Abstract

This paper presents a depth recovery method that gives the depth of any scene from its defocused images. The method combines depth from defocusing and depth from automatic focusing techniques. Blur information in defocused images is utilised to measure depth in a way similar to determining depth from automatic focusing but without searching for sharp images of objects. The proposed method does not need special scene illumination and involves only a single camera. Therefore, there are no correspondence, occlusion and intrusive emissions problems. The paper gives experimental results which demonstrate the accuracy of the method.

© 2007 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2006

V. Aslantas and M. Tunçkanat, "Depth of General Scenes from Defocused Images Using Multilayer Feedforward Network," LNCS 3949, 41-48 (2006).

2005

Bilal Ahmad and Tae-Sun Choi, "A heuristic approach for finding best focused shape," IEEE Trans. Circuits Syst. 15, 566-574 (2005).

2003

P. Favaro, A. Mennucci, and S. Soatto, "Observing Shape from Defocused Images," Int. J. Comput. Vision 52, 25-43 (2003).
[CrossRef]

2001

D. Z. F. Deschenes, "Depth from Defocus Estimation in Spatial Domain," Computer Vision and Image Understanding 81, 143-165 (2001).
[CrossRef]

M. Asif, and T. S. Choi, "Shape from focus using multilayer feedforward neural networks," IEEE Trans. Image Process. 10, 1670-1675 (2001).
[CrossRef]

J. Rayala, S. Gupta, and S. K. Mullick, "Estimation of depth from defocus as polynomial system identification," IEE Proceedings, Vision, Image and Signal Processing 148, 356-362 (2001).
[CrossRef]

1999

N. Asada, H. Fujiwara, and T. Matsuyama, "Particle depth measurement based on depth-from-defocus," Opt. Laser Technol. 31, 95-102 (1999).
[CrossRef]

D. T. Pham and V. Aslantas, "Depth from Defocusing using a Neural Network," J. Pattern Recogn. 32, 715-727 (1999).
[CrossRef]

1998

M. Subbarao and J. K. Tyan, "Selecting the optimal focus measure for autofocusing and depth-from-focus," IEEE Trans. Pattern Anal. Mach. Intell. 20, 864-870 (1998).
[CrossRef]

N. Asada, H. Fujiwara and T. Matsuyama, "Edge and depth from focus," Int. J. Comput. Vision 26, 153-163 (1998).
[CrossRef]

M. Watanabe and S. K. Nayar, "Rational filters for passive depth from defocus," Int. J. Comput. Vision 27, 203-225 (1998).
[CrossRef]

1995

M. Subbarao and T. Choi, "Accurate Recovery of Three Dimensional Shape from Focus," IEEE Trans. Pattern Anal. Mach. Intell. 17, 266-274 (1995).
[CrossRef]

S. Xu, D. W. Capson, and T. M. Caelli, "Range Measurement from Defocus Gradient," Mach. Vision Appl. 8, 179-186 (1995).
[CrossRef]

1994

L. F. Holeva, "Range Estimation from Camera Blur by Regularised Adaptive Identification," Int. J. Pattern Recogn. Artif. Intell. 8, 1273-1300 (1994).
[CrossRef]

A. P. Pentland, S. Scherock, T. Darrell, and B. Girod, "Simple Range Cameras based on Focal Error," J. Opt. Soc. Am. A 11, 2925-2934 (1994).
[CrossRef]

M. Subbarao and G. Surya, "Depth from Defocus: A Spatial Domain Approach," Int. J. Comput. Vision 13, 271-294 (1994).
[CrossRef]

1993

J. Ens and P. Lawrence, "Investigation of Methods for Determining Depth from Focus," IEEE Trans. Pattern Anal. Mach. Intell. 15, 97-108 (1993).
[CrossRef]

M. Subbarao, T. Choi, and A. Nikzat, "Focusing Techniques," Optical Engineering,  32, 2824-2836 (1993).
[CrossRef]

T. T. E. Yeo, S. H. Ong, Jayasooriah, and R. Sinniah, "Autofocusing for Tissue Microscopy," J. Image and Vision Computing,  11, 629-639 (1993).
[CrossRef]

1992

R. V. Dantu, N. J. Dimopoulos, R. V. Patel, and A. J. Al-Khalili, "Depth Perception using Blurring and its Application in VLSI Wafer Probing," Mach. Vision Appl. 5, 35-45 (1992).
[CrossRef]

S. H. Lai, C. W. Fu, and S. Chang, "A Generalised Depth Estimation Algorithm with a Single Image," IEEE Trans. Pattern Anal. Mach. Intell. 14, 405-411 (1992).
[CrossRef]

1991

C. Cardillo and M. A. Sid-Ahmed, "3-D Position Sensing using Passive Monocular Vision System," IEEE Trans. Pattern Anal. Mach. Intell. 13, 809-813 (1991).
[CrossRef]

L. Firestone, K. Cook, K. Culp, N. Talsania, and Jr. K . Preston, "Comparison of Autofocus Methods for Automated Microscopy," Cytometry,  12, 195-206 (1991).
[CrossRef] [PubMed]

1990

T. Darell and K. Wohn, "Depth from Focus using a Pyramid Architecture," Pattern Recogn. Lett. 11, 787-796 (1990).
[CrossRef]

1987

E. P. Krotkov, "Focusing," Int. J. Compt. Vision 1, 223-237 (1987).
[CrossRef]

P. Grossmann, "Depth from Focus," Pattern Recogn. Lett. 5, 63-69 (1987).
[CrossRef]

A. P. Pentland, "A New Sense for Depth of Field," IEEE Trans. Pattern Anal. Mach. Intell. 9, 523-531 (1987).
[CrossRef] [PubMed]

1985

F. C. A. Groen, I. T. Young, and G. Ligthart, "A Comparison of Different Focus Functions for use in Autofocus Algorithms," Cytometry,  6, 81-91 (1985).
[CrossRef] [PubMed]

1976

R. A. Jarvis, "Focus Optimisation Criteria for Computer Image Processing," Microscope,  24, 163-180 (1976).

Al-Khalili, A. J.

R. V. Dantu, N. J. Dimopoulos, R. V. Patel, and A. J. Al-Khalili, "Depth Perception using Blurring and its Application in VLSI Wafer Probing," Mach. Vision Appl. 5, 35-45 (1992).
[CrossRef]

Asada, N.

N. Asada, H. Fujiwara, and T. Matsuyama, "Particle depth measurement based on depth-from-defocus," Opt. Laser Technol. 31, 95-102 (1999).
[CrossRef]

N. Asada, H. Fujiwara and T. Matsuyama, "Edge and depth from focus," Int. J. Comput. Vision 26, 153-163 (1998).
[CrossRef]

Asif, M.

M. Asif, and T. S. Choi, "Shape from focus using multilayer feedforward neural networks," IEEE Trans. Image Process. 10, 1670-1675 (2001).
[CrossRef]

Aslantas, V.

V. Aslantas and M. Tunçkanat, "Depth of General Scenes from Defocused Images Using Multilayer Feedforward Network," LNCS 3949, 41-48 (2006).

D. T. Pham and V. Aslantas, "Depth from Defocusing using a Neural Network," J. Pattern Recogn. 32, 715-727 (1999).
[CrossRef]

Caelli, T. M.

S. Xu, D. W. Capson, and T. M. Caelli, "Range Measurement from Defocus Gradient," Mach. Vision Appl. 8, 179-186 (1995).
[CrossRef]

Capson, D. W.

S. Xu, D. W. Capson, and T. M. Caelli, "Range Measurement from Defocus Gradient," Mach. Vision Appl. 8, 179-186 (1995).
[CrossRef]

Cardillo, C.

C. Cardillo and M. A. Sid-Ahmed, "3-D Position Sensing using Passive Monocular Vision System," IEEE Trans. Pattern Anal. Mach. Intell. 13, 809-813 (1991).
[CrossRef]

Chang, S.

S. H. Lai, C. W. Fu, and S. Chang, "A Generalised Depth Estimation Algorithm with a Single Image," IEEE Trans. Pattern Anal. Mach. Intell. 14, 405-411 (1992).
[CrossRef]

Choi, T.

M. Subbarao and T. Choi, "Accurate Recovery of Three Dimensional Shape from Focus," IEEE Trans. Pattern Anal. Mach. Intell. 17, 266-274 (1995).
[CrossRef]

M. Subbarao, T. Choi, and A. Nikzat, "Focusing Techniques," Optical Engineering,  32, 2824-2836 (1993).
[CrossRef]

Choi, T. S.

M. Asif, and T. S. Choi, "Shape from focus using multilayer feedforward neural networks," IEEE Trans. Image Process. 10, 1670-1675 (2001).
[CrossRef]

Cook, K.

L. Firestone, K. Cook, K. Culp, N. Talsania, and Jr. K . Preston, "Comparison of Autofocus Methods for Automated Microscopy," Cytometry,  12, 195-206 (1991).
[CrossRef] [PubMed]

Culp, K.

L. Firestone, K. Cook, K. Culp, N. Talsania, and Jr. K . Preston, "Comparison of Autofocus Methods for Automated Microscopy," Cytometry,  12, 195-206 (1991).
[CrossRef] [PubMed]

Dantu, R. V.

R. V. Dantu, N. J. Dimopoulos, R. V. Patel, and A. J. Al-Khalili, "Depth Perception using Blurring and its Application in VLSI Wafer Probing," Mach. Vision Appl. 5, 35-45 (1992).
[CrossRef]

Darell, T.

T. Darell and K. Wohn, "Depth from Focus using a Pyramid Architecture," Pattern Recogn. Lett. 11, 787-796 (1990).
[CrossRef]

Darrell, T.

Deschenes, D. Z. F.

D. Z. F. Deschenes, "Depth from Defocus Estimation in Spatial Domain," Computer Vision and Image Understanding 81, 143-165 (2001).
[CrossRef]

Dimopoulos, N. J.

R. V. Dantu, N. J. Dimopoulos, R. V. Patel, and A. J. Al-Khalili, "Depth Perception using Blurring and its Application in VLSI Wafer Probing," Mach. Vision Appl. 5, 35-45 (1992).
[CrossRef]

Ens, J.

J. Ens and P. Lawrence, "Investigation of Methods for Determining Depth from Focus," IEEE Trans. Pattern Anal. Mach. Intell. 15, 97-108 (1993).
[CrossRef]

Favaro, P.

P. Favaro, A. Mennucci, and S. Soatto, "Observing Shape from Defocused Images," Int. J. Comput. Vision 52, 25-43 (2003).
[CrossRef]

Firestone, L.

L. Firestone, K. Cook, K. Culp, N. Talsania, and Jr. K . Preston, "Comparison of Autofocus Methods for Automated Microscopy," Cytometry,  12, 195-206 (1991).
[CrossRef] [PubMed]

Fu, C. W.

S. H. Lai, C. W. Fu, and S. Chang, "A Generalised Depth Estimation Algorithm with a Single Image," IEEE Trans. Pattern Anal. Mach. Intell. 14, 405-411 (1992).
[CrossRef]

Fujiwara, H.

N. Asada, H. Fujiwara, and T. Matsuyama, "Particle depth measurement based on depth-from-defocus," Opt. Laser Technol. 31, 95-102 (1999).
[CrossRef]

N. Asada, H. Fujiwara and T. Matsuyama, "Edge and depth from focus," Int. J. Comput. Vision 26, 153-163 (1998).
[CrossRef]

Girod, B.

Groen, F. C. A.

F. C. A. Groen, I. T. Young, and G. Ligthart, "A Comparison of Different Focus Functions for use in Autofocus Algorithms," Cytometry,  6, 81-91 (1985).
[CrossRef] [PubMed]

Grossmann, P.

P. Grossmann, "Depth from Focus," Pattern Recogn. Lett. 5, 63-69 (1987).
[CrossRef]

Gupta, S.

J. Rayala, S. Gupta, and S. K. Mullick, "Estimation of depth from defocus as polynomial system identification," IEE Proceedings, Vision, Image and Signal Processing 148, 356-362 (2001).
[CrossRef]

Holeva, L. F.

L. F. Holeva, "Range Estimation from Camera Blur by Regularised Adaptive Identification," Int. J. Pattern Recogn. Artif. Intell. 8, 1273-1300 (1994).
[CrossRef]

Jarvis, R. A.

R. A. Jarvis, "Focus Optimisation Criteria for Computer Image Processing," Microscope,  24, 163-180 (1976).

Krotkov, E. P.

E. P. Krotkov, "Focusing," Int. J. Compt. Vision 1, 223-237 (1987).
[CrossRef]

Lai, S. H.

S. H. Lai, C. W. Fu, and S. Chang, "A Generalised Depth Estimation Algorithm with a Single Image," IEEE Trans. Pattern Anal. Mach. Intell. 14, 405-411 (1992).
[CrossRef]

Lawrence, P.

J. Ens and P. Lawrence, "Investigation of Methods for Determining Depth from Focus," IEEE Trans. Pattern Anal. Mach. Intell. 15, 97-108 (1993).
[CrossRef]

Ligthart, G.

F. C. A. Groen, I. T. Young, and G. Ligthart, "A Comparison of Different Focus Functions for use in Autofocus Algorithms," Cytometry,  6, 81-91 (1985).
[CrossRef] [PubMed]

Matsuyama, T.

N. Asada, H. Fujiwara, and T. Matsuyama, "Particle depth measurement based on depth-from-defocus," Opt. Laser Technol. 31, 95-102 (1999).
[CrossRef]

N. Asada, H. Fujiwara and T. Matsuyama, "Edge and depth from focus," Int. J. Comput. Vision 26, 153-163 (1998).
[CrossRef]

Mennucci, A.

P. Favaro, A. Mennucci, and S. Soatto, "Observing Shape from Defocused Images," Int. J. Comput. Vision 52, 25-43 (2003).
[CrossRef]

Mullick, S. K.

J. Rayala, S. Gupta, and S. K. Mullick, "Estimation of depth from defocus as polynomial system identification," IEE Proceedings, Vision, Image and Signal Processing 148, 356-362 (2001).
[CrossRef]

Nayar, S. K.

M. Watanabe and S. K. Nayar, "Rational filters for passive depth from defocus," Int. J. Comput. Vision 27, 203-225 (1998).
[CrossRef]

Nikzat, A.

M. Subbarao, T. Choi, and A. Nikzat, "Focusing Techniques," Optical Engineering,  32, 2824-2836 (1993).
[CrossRef]

Ong, S. H.

T. T. E. Yeo, S. H. Ong, Jayasooriah, and R. Sinniah, "Autofocusing for Tissue Microscopy," J. Image and Vision Computing,  11, 629-639 (1993).
[CrossRef]

Patel, R. V.

R. V. Dantu, N. J. Dimopoulos, R. V. Patel, and A. J. Al-Khalili, "Depth Perception using Blurring and its Application in VLSI Wafer Probing," Mach. Vision Appl. 5, 35-45 (1992).
[CrossRef]

Pentland, A. P.

Pham, D. T.

D. T. Pham and V. Aslantas, "Depth from Defocusing using a Neural Network," J. Pattern Recogn. 32, 715-727 (1999).
[CrossRef]

Preston, Jr.K

L. Firestone, K. Cook, K. Culp, N. Talsania, and Jr. K . Preston, "Comparison of Autofocus Methods for Automated Microscopy," Cytometry,  12, 195-206 (1991).
[CrossRef] [PubMed]

Rayala, J.

J. Rayala, S. Gupta, and S. K. Mullick, "Estimation of depth from defocus as polynomial system identification," IEE Proceedings, Vision, Image and Signal Processing 148, 356-362 (2001).
[CrossRef]

Scherock, S.

Sid-Ahmed, M. A.

C. Cardillo and M. A. Sid-Ahmed, "3-D Position Sensing using Passive Monocular Vision System," IEEE Trans. Pattern Anal. Mach. Intell. 13, 809-813 (1991).
[CrossRef]

Soatto, S.

P. Favaro, A. Mennucci, and S. Soatto, "Observing Shape from Defocused Images," Int. J. Comput. Vision 52, 25-43 (2003).
[CrossRef]

Subbarao, M.

M. Subbarao and J. K. Tyan, "Selecting the optimal focus measure for autofocusing and depth-from-focus," IEEE Trans. Pattern Anal. Mach. Intell. 20, 864-870 (1998).
[CrossRef]

M. Subbarao and T. Choi, "Accurate Recovery of Three Dimensional Shape from Focus," IEEE Trans. Pattern Anal. Mach. Intell. 17, 266-274 (1995).
[CrossRef]

M. Subbarao and G. Surya, "Depth from Defocus: A Spatial Domain Approach," Int. J. Comput. Vision 13, 271-294 (1994).
[CrossRef]

M. Subbarao, T. Choi, and A. Nikzat, "Focusing Techniques," Optical Engineering,  32, 2824-2836 (1993).
[CrossRef]

Surya, G.

M. Subbarao and G. Surya, "Depth from Defocus: A Spatial Domain Approach," Int. J. Comput. Vision 13, 271-294 (1994).
[CrossRef]

Talsania, N.

L. Firestone, K. Cook, K. Culp, N. Talsania, and Jr. K . Preston, "Comparison of Autofocus Methods for Automated Microscopy," Cytometry,  12, 195-206 (1991).
[CrossRef] [PubMed]

Tunçkanat, M.

V. Aslantas and M. Tunçkanat, "Depth of General Scenes from Defocused Images Using Multilayer Feedforward Network," LNCS 3949, 41-48 (2006).

Tyan, J. K.

M. Subbarao and J. K. Tyan, "Selecting the optimal focus measure for autofocusing and depth-from-focus," IEEE Trans. Pattern Anal. Mach. Intell. 20, 864-870 (1998).
[CrossRef]

Watanabe, M.

M. Watanabe and S. K. Nayar, "Rational filters for passive depth from defocus," Int. J. Comput. Vision 27, 203-225 (1998).
[CrossRef]

Wohn, K.

T. Darell and K. Wohn, "Depth from Focus using a Pyramid Architecture," Pattern Recogn. Lett. 11, 787-796 (1990).
[CrossRef]

Xu, S.

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Figures (8)

Fig. 1.
Fig. 1.

Basic image formation geometry

Fig. 2.
Fig. 2.

Plot of theoretical blur circle radius versus depth for an f/2.8, 50mm lens [camera focused on an object 1m away from the lens].

Fig. 3.
Fig. 3.

Cross sections of three edges. (The step edge was placed at a distance of 200mm from the lens. Blurred edge 1 was obtained using camera parameters DLS1=75.0mm, F1=50.0mm and f1=1.4. The camera parameters used for the blurred edge 2 were DLS2=74.0mm, F2=47.49mm and f2=2.0.)

Fig. 4.
Fig. 4.

Different camera parameters giving the same sharpness value. B is the point of best focus

Fig. 5.
Fig. 5.

Possible focusing positions for an object placed in front of the camera. B corresponds to the object location. (Arrows show direction of camera movements)

Fig. 6.
Fig. 6.

(a) Cross section at points A and B (assuming a pin-hole camera with infinite depth of field) (b) the camera is focused at point B (c) the camera is focused at point A (d) after the movement required for depth computation by DFAD

Fig. 7.
Fig. 7.

Images of the objects used in the experiments

Fig. 8.
Fig. 8.

(a) Estimated depth vs. real depth (b) Errors for different depths

Tables (1)

Tables Icon

Table 1 Parameter adjustments and depth computation. “+” and “-” indicate that this camera parameter needs to be increased or decreased, respectively

Equations (19)

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

1 D OL + 1 D LF = 1 F
R = 2 D LF
δ = D LS D LF
L = F f
R = F D LS F D LF 2 f D LF
R = D OL ( D LS F ) FD LS 2 fD OL
D OL = FD LS D LS F 2 fR
δ = D LF D LS
D OL = FD LS D LS F + 2 fR
D OL = FD LS D LS F
R 1 = D OL ( D LS 1 F 1 ) F 1 D LS 1 2 f 1 D OL
R 2 = ( D OL + d ) ( D LS 2 F 2 ) F 2 D LS 2 2 f 2 ( D OL + d )
D OL 2 + [ d ( D LS 1 F 1 f 2 D LS 2 F 2 f 1 ) ( D LS 1 F 1 ) f 2 ( D LS 2 F 2 ) f 1 ] D OL D LS 1 F 1 f 2 d ( D LS 1 F 1 ) f 2 ( D LS 2 F 2 ) f 1 = 0
D OL 2 + [ d ( D LS 1 F 1 f 2 + D LS 2 F 2 f 1 ) ( D LS 1 F 1 ) f 2 + ( D LS 2 F 2 ) f 1 ] D OL D LS 1 F 1 f 2 d ( D LS 1 F 1 ) f 2 + ( D LS 2 F 2 ) f 1 = 0
max x N y N Z ( x , y ) 2 for Z ( x , y ) 2 > T
[ 1 0 1 2 0 2 1 0 1 ] [ 1 2 1 0 0 0 1 2 1 ]
I ( x , y ) = 1 n i = 1 n I i ( x , y )
D OL 2 + [ d D 0 ] D OL D 0 f 2 d ( f 2 f 1 ) = 0
D 0 = D LS F D LS F

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