virtual cameras.

Fig. 4.
Fig. 4.

Structure of a microprism array lens.

Fig. 5.
Fig. 5.

Ray refraction of a vertical plane.

Fig. 6.
Fig. 6.

Geometry of optical virtual image by prism.

Fig. 7.
Fig. 7.

Ray refraction of an arbitrary plane.

Fig. 8.
Fig. 8.

Correspondence configuration of single-lens biprism stereovision system.

Fig. 9.
Fig. 9.

Virtual points of multiocular prism.

Fig. 10.
Fig. 10.

System setup and multiocular prism.

Fig. 11.
Fig. 11.

Corresponding epipolar lines of feature points according to two-, three-, and four-ocular prisms.

Fig. 12.
Fig. 12.

Structural comparison of virtual points, virtual cameras, and our method.

Fig. 13.
Fig. 13.

Left and right image position of a segment in different depth.

Fig. 14.
Fig. 14.

Left and right image of the camera optical center corresponding to different depths.

Fig. 15.
Fig. 15.

Distribution map of distance error reference. (a) Map of a two-ocular prism; (b) map of a three-ocular prism; (c) map of a four-ocular prism.

Tables (2)

Tables Icon

Table 1. Recovered Depth by Three Methods

Tables Icon

Table 2. Results for Two-, Three-, and Four-ocular Prisms Reconstructive Errors

Equations (36)

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

t=ttanα/tanα.
{xr=xyr=yzr=(zt)tanα1/tanα2+t,
{xr=Trsinβ+xyr=yrzr=zrTrcosβ,
Tr=cosβ(1tanα3/tanα4)(zrtxtanβ).
{xr=Trsinβ+xyr=yzr=(zt)tanα1/tanα2+tTrcosβ.
xr/zr=xr/f.
{A1x+B1z+C1=0A2x+B2z+C2=0.
yr/zr=yr/f.
y=yr=zryr/f.
AB=x0n+y0ny+z0nz+d.
tanα=BC/AB.
tanα=BC/AB.
AA=ABAB=ABtanα/tanαAB=AB(tanα/α1)=(x0nx+y0ny+z0nz+d)(tanα/tanα1).
AA=[(xx0)2+(yy0)2+(zz0)2]1/2.
(xx0)/nx=(yy0)/ny=(zz0)/nz.
AA=(zz0)(nx2/nz2+ny2/nz2+1)1/2.
z=QnxSx0+QnySy0+Qnz+SSz0+QdS.
x=Qnx2+SnzSnzx0+QnxnySnzy0+QnxSz0+QdnxSnz.
y=QnxnySnzx0+Qny2+SnzSnzy0+QnySz0+QdnySnz.
[xyz1]=[Qnx2+SnzSnzQnxnySnzQnxSQdnxSnzQnxnySnzQny2+SnzSnzQnySQdnySnzQnxSQnySQnz+SSQdS0001][x0y0z01]A=M1A.
tanα/tanα=ncosα/ncosα.
Q=nV·NnV·N1.
AA=ABAB=ABABtanα/tanα=AB(1tanα/α)=(x0nx+y0ny+z0nz+d)(tanα/tanα1).
AA=(zz0)(nx2/nz2+ny2/nz2+1)1/2.
A=M2A.
V=nnV+N([1(nn)2(1(V·N)2)]1/2nn(V·N)).
V=f(V,N).
A=M2M1A=MA.
V=f[f(V,N),Nb]=F(V,N,Nb).
Pl=MlPl.
Vl=F(Vl,N,Nb).
P1=M1P1.
spr1¯=MintP1,
spr1¯=MintM1P1.
{P1=M1P1P2=M2P2Pm=MmPm.
{V1=F(V1,N1,Nb)V2=F(V2,N2,Nb)Vm=F(Vm,Nm,Nb).

Metrics