Abstract

In this paper, we propose a method to deduce the dynamic modulation transfer function (DMTF) of a space-variant sampling retina-like sensor and demonstrate its utilization in the forward motion imaging process. With the analysis of sampling and the motion imaging property of the sensor, DMTF has been derived. Next, the performance of DMTF between a retina-like sensor and a rectilinear sensor is compared, and the results show that the degradation of DMTF in forward motion is less than that of a rectilinear sensor. Then, the output images are obtained through simulation based on DMTF, and they are compared with that obtained from a CMOS camera with the same forward motion conditions. The Pearson correlation coefficients between the two kinds of images are all larger than 0.85. Thus, the effectiveness of DMTF is shown.

© 2014 Optical Society of America

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References

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  1. V. Javier Traver and A. Bernardino, “A review of log-polar imaging for visual perception in robotics,” Robot. Auton. Syst. 58, 378–398 (2010).
    [CrossRef]
  2. F. Berton, G. Sandini, and G. Metta, “Anthropomorphic visual sensors,” Encycl. Sens. 10, 1–16 (2006).
  3. G. Sandini, P. Questa, D. Scheffer, B. Diericks, and A. Mannucci, “A retina-like CMOS sensor and its applications,” in Proceedings of the 2000 IEEE Sensor Array and Multichannel Signal Processing Workshop (IEEE, 2000), pp. 514–519.
  4. X. Zhang and L. P. Tay, “A spatial variant approach for vergence control in complex scenes,” Image Vis. Comput. 29, 64–77 (2011).
    [CrossRef]
  5. P. Gamba, L. Lombardi, and M. Porta, “Log-map analysis,” Parallel Comput. 34, 757–764 (2008).
    [CrossRef]
  6. F. Pardo, B. Dierickx, and D. Scheffer, “Space-variant nonorthogonal structure CMOS image sensor design,” IEEE J. Solid-State Circuits 33, 842–849 (1998).
    [CrossRef]
  7. Y. Song, Q. Hao, J. Cao, F. Fan, T. Liu, and L. Li, “Modeling and simulation of the retina-like image sensor based on space-variant lens array,” Appl. Opt. 52, 2584–2594 (2013).
    [CrossRef]
  8. G. Sandini, J. Santos-Victor, T. Pajdla, and F. Berton, “OMNIVIEWS: direct omnidirectional imaging based on a retina-like sensor,” in Proceedings of IEEE Sensors (IEEE, 2002), Vol. 21, pp. 27–30.
  9. J. A. Boluda and J. Domingo, “On the advantages of combining differential algorithms and log-polar vision for detection of self-motion from a mobile robot,” Robot. Auton. Syst. 37, 283–296 (2001).
    [CrossRef]
  10. V. J. Traver and F. Pla, “Log-polar mapping template design: from task-level requirements to geometry parameters,” Image Vis. Comput. 26, 1354–1370 (2008).
    [CrossRef]
  11. F. Wang, F. Cao, T. Bai, and Y. Su, “Optimization of retina-like sensor parameters based on visual task requirements,” Opt. Eng. 52, 043206 (2013).
    [CrossRef]
  12. F. Wang, F. Cao, and T. Bai, “Modulation transfer function of spatially variant sampling retina-like sensor,” Optik 124, 1342–1345 (2013).
    [CrossRef]
  13. B. J. Thelen, R. G. Paxman, D. A. Carrara, and J. H. Seldin, “Overcoming turbulence-induced space-variant blur by using phase-diverse speckle,” J. Opt. Soc. Am. A 26, 206–218 (2009).
    [CrossRef]
  14. M. Sorel and J. Flusser, “Space-variant restoration of images degraded by camera motion blur,” IEEE Trans. Image Process. 17, 105–116 (2008).
    [CrossRef]
  15. J. W. Stayman and J. A. Fessler, “Compensation for nonuniform resolution using penalized-likelihood reconstruction in space-variant imaging systems,” IEEE Trans. Med. Imaging 23, 269–284 (2004).
    [CrossRef]
  16. I. Klapp and Y. Yitzhaky, “Angular motion point spread function model considering aberrations and defocus effects,” J. Opt. Soc. Am. A 23, 1856–1864 (2006).
    [CrossRef]
  17. A. A. S. Awwal, A. K. Cherri, M. A. Karim, and D. Moon, “Dynamic modulation transfer function of a display system,” Appl. Opt. 30, 201–205 (1991).
    [CrossRef]
  18. Y. Zhang, K. Teunissen, W. Song, and X. Li, “Dynamic modulation transfer function: a method to characterize the temporal performance of liquid-crystal displays,” Opt. Lett. 33, 533–535 (2008).
    [CrossRef]
  19. J. C. Feltz and M. A. Karim, “Modulation transfer function of charge-coupled devices,” Appl. Opt. 29, 717–722 (1990).
    [CrossRef]
  20. J. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, 1978).
  21. K. J. Barnard and G. D. Boreman, “Modulation transfer function of hexagonal staring focal plane arrays,” Opt. Eng. 30, 1915–1919 (1991).
    [CrossRef]
  22. D. N. Sitter, J. S. Goddard, and R. K. Ferrell, “Method for the measurement of the modulation transfer function of sampled imaging systems from bar-target patterns,” Appl. Opt. 34, 746–751 (1995).
    [CrossRef]
  23. R. H. Vollmerhausen, D. Reago, and R. G. Driggers, Analysis and Evaluation of Sampled Imaging Systems (SPIE, 2010).
  24. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2005).
  25. F. Cao, K. Yan, F. Wang, and L. Zhang, “Imaging superiority of non-rectangular detector array in forward motion,” Trans. Beijing Inst. Technol. 31, 699–702 (2011) (in Chinese).
  26. A. Stern and N. Kopeika, “Analytical method to calculate optical transfer functions for image motion and vibrations using moments,” J. Opt. Soc. Am. A 14, 388–396 (1997).
    [CrossRef]
  27. T. Bai and W. Jin, Principles and Techniques of Optical Imaging (Beijing Institute of Technology, 2006).
  28. J. Lee Rodgers and W. A. Nicewander, “Thirteen ways to look at the correlation coefficient,” Am. Stat. 42, 59–66 (1988).
    [CrossRef]

2013

F. Wang, F. Cao, T. Bai, and Y. Su, “Optimization of retina-like sensor parameters based on visual task requirements,” Opt. Eng. 52, 043206 (2013).
[CrossRef]

F. Wang, F. Cao, and T. Bai, “Modulation transfer function of spatially variant sampling retina-like sensor,” Optik 124, 1342–1345 (2013).
[CrossRef]

Y. Song, Q. Hao, J. Cao, F. Fan, T. Liu, and L. Li, “Modeling and simulation of the retina-like image sensor based on space-variant lens array,” Appl. Opt. 52, 2584–2594 (2013).
[CrossRef]

2011

X. Zhang and L. P. Tay, “A spatial variant approach for vergence control in complex scenes,” Image Vis. Comput. 29, 64–77 (2011).
[CrossRef]

F. Cao, K. Yan, F. Wang, and L. Zhang, “Imaging superiority of non-rectangular detector array in forward motion,” Trans. Beijing Inst. Technol. 31, 699–702 (2011) (in Chinese).

2010

V. Javier Traver and A. Bernardino, “A review of log-polar imaging for visual perception in robotics,” Robot. Auton. Syst. 58, 378–398 (2010).
[CrossRef]

2009

2008

Y. Zhang, K. Teunissen, W. Song, and X. Li, “Dynamic modulation transfer function: a method to characterize the temporal performance of liquid-crystal displays,” Opt. Lett. 33, 533–535 (2008).
[CrossRef]

P. Gamba, L. Lombardi, and M. Porta, “Log-map analysis,” Parallel Comput. 34, 757–764 (2008).
[CrossRef]

M. Sorel and J. Flusser, “Space-variant restoration of images degraded by camera motion blur,” IEEE Trans. Image Process. 17, 105–116 (2008).
[CrossRef]

V. J. Traver and F. Pla, “Log-polar mapping template design: from task-level requirements to geometry parameters,” Image Vis. Comput. 26, 1354–1370 (2008).
[CrossRef]

2006

2004

J. W. Stayman and J. A. Fessler, “Compensation for nonuniform resolution using penalized-likelihood reconstruction in space-variant imaging systems,” IEEE Trans. Med. Imaging 23, 269–284 (2004).
[CrossRef]

2001

J. A. Boluda and J. Domingo, “On the advantages of combining differential algorithms and log-polar vision for detection of self-motion from a mobile robot,” Robot. Auton. Syst. 37, 283–296 (2001).
[CrossRef]

1998

F. Pardo, B. Dierickx, and D. Scheffer, “Space-variant nonorthogonal structure CMOS image sensor design,” IEEE J. Solid-State Circuits 33, 842–849 (1998).
[CrossRef]

1997

1995

1991

A. A. S. Awwal, A. K. Cherri, M. A. Karim, and D. Moon, “Dynamic modulation transfer function of a display system,” Appl. Opt. 30, 201–205 (1991).
[CrossRef]

K. J. Barnard and G. D. Boreman, “Modulation transfer function of hexagonal staring focal plane arrays,” Opt. Eng. 30, 1915–1919 (1991).
[CrossRef]

1990

1988

J. Lee Rodgers and W. A. Nicewander, “Thirteen ways to look at the correlation coefficient,” Am. Stat. 42, 59–66 (1988).
[CrossRef]

Awwal, A. A. S.

Bai, T.

F. Wang, F. Cao, and T. Bai, “Modulation transfer function of spatially variant sampling retina-like sensor,” Optik 124, 1342–1345 (2013).
[CrossRef]

F. Wang, F. Cao, T. Bai, and Y. Su, “Optimization of retina-like sensor parameters based on visual task requirements,” Opt. Eng. 52, 043206 (2013).
[CrossRef]

T. Bai and W. Jin, Principles and Techniques of Optical Imaging (Beijing Institute of Technology, 2006).

Barnard, K. J.

K. J. Barnard and G. D. Boreman, “Modulation transfer function of hexagonal staring focal plane arrays,” Opt. Eng. 30, 1915–1919 (1991).
[CrossRef]

Bernardino, A.

V. Javier Traver and A. Bernardino, “A review of log-polar imaging for visual perception in robotics,” Robot. Auton. Syst. 58, 378–398 (2010).
[CrossRef]

Berton, F.

F. Berton, G. Sandini, and G. Metta, “Anthropomorphic visual sensors,” Encycl. Sens. 10, 1–16 (2006).

G. Sandini, J. Santos-Victor, T. Pajdla, and F. Berton, “OMNIVIEWS: direct omnidirectional imaging based on a retina-like sensor,” in Proceedings of IEEE Sensors (IEEE, 2002), Vol. 21, pp. 27–30.

Boluda, J. A.

J. A. Boluda and J. Domingo, “On the advantages of combining differential algorithms and log-polar vision for detection of self-motion from a mobile robot,” Robot. Auton. Syst. 37, 283–296 (2001).
[CrossRef]

Boreman, G. D.

K. J. Barnard and G. D. Boreman, “Modulation transfer function of hexagonal staring focal plane arrays,” Opt. Eng. 30, 1915–1919 (1991).
[CrossRef]

Cao, F.

F. Wang, F. Cao, T. Bai, and Y. Su, “Optimization of retina-like sensor parameters based on visual task requirements,” Opt. Eng. 52, 043206 (2013).
[CrossRef]

F. Wang, F. Cao, and T. Bai, “Modulation transfer function of spatially variant sampling retina-like sensor,” Optik 124, 1342–1345 (2013).
[CrossRef]

F. Cao, K. Yan, F. Wang, and L. Zhang, “Imaging superiority of non-rectangular detector array in forward motion,” Trans. Beijing Inst. Technol. 31, 699–702 (2011) (in Chinese).

Cao, J.

Carrara, D. A.

Cherri, A. K.

Diericks, B.

G. Sandini, P. Questa, D. Scheffer, B. Diericks, and A. Mannucci, “A retina-like CMOS sensor and its applications,” in Proceedings of the 2000 IEEE Sensor Array and Multichannel Signal Processing Workshop (IEEE, 2000), pp. 514–519.

Dierickx, B.

F. Pardo, B. Dierickx, and D. Scheffer, “Space-variant nonorthogonal structure CMOS image sensor design,” IEEE J. Solid-State Circuits 33, 842–849 (1998).
[CrossRef]

Domingo, J.

J. A. Boluda and J. Domingo, “On the advantages of combining differential algorithms and log-polar vision for detection of self-motion from a mobile robot,” Robot. Auton. Syst. 37, 283–296 (2001).
[CrossRef]

Driggers, R. G.

R. H. Vollmerhausen, D. Reago, and R. G. Driggers, Analysis and Evaluation of Sampled Imaging Systems (SPIE, 2010).

Fan, F.

Feltz, J. C.

Ferrell, R. K.

Fessler, J. A.

J. W. Stayman and J. A. Fessler, “Compensation for nonuniform resolution using penalized-likelihood reconstruction in space-variant imaging systems,” IEEE Trans. Med. Imaging 23, 269–284 (2004).
[CrossRef]

Flusser, J.

M. Sorel and J. Flusser, “Space-variant restoration of images degraded by camera motion blur,” IEEE Trans. Image Process. 17, 105–116 (2008).
[CrossRef]

Gamba, P.

P. Gamba, L. Lombardi, and M. Porta, “Log-map analysis,” Parallel Comput. 34, 757–764 (2008).
[CrossRef]

Gaskill, J.

J. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, 1978).

Goddard, J. S.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2005).

Hao, Q.

Javier Traver, V.

V. Javier Traver and A. Bernardino, “A review of log-polar imaging for visual perception in robotics,” Robot. Auton. Syst. 58, 378–398 (2010).
[CrossRef]

Jin, W.

T. Bai and W. Jin, Principles and Techniques of Optical Imaging (Beijing Institute of Technology, 2006).

Karim, M. A.

Klapp, I.

Kopeika, N.

Lee Rodgers, J.

J. Lee Rodgers and W. A. Nicewander, “Thirteen ways to look at the correlation coefficient,” Am. Stat. 42, 59–66 (1988).
[CrossRef]

Li, L.

Li, X.

Liu, T.

Lombardi, L.

P. Gamba, L. Lombardi, and M. Porta, “Log-map analysis,” Parallel Comput. 34, 757–764 (2008).
[CrossRef]

Mannucci, A.

G. Sandini, P. Questa, D. Scheffer, B. Diericks, and A. Mannucci, “A retina-like CMOS sensor and its applications,” in Proceedings of the 2000 IEEE Sensor Array and Multichannel Signal Processing Workshop (IEEE, 2000), pp. 514–519.

Metta, G.

F. Berton, G. Sandini, and G. Metta, “Anthropomorphic visual sensors,” Encycl. Sens. 10, 1–16 (2006).

Moon, D.

Nicewander, W. A.

J. Lee Rodgers and W. A. Nicewander, “Thirteen ways to look at the correlation coefficient,” Am. Stat. 42, 59–66 (1988).
[CrossRef]

Pajdla, T.

G. Sandini, J. Santos-Victor, T. Pajdla, and F. Berton, “OMNIVIEWS: direct omnidirectional imaging based on a retina-like sensor,” in Proceedings of IEEE Sensors (IEEE, 2002), Vol. 21, pp. 27–30.

Pardo, F.

F. Pardo, B. Dierickx, and D. Scheffer, “Space-variant nonorthogonal structure CMOS image sensor design,” IEEE J. Solid-State Circuits 33, 842–849 (1998).
[CrossRef]

Paxman, R. G.

Pla, F.

V. J. Traver and F. Pla, “Log-polar mapping template design: from task-level requirements to geometry parameters,” Image Vis. Comput. 26, 1354–1370 (2008).
[CrossRef]

Porta, M.

P. Gamba, L. Lombardi, and M. Porta, “Log-map analysis,” Parallel Comput. 34, 757–764 (2008).
[CrossRef]

Questa, P.

G. Sandini, P. Questa, D. Scheffer, B. Diericks, and A. Mannucci, “A retina-like CMOS sensor and its applications,” in Proceedings of the 2000 IEEE Sensor Array and Multichannel Signal Processing Workshop (IEEE, 2000), pp. 514–519.

Reago, D.

R. H. Vollmerhausen, D. Reago, and R. G. Driggers, Analysis and Evaluation of Sampled Imaging Systems (SPIE, 2010).

Sandini, G.

F. Berton, G. Sandini, and G. Metta, “Anthropomorphic visual sensors,” Encycl. Sens. 10, 1–16 (2006).

G. Sandini, P. Questa, D. Scheffer, B. Diericks, and A. Mannucci, “A retina-like CMOS sensor and its applications,” in Proceedings of the 2000 IEEE Sensor Array and Multichannel Signal Processing Workshop (IEEE, 2000), pp. 514–519.

G. Sandini, J. Santos-Victor, T. Pajdla, and F. Berton, “OMNIVIEWS: direct omnidirectional imaging based on a retina-like sensor,” in Proceedings of IEEE Sensors (IEEE, 2002), Vol. 21, pp. 27–30.

Santos-Victor, J.

G. Sandini, J. Santos-Victor, T. Pajdla, and F. Berton, “OMNIVIEWS: direct omnidirectional imaging based on a retina-like sensor,” in Proceedings of IEEE Sensors (IEEE, 2002), Vol. 21, pp. 27–30.

Scheffer, D.

F. Pardo, B. Dierickx, and D. Scheffer, “Space-variant nonorthogonal structure CMOS image sensor design,” IEEE J. Solid-State Circuits 33, 842–849 (1998).
[CrossRef]

G. Sandini, P. Questa, D. Scheffer, B. Diericks, and A. Mannucci, “A retina-like CMOS sensor and its applications,” in Proceedings of the 2000 IEEE Sensor Array and Multichannel Signal Processing Workshop (IEEE, 2000), pp. 514–519.

Seldin, J. H.

Sitter, D. N.

Song, W.

Song, Y.

Sorel, M.

M. Sorel and J. Flusser, “Space-variant restoration of images degraded by camera motion blur,” IEEE Trans. Image Process. 17, 105–116 (2008).
[CrossRef]

Stayman, J. W.

J. W. Stayman and J. A. Fessler, “Compensation for nonuniform resolution using penalized-likelihood reconstruction in space-variant imaging systems,” IEEE Trans. Med. Imaging 23, 269–284 (2004).
[CrossRef]

Stern, A.

Su, Y.

F. Wang, F. Cao, T. Bai, and Y. Su, “Optimization of retina-like sensor parameters based on visual task requirements,” Opt. Eng. 52, 043206 (2013).
[CrossRef]

Tay, L. P.

X. Zhang and L. P. Tay, “A spatial variant approach for vergence control in complex scenes,” Image Vis. Comput. 29, 64–77 (2011).
[CrossRef]

Teunissen, K.

Thelen, B. J.

Traver, V. J.

V. J. Traver and F. Pla, “Log-polar mapping template design: from task-level requirements to geometry parameters,” Image Vis. Comput. 26, 1354–1370 (2008).
[CrossRef]

Vollmerhausen, R. H.

R. H. Vollmerhausen, D. Reago, and R. G. Driggers, Analysis and Evaluation of Sampled Imaging Systems (SPIE, 2010).

Wang, F.

F. Wang, F. Cao, and T. Bai, “Modulation transfer function of spatially variant sampling retina-like sensor,” Optik 124, 1342–1345 (2013).
[CrossRef]

F. Wang, F. Cao, T. Bai, and Y. Su, “Optimization of retina-like sensor parameters based on visual task requirements,” Opt. Eng. 52, 043206 (2013).
[CrossRef]

F. Cao, K. Yan, F. Wang, and L. Zhang, “Imaging superiority of non-rectangular detector array in forward motion,” Trans. Beijing Inst. Technol. 31, 699–702 (2011) (in Chinese).

Yan, K.

F. Cao, K. Yan, F. Wang, and L. Zhang, “Imaging superiority of non-rectangular detector array in forward motion,” Trans. Beijing Inst. Technol. 31, 699–702 (2011) (in Chinese).

Yitzhaky, Y.

Zhang, L.

F. Cao, K. Yan, F. Wang, and L. Zhang, “Imaging superiority of non-rectangular detector array in forward motion,” Trans. Beijing Inst. Technol. 31, 699–702 (2011) (in Chinese).

Zhang, X.

X. Zhang and L. P. Tay, “A spatial variant approach for vergence control in complex scenes,” Image Vis. Comput. 29, 64–77 (2011).
[CrossRef]

Zhang, Y.

Am. Stat.

J. Lee Rodgers and W. A. Nicewander, “Thirteen ways to look at the correlation coefficient,” Am. Stat. 42, 59–66 (1988).
[CrossRef]

Appl. Opt.

Encycl. Sens.

F. Berton, G. Sandini, and G. Metta, “Anthropomorphic visual sensors,” Encycl. Sens. 10, 1–16 (2006).

IEEE J. Solid-State Circuits

F. Pardo, B. Dierickx, and D. Scheffer, “Space-variant nonorthogonal structure CMOS image sensor design,” IEEE J. Solid-State Circuits 33, 842–849 (1998).
[CrossRef]

IEEE Trans. Image Process.

M. Sorel and J. Flusser, “Space-variant restoration of images degraded by camera motion blur,” IEEE Trans. Image Process. 17, 105–116 (2008).
[CrossRef]

IEEE Trans. Med. Imaging

J. W. Stayman and J. A. Fessler, “Compensation for nonuniform resolution using penalized-likelihood reconstruction in space-variant imaging systems,” IEEE Trans. Med. Imaging 23, 269–284 (2004).
[CrossRef]

Image Vis. Comput.

V. J. Traver and F. Pla, “Log-polar mapping template design: from task-level requirements to geometry parameters,” Image Vis. Comput. 26, 1354–1370 (2008).
[CrossRef]

X. Zhang and L. P. Tay, “A spatial variant approach for vergence control in complex scenes,” Image Vis. Comput. 29, 64–77 (2011).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

K. J. Barnard and G. D. Boreman, “Modulation transfer function of hexagonal staring focal plane arrays,” Opt. Eng. 30, 1915–1919 (1991).
[CrossRef]

F. Wang, F. Cao, T. Bai, and Y. Su, “Optimization of retina-like sensor parameters based on visual task requirements,” Opt. Eng. 52, 043206 (2013).
[CrossRef]

Opt. Lett.

Optik

F. Wang, F. Cao, and T. Bai, “Modulation transfer function of spatially variant sampling retina-like sensor,” Optik 124, 1342–1345 (2013).
[CrossRef]

Parallel Comput.

P. Gamba, L. Lombardi, and M. Porta, “Log-map analysis,” Parallel Comput. 34, 757–764 (2008).
[CrossRef]

Robot. Auton. Syst.

V. Javier Traver and A. Bernardino, “A review of log-polar imaging for visual perception in robotics,” Robot. Auton. Syst. 58, 378–398 (2010).
[CrossRef]

J. A. Boluda and J. Domingo, “On the advantages of combining differential algorithms and log-polar vision for detection of self-motion from a mobile robot,” Robot. Auton. Syst. 37, 283–296 (2001).
[CrossRef]

Trans. Beijing Inst. Technol.

F. Cao, K. Yan, F. Wang, and L. Zhang, “Imaging superiority of non-rectangular detector array in forward motion,” Trans. Beijing Inst. Technol. 31, 699–702 (2011) (in Chinese).

Other

J. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, 1978).

R. H. Vollmerhausen, D. Reago, and R. G. Driggers, Analysis and Evaluation of Sampled Imaging Systems (SPIE, 2010).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2005).

G. Sandini, J. Santos-Victor, T. Pajdla, and F. Berton, “OMNIVIEWS: direct omnidirectional imaging based on a retina-like sensor,” in Proceedings of IEEE Sensors (IEEE, 2002), Vol. 21, pp. 27–30.

G. Sandini, P. Questa, D. Scheffer, B. Diericks, and A. Mannucci, “A retina-like CMOS sensor and its applications,” in Proceedings of the 2000 IEEE Sensor Array and Multichannel Signal Processing Workshop (IEEE, 2000), pp. 514–519.

T. Bai and W. Jin, Principles and Techniques of Optical Imaging (Beijing Institute of Technology, 2006).

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Figures (11)

Fig. 1.
Fig. 1.

Pixel arrangement of the retina-like sensor.

Fig. 2.
Fig. 2.

Process of forward motion imaging.

Fig. 3.
Fig. 3.

DMTF of (a) the rectilinear sensor and (b) the retina-like senor (ξ=0.01).

Fig. 4.
Fig. 4.

DMTF of (a) the rectilinear sensor and (b) the retina-like senor (ξ=0.1).

Fig. 5.
Fig. 5.

DMTF of (a) the rectilinear sensor and (b) the retina-like senor (ξ=0.3).

Fig. 6.
Fig. 6.

Differences between MTF and DMTF for the two sensors. (a) Value of Δi for the two sensors (ξ=0.01). (b) Value of Δi for the two sensors (ξ=0.1).

Fig. 7.
Fig. 7.

3D DMTFs of (a) the rectilinear and (b) the retina-like senor (ξ=0.02).

Fig. 8.
Fig. 8.

Schematic diagram of the experimental setup.

Fig. 9.
Fig. 9.

Static image.

Fig. 10.
Fig. 10.

(a) Experimental image and (b) simulated image (ξ=0.123).

Fig. 11.
Fig. 11.

(a) Experimental image and (b) simulated image (ξ=0.343).

Tables (3)

Tables Icon

Table 1. Computation Results of Degradation of DMTF for a Retina-Like Sensor and a Rectilinear Sensor when the Motion Degeneration Degree is 0.01

Tables Icon

Table 2. Motion Degeneration Degrees

Tables Icon

Table 3. Pearson Correlation Coefficients of the Experimental Image and the Simulated Image

Equations (21)

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

sampi=comb(xri+yri,xriyri)×[circ(rri)circ(rri1)],
oi=[sin(x,y)*circ(r/Ri)]×sampi(x,y)=[sin(x,y)*circ(r/Ri)]×comb(xri+yri,xriyri)×[circ(rri)circ(rri1)],
Oi=[K×Sin(fx,fy)×J1(2πfrRi)fr]*comb(ri2fx+ri2fy,ri2fxri2fy)*[riJ1(2πfrri)frri1J1(2πfrri1)fr],
Sin(fx,fy)=0iffx2+fy2(1rN),
OiK×Sin(fx,fy)×J1(2πfrRi)fr.
MTFi=Oi(fx,fy)/Sin(fx,fy)Oi(0,0)/Sin(0,0)=J1(2πfrRi)fr.
DMTFi=MTFi×MTFim,
dr(t)=r(t)r(0)=r(0)vtL0vt.
vr=r(0)L0v(L0vt)2.
vr=r(0)vL0+2r(0)v2tL02+3r(0)v3t2L03+.
vr=r(0)vL0.
lr(t)=vrt,0<t<T.
OTFm(w)=0mnn!(jw)n,mn=1T0Tlrn(t)dt.
OTFm(w)=0mnn!(jw)n=0vrnTn(n+1)!(jw)n=sinc(vrTw2)exp(jvrT2w).
MTFim(fr)=sinc(πvrTfr).
DMTFi=MTFi×MTFim=J1(2πfrRi)fr×sinc(frr(0)vL0T).
DMTFi=J1(2πRifr)fr×sinc[frξr(0)].
DMTFi_r=sinc(rdfr)sinc[frξr(0)],
MTFr=sinc(rdfr),
Δi=MTFiDMTFi=MTFi×{1sinc[frξr(0)]}.
ρX,Y=i=1n(XiX¯)(YiY¯)i=1n(XiX¯)2i=1n(YiY¯)2,

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