Abstract

Algorithms and integrated optoelectronic architectures for parallel image processing and adaptive optics applications are proposed and analyzed. Image processing is performed on the basis of an evolution equation with anisotropic gain that is introduced. The key components of the image-processing scheme are a coherent optical system for on-the-fly image-edge detection and an analog very large scale integration system for parallel implementation of the evolution equation with anisotropic gain. Examples of video data processing for edge enhancement, imaging through turbulent media, depth estimation from visual data, and motion tracking are presented.

© 1999 Optical Society of America

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1998 (3)

1997 (3)

M. A. Vorontsov, G. W. Carhart, D. V. Pruidze, J. C. Ricklin, D. G. Voelz, “Adaptive imaging system for phase-distorted extended source and multiple-distance objects,” Appl. Opt. 36, 3319–3328 (1997).
[CrossRef] [PubMed]

M. C. Roggeman, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, J. H. Comtois, “Use of micro-electro-mechanical deformable mirrors to control aberrations in optical systems: theoretical and experimental results,” Opt. Eng. 36, 1326–1338 (1997).
[CrossRef]

A. Moini, A. Bouzerdoum, K. Eshraghian, A. Yakovleff, X. T. Nguyen, A. Blanksby, R. Beare, D. Abbott, R. E. Bogner, “An insect vision-based motion detection chip,” IEEE J. Solid-State Circuits 32, 279–284 (1997).
[CrossRef]

1996 (2)

G. Andreou, K. A. Boahen, “Translinear circuits in subthreshold MOS,” Analog Integr. Circuits Signal Process. 9, 141–166 (1996).
[CrossRef]

J. Gourlay, A. O’Hara, A. J. Stevens, D. G. Vass, “A comparative investigation into planarized liquid crystal over silicon spatial light modulators,” J. Mod. Opt. 43, 181–198 (1996); http://www.ph.ed.ac.uk/optics/research/slm.html
[CrossRef]

1994 (2)

“Atmospheric Compensation Technology” (special issues in J. Opt. Soc. Am. 11(1) and (2) (1994); R. K. Tyson, Principles of Adaptive Optics (Academic, San Diego, Calif., 1991).

M. C. Roggemann, C. A. Stoudt, B. M. Welsh, “Image spectrum signal-to-noise ratio improvement by statistical frame selection for adaptive optics imaging through atmospheric turbulence,” Opt. Eng. 33, 3254–3264 (1994).
[CrossRef]

1993 (1)

K. M. Johnson, D. J. McKnight, I. Underwood, “Smart spatial light modulators using liquid crystals on silicon,” IEEE J. Quantum Electron. 2, 699–714 (1993);S. Serati, G. Sharp, R. Serati, D. McKnight, J. Stookley, “128 128 analog liquid crystal spatial light modulator,” in Optical Pattern Recognition VI, D. P. Casasent, T. Chao, eds., Proc. SPIE2490, 378–387 (1995); http://www.bnonlinear.com/
[CrossRef]

1992 (1)

F. Catte, P. Lions, J. Morel, T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29, 182–193 (1992).
[CrossRef]

1991 (1)

W. Bair, C. Koch, “An analog VLSI chip for finding edges from zero-crossing,” Neural Inf. Process. Syst. 3, 399–405 (1991).

1990 (1)

P. Perona, J. Malik, “Scale space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern. Anal. Mach. Intell. 12, 629–630 (1990).
[CrossRef]

1989 (1)

D. Mumford, J. Shah, “Optimal approximations by piecewise smooth functions and associated variational problems,” Commun. Pure Appl. Math. 42, 577–685 (1989).
[CrossRef]

1982 (1)

1981 (1)

D. Terzopoulos, “Regularization of inverse visual problems involving discontinuities,” IEEE Trans. Pattern. Anal. Mach. Intell. 8, 413–424 (1981).

1979 (1)

Abbott, D.

A. Moini, A. Bouzerdoum, K. Eshraghian, A. Yakovleff, X. T. Nguyen, A. Blanksby, R. Beare, D. Abbott, R. E. Bogner, “An insect vision-based motion detection chip,” IEEE J. Solid-State Circuits 32, 279–284 (1997).
[CrossRef]

Andreou, G.

G. Andreou, K. A. Boahen, “Translinear circuits in subthreshold MOS,” Analog Integr. Circuits Signal Process. 9, 141–166 (1996).
[CrossRef]

Bair, W.

W. Bair, C. Koch, “An analog VLSI chip for finding edges from zero-crossing,” Neural Inf. Process. Syst. 3, 399–405 (1991).

Beare, R.

A. Moini, A. Bouzerdoum, K. Eshraghian, A. Yakovleff, X. T. Nguyen, A. Blanksby, R. Beare, D. Abbott, R. E. Bogner, “An insect vision-based motion detection chip,” IEEE J. Solid-State Circuits 32, 279–284 (1997).
[CrossRef]

Blanksby, A.

A. Moini, A. Bouzerdoum, K. Eshraghian, A. Yakovleff, X. T. Nguyen, A. Blanksby, R. Beare, D. Abbott, R. E. Bogner, “An insect vision-based motion detection chip,” IEEE J. Solid-State Circuits 32, 279–284 (1997).
[CrossRef]

Boahen, K. A.

G. Andreou, K. A. Boahen, “Translinear circuits in subthreshold MOS,” Analog Integr. Circuits Signal Process. 9, 141–166 (1996).
[CrossRef]

Bogner, R. E.

A. Moini, A. Bouzerdoum, K. Eshraghian, A. Yakovleff, X. T. Nguyen, A. Blanksby, R. Beare, D. Abbott, R. E. Bogner, “An insect vision-based motion detection chip,” IEEE J. Solid-State Circuits 32, 279–284 (1997).
[CrossRef]

Bouzerdoum, A.

A. Moini, A. Bouzerdoum, K. Eshraghian, A. Yakovleff, X. T. Nguyen, A. Blanksby, R. Beare, D. Abbott, R. E. Bogner, “An insect vision-based motion detection chip,” IEEE J. Solid-State Circuits 32, 279–284 (1997).
[CrossRef]

Bright, V. M.

M. C. Roggeman, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, J. H. Comtois, “Use of micro-electro-mechanical deformable mirrors to control aberrations in optical systems: theoretical and experimental results,” Opt. Eng. 36, 1326–1338 (1997).
[CrossRef]

Carhart, G. W.

Catte, F.

F. Catte, P. Lions, J. Morel, T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29, 182–193 (1992).
[CrossRef]

Coll, T.

F. Catte, P. Lions, J. Morel, T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29, 182–193 (1992).
[CrossRef]

Comtois, J. H.

M. C. Roggeman, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, J. H. Comtois, “Use of micro-electro-mechanical deformable mirrors to control aberrations in optical systems: theoretical and experimental results,” Opt. Eng. 36, 1326–1338 (1997).
[CrossRef]

Cowan, W. D.

M. C. Roggeman, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, J. H. Comtois, “Use of micro-electro-mechanical deformable mirrors to control aberrations in optical systems: theoretical and experimental results,” Opt. Eng. 36, 1326–1338 (1997).
[CrossRef]

Delbrück, T.

T. Delbrück, “A chip that focuses an image on itself,” in Proceedings of the workshop on Analog Integrated Neural Systems, Analog VLSI Implementation of Neural Systems, C. Mead, M. Ismail, eds. (Kluwer Academic, Boston, 1989), pp. 171–188.

Eshraghian, K.

A. Moini, A. Bouzerdoum, K. Eshraghian, A. Yakovleff, X. T. Nguyen, A. Blanksby, R. Beare, D. Abbott, R. E. Bogner, “An insect vision-based motion detection chip,” IEEE J. Solid-State Circuits 32, 279–284 (1997).
[CrossRef]

Faugeras, O.

O. Faugeras, Three-Dimensional Computer Vision (MIT Press, Cambridge, Mass., 1993).

Fried, D. L.

Gourlay, J.

J. Gourlay, A. O’Hara, A. J. Stevens, D. G. Vass, “A comparative investigation into planarized liquid crystal over silicon spatial light modulators,” J. Mod. Opt. 43, 181–198 (1996); http://www.ph.ed.ac.uk/optics/research/slm.html
[CrossRef]

Hick, S. R.

M. C. Roggeman, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, J. H. Comtois, “Use of micro-electro-mechanical deformable mirrors to control aberrations in optical systems: theoretical and experimental results,” Opt. Eng. 36, 1326–1338 (1997).
[CrossRef]

Johnson, K. M.

K. M. Johnson, D. J. McKnight, I. Underwood, “Smart spatial light modulators using liquid crystals on silicon,” IEEE J. Quantum Electron. 2, 699–714 (1993);S. Serati, G. Sharp, R. Serati, D. McKnight, J. Stookley, “128 128 analog liquid crystal spatial light modulator,” in Optical Pattern Recognition VI, D. P. Casasent, T. Chao, eds., Proc. SPIE2490, 378–387 (1995); http://www.bnonlinear.com/
[CrossRef]

Koch, C.

W. Bair, C. Koch, “An analog VLSI chip for finding edges from zero-crossing,” Neural Inf. Process. Syst. 3, 399–405 (1991).

Lions, P.

F. Catte, P. Lions, J. Morel, T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29, 182–193 (1992).
[CrossRef]

Malik, J.

P. Perona, J. Malik, “Scale space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern. Anal. Mach. Intell. 12, 629–630 (1990).
[CrossRef]

McKnight, D. J.

K. M. Johnson, D. J. McKnight, I. Underwood, “Smart spatial light modulators using liquid crystals on silicon,” IEEE J. Quantum Electron. 2, 699–714 (1993);S. Serati, G. Sharp, R. Serati, D. McKnight, J. Stookley, “128 128 analog liquid crystal spatial light modulator,” in Optical Pattern Recognition VI, D. P. Casasent, T. Chao, eds., Proc. SPIE2490, 378–387 (1995); http://www.bnonlinear.com/
[CrossRef]

Mead, C. A.

C. A. Mead, Analog VLSI and Neural Systems (Addison-Wesley, Reading, Mass., 1989); C. Koch, H. Li, eds., Vision Chips: Implementing Vision Algorithms with Analog VLSI Circuits (IEEE Computer Society Press, Los Alamitos, Calif., 1994); A. Moini, “Vision chips or seeing silicon,” Tech. Rep. (Centre for High Performance Integrated Technologies and Systems, The University of Adelaide, Adelaide, Australia, 1997) ( http://www.eleceng.adelaide.edu.au/Groups/GAAS/Bugeye/visionchips/vision_chips ).

Moini, A.

A. Moini, A. Bouzerdoum, K. Eshraghian, A. Yakovleff, X. T. Nguyen, A. Blanksby, R. Beare, D. Abbott, R. E. Bogner, “An insect vision-based motion detection chip,” IEEE J. Solid-State Circuits 32, 279–284 (1997).
[CrossRef]

Morel, J.

F. Catte, P. Lions, J. Morel, T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29, 182–193 (1992).
[CrossRef]

Mumford, D.

D. Mumford, J. Shah, “Optimal approximations by piecewise smooth functions and associated variational problems,” Commun. Pure Appl. Math. 42, 577–685 (1989).
[CrossRef]

Nguyen, X. T.

A. Moini, A. Bouzerdoum, K. Eshraghian, A. Yakovleff, X. T. Nguyen, A. Blanksby, R. Beare, D. Abbott, R. E. Bogner, “An insect vision-based motion detection chip,” IEEE J. Solid-State Circuits 32, 279–284 (1997).
[CrossRef]

O’Hara, A.

J. Gourlay, A. O’Hara, A. J. Stevens, D. G. Vass, “A comparative investigation into planarized liquid crystal over silicon spatial light modulators,” J. Mod. Opt. 43, 181–198 (1996); http://www.ph.ed.ac.uk/optics/research/slm.html
[CrossRef]

Pauwels, E.

M. Proesmans, E. Pauwels, L. Van Gool, “Coupled geometry-driven diffusion equations for low-level vision,” in Geometry-Driven Diffusion in Computer Vision, Bart M. ter Haar Romey, ed. (Kluwer Academic, Dordrecht, The Netherlands, 1994), pp. 191–198.

Perona, P.

P. Perona, J. Malik, “Scale space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern. Anal. Mach. Intell. 12, 629–630 (1990).
[CrossRef]

Proesmans, M.

M. Proesmans, E. Pauwels, L. Van Gool, “Coupled geometry-driven diffusion equations for low-level vision,” in Geometry-Driven Diffusion in Computer Vision, Bart M. ter Haar Romey, ed. (Kluwer Academic, Dordrecht, The Netherlands, 1994), pp. 191–198.

Pruidze, D. V.

Ricklin, J. C.

Roberts, P. C.

M. C. Roggeman, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, J. H. Comtois, “Use of micro-electro-mechanical deformable mirrors to control aberrations in optical systems: theoretical and experimental results,” Opt. Eng. 36, 1326–1338 (1997).
[CrossRef]

Roggeman, M. C.

M. C. Roggeman, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, J. H. Comtois, “Use of micro-electro-mechanical deformable mirrors to control aberrations in optical systems: theoretical and experimental results,” Opt. Eng. 36, 1326–1338 (1997).
[CrossRef]

Roggemann, M. C.

M. C. Roggemann, C. A. Stoudt, B. M. Welsh, “Image spectrum signal-to-noise ratio improvement by statistical frame selection for adaptive optics imaging through atmospheric turbulence,” Opt. Eng. 33, 3254–3264 (1994).
[CrossRef]

M. C. Roggemann, B. M. Welsh, Imaging through Turbulence (CRC Press, Boca Raton, Fla., 1996).

Russ, J. C.

J. C. Russ, The Image Processing Handbook, 3rd ed. (CRC Press/IEEE Press, London, 1998); K. R. Castleman, Digital Image Processing (Prentice-Hall, New York, 1995).

Shah, J.

D. Mumford, J. Shah, “Optimal approximations by piecewise smooth functions and associated variational problems,” Commun. Pure Appl. Math. 42, 577–685 (1989).
[CrossRef]

Sivokon, V. P.

Stevens, A. J.

J. Gourlay, A. O’Hara, A. J. Stevens, D. G. Vass, “A comparative investigation into planarized liquid crystal over silicon spatial light modulators,” J. Mod. Opt. 43, 181–198 (1996); http://www.ph.ed.ac.uk/optics/research/slm.html
[CrossRef]

Stoudt, C. A.

M. C. Roggemann, C. A. Stoudt, B. M. Welsh, “Image spectrum signal-to-noise ratio improvement by statistical frame selection for adaptive optics imaging through atmospheric turbulence,” Opt. Eng. 33, 3254–3264 (1994).
[CrossRef]

Terzopoulos, D.

D. Terzopoulos, “Regularization of inverse visual problems involving discontinuities,” IEEE Trans. Pattern. Anal. Mach. Intell. 8, 413–424 (1981).

Trivedi, M. M.

M. M. Trivedi, Image Processing and Analysis (Van Nostrand Reinhold, New York, 1992).

Underwood, I.

K. M. Johnson, D. J. McKnight, I. Underwood, “Smart spatial light modulators using liquid crystals on silicon,” IEEE J. Quantum Electron. 2, 699–714 (1993);S. Serati, G. Sharp, R. Serati, D. McKnight, J. Stookley, “128 128 analog liquid crystal spatial light modulator,” in Optical Pattern Recognition VI, D. P. Casasent, T. Chao, eds., Proc. SPIE2490, 378–387 (1995); http://www.bnonlinear.com/
[CrossRef]

Van Gool, L.

M. Proesmans, E. Pauwels, L. Van Gool, “Coupled geometry-driven diffusion equations for low-level vision,” in Geometry-Driven Diffusion in Computer Vision, Bart M. ter Haar Romey, ed. (Kluwer Academic, Dordrecht, The Netherlands, 1994), pp. 191–198.

Vass, D. G.

J. Gourlay, A. O’Hara, A. J. Stevens, D. G. Vass, “A comparative investigation into planarized liquid crystal over silicon spatial light modulators,” J. Mod. Opt. 43, 181–198 (1996); http://www.ph.ed.ac.uk/optics/research/slm.html
[CrossRef]

Voelz, D. G.

Vorontsov, M. A.

Welsh, B. M.

M. C. Roggeman, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, J. H. Comtois, “Use of micro-electro-mechanical deformable mirrors to control aberrations in optical systems: theoretical and experimental results,” Opt. Eng. 36, 1326–1338 (1997).
[CrossRef]

M. C. Roggemann, C. A. Stoudt, B. M. Welsh, “Image spectrum signal-to-noise ratio improvement by statistical frame selection for adaptive optics imaging through atmospheric turbulence,” Opt. Eng. 33, 3254–3264 (1994).
[CrossRef]

M. C. Roggemann, B. M. Welsh, Imaging through Turbulence (CRC Press, Boca Raton, Fla., 1996).

Yakovleff, A.

A. Moini, A. Bouzerdoum, K. Eshraghian, A. Yakovleff, X. T. Nguyen, A. Blanksby, R. Beare, D. Abbott, R. E. Bogner, “An insect vision-based motion detection chip,” IEEE J. Solid-State Circuits 32, 279–284 (1997).
[CrossRef]

Analog Integr. Circuits Signal Process. (1)

G. Andreou, K. A. Boahen, “Translinear circuits in subthreshold MOS,” Analog Integr. Circuits Signal Process. 9, 141–166 (1996).
[CrossRef]

Appl. Opt. (1)

Atmospheric Compensation Technology (1)

“Atmospheric Compensation Technology” (special issues in J. Opt. Soc. Am. 11(1) and (2) (1994); R. K. Tyson, Principles of Adaptive Optics (Academic, San Diego, Calif., 1991).

Commun. Pure Appl. Math. (1)

D. Mumford, J. Shah, “Optimal approximations by piecewise smooth functions and associated variational problems,” Commun. Pure Appl. Math. 42, 577–685 (1989).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. M. Johnson, D. J. McKnight, I. Underwood, “Smart spatial light modulators using liquid crystals on silicon,” IEEE J. Quantum Electron. 2, 699–714 (1993);S. Serati, G. Sharp, R. Serati, D. McKnight, J. Stookley, “128 128 analog liquid crystal spatial light modulator,” in Optical Pattern Recognition VI, D. P. Casasent, T. Chao, eds., Proc. SPIE2490, 378–387 (1995); http://www.bnonlinear.com/
[CrossRef]

IEEE J. Solid-State Circuits (1)

A. Moini, A. Bouzerdoum, K. Eshraghian, A. Yakovleff, X. T. Nguyen, A. Blanksby, R. Beare, D. Abbott, R. E. Bogner, “An insect vision-based motion detection chip,” IEEE J. Solid-State Circuits 32, 279–284 (1997).
[CrossRef]

IEEE Trans. Pattern. Anal. Mach. Intell. (2)

D. Terzopoulos, “Regularization of inverse visual problems involving discontinuities,” IEEE Trans. Pattern. Anal. Mach. Intell. 8, 413–424 (1981).

P. Perona, J. Malik, “Scale space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern. Anal. Mach. Intell. 12, 629–630 (1990).
[CrossRef]

J. Mod. Opt. (1)

J. Gourlay, A. O’Hara, A. J. Stevens, D. G. Vass, “A comparative investigation into planarized liquid crystal over silicon spatial light modulators,” J. Mod. Opt. 43, 181–198 (1996); http://www.ph.ed.ac.uk/optics/research/slm.html
[CrossRef]

J. Opt. Soc. Am. (2)

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

Neural Inf. Process. Syst. (1)

W. Bair, C. Koch, “An analog VLSI chip for finding edges from zero-crossing,” Neural Inf. Process. Syst. 3, 399–405 (1991).

Opt. Eng. (2)

M. C. Roggemann, C. A. Stoudt, B. M. Welsh, “Image spectrum signal-to-noise ratio improvement by statistical frame selection for adaptive optics imaging through atmospheric turbulence,” Opt. Eng. 33, 3254–3264 (1994).
[CrossRef]

M. C. Roggeman, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, J. H. Comtois, “Use of micro-electro-mechanical deformable mirrors to control aberrations in optical systems: theoretical and experimental results,” Opt. Eng. 36, 1326–1338 (1997).
[CrossRef]

Opt. Lett. (1)

Partial Differential Equations and Geometry-Driven Diffusion in Image Processing and Analysis (1)

“Partial Differential Equations and Geometry-Driven Diffusion in Image Processing and Analysis” special issue of IEEE Trans. Image Process. 7(3), (1998).

SIAM J. Numer. Anal. (1)

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Figures (15)

Fig. 1
Fig. 1

Schematic of the image-processing system for analog modeling of the diffusion equation with anisotropic gain [Eq. (4)].

Fig. 2
Fig. 2

Real-time image-edge-detection system based on phase-image diffraction.

Fig. 3
Fig. 3

Input image g(r) (a) and output images Id(r) [(b)–(d)] for the optical edge-image-detection system for different propagation distances l=L/(kb2): (b) l=0.4, (c) l=0.8, and (d) l=2.4. (The face has been obscured in this and subsequent figures to protect the privacy of the individual.)

Fig. 4
Fig. 4

Edge-image maps calculated with formula (8) for (a) and (b) and formula (10) for (c) and (d). The Gaussian kernel variance is a=2b for (a) and (c) and a=4b for (b) and (d) (b is the pixel size). The corresponding input g(r) and edge image Id(r) are shown in Figs. 3(a) and 3(b).

Fig. 5
Fig. 5

Processing of a single image frame based on PDE process (3): Input and processed images are shown in (a) and (c), respectively; the corresponding edge maps Jg(r) and Jf(r) are shown in (b) and (d). Parameters used in the calculations are τ=1, α=0.001, β=40, l=1.2, μ=1.25π, and a=2b.

Fig. 6
Fig. 6

Image processing based on PDE process (11): (a) original image corrupted by 25% Gaussian noise, (b) smoothed image g˜(r), (c) corresponding edge map J˜g(r). The processed image is shown in (d). Parameters used in the calculations are τ=1, α=0.001, β=20, l=1.2, μ=1.5π, and a=3.5b.

Fig. 7
Fig. 7

Image processing by nonlinear PDE process (13) for the input image in Fig. 6(a): (a) processed image, (b) corresponding edge map Jf(r). Parameters used in the calculations are the same as for Fig. 6.

Fig. 8
Fig. 8

Signal-processing schematic for an analog implementation of PDE process (13).

Fig. 9
Fig. 9

Computer-generated video data corresponding to the simplified model for anisoplanatic imaging conditions: (a) original image g(r), (b) smoothed image g˜(r) used as a background, (c) sample of image frame with lucky region for κ=0, (d) image sample from generated video data (κ=1), (e) image frame obtained by averaging 250 frames with zero background, (f) image frame obtained by video data averaging. Window-function width a=32b.

Fig. 10
Fig. 10

Normalized image-quality-metric evolution curves for the input Qg(t) (curve 1) and for the output Qf(t) video data (curves 2–4), with use of PDE process (15) (curves 2 and 3), with image-quality map (8) (curve 2), and with image-quality map (10) (curve 3). Curve 4 corresponds to image processing with PDE (17) and image-quality map (8). Image-quality metrics are normalized by the quality-metric value Q0 corresponding to the original image in Fig. 9(a).

Fig. 11
Fig. 11

Processing of video data that model an anisoplanatic imaging scenario with (a)–(c) evolution equation (15) and (d) Eq. (17). The output (synthetic) image (a) and the time-averaged images (b) and (d) were obtained with image-quality map (8), and the synthetic image (c) was obtained with image-quality map (10). The output (synthetic) images in (a) and (c) correspond to t=250τ. Parameters used in the calculations are τ=1, β=20, l=0.8, μ=1.5π, and a=3b.

Fig. 12
Fig. 12

Schematic of hybrid imaging system incorporating on-the-fly spatiotemporal image processing and adaptive wave-front correction.

Fig. 13
Fig. 13

Image processing of video data obtained with a camera that has a movable lens: (a)–(e) samples of images from the input video data, (f) processed image with deep field of view. Images (a)–(e) correspond to a camera lens focused on objects O5O1 placed at different distances L from the camera: (a) O5, L5=476 in.; (b) O4, L4=226 in.; (c) O3, L3=124 in.; (d) O2, L2=95 in.; (e) O1, L1=67 in.

Fig. 14
Fig. 14

Evolution curves for the input (curve 1) and the output (processed) video data (curve 2). The local maxima marked by the arrows in curve 1 correspond to images shown in Figs. 13(a)–(e). The parameters used for evolution equation (17) integration were τ=1, β=20, l=1.2, μ=1.5π, and a=4b.

Fig. 15
Fig. 15

Processing of video data containing 150 frames with a moving ball: (a) sample image frame from the input video data, (b) processed image.

Equations (22)

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E(f )=12 Ω{α|f(r)|2+βJg(r)[f(r)-g(r)]2}d2r,
f(r, t)t=-δfE,δfE=-α2f+βJg(f-g).
f(r, t)t=α2f(r, t)-βJg(r)[f(r, t)-g(r)].
τ f(r, t)t=α2f(r, t)-βJg(r, t)[f(r, t)-g(r, t)],
A(r, z=0)=A0 exp[iu(r)]=A0 exp[iμg(r)],
-2ik A(r, z)z=2A(r, z),
Id(r, t)I0[1-μL/(kb2)2g(r)].
Jg(r)=|Id(r)-I0|G(r-r, a)d2r,
Jg(r)κ|2g(r)|G(r-r, a)d2r,
Jg(r)=[Id(r)-I0]2G(r-r, a)d2r.
f(r, t)t=α2f(r, t)-βJ˜g(r)[f(r, t)-g(r)],
Jf(r, t)=|Idf(r, t)-I0|G(r-r, a)d2r,
f(r, t)t=α2f(r, t)-βJf(r)[f(r, t)-g(r)]
gn(r)=g(r)G(r-rn, a)+κg˜(r)×[1-G(r-rn, α)]
τ f(r, t)t=-βJg(r, t)[f(r, t)-g(r, t)].
Qg(t)=ΩJg(r, t)d2r,Qf(t)=ΩJf(r, t)d2r.
τ f(r, t)t=-βδ(r, t)[f(r, t)-g(r, t)],
δ(r, t)=Jg(r, t)-Jf(r, t)forJg(r, t)>Jf(r, t)0otherwise.
-2k az=2(aϕ)+a2ϕ,
2ka ϕz=2a-a[(ϕ/x)2+(ϕ/y)2].
kI/z=-I2ϕ,
2k ϕz=(ϕ/x)2+(ϕ/y)2,

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