Abstract

The paper describes a volumetric approach to depth estimation for robot navigation with use of only an approximately calibrated translating camera. Our approach is related to techniques for photo-realistic object reconstruction but with the emphasis on issues associated with navigation. The technique performs three-dimensional matching by a process of image interpolation and can adjust for errors in camera position. The reconstruction is achieved from a small angular range of scene views, and the technique is demonstrated to be insensitive to large errors in the camera positions. The ability to correct for more critical errors such as the camera orientation is shown to significantly improve the algorithm’s performance. Our technique is demonstrated on real image sequences and compares favorably with techniques based on optical flow.

© 2002 Optical Society of America

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References

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  1. R. M. Haralick, L. G. Shapiro, Computer and Robot Vision (Addison-Wesley, Reading, Mass., 1993), Vol. 2.
  2. B. K. P. Horn, B. G. Schunck, “Determining optical flow,” Artif. Intel. 17, 185–203 (1981).
    [CrossRef]
  3. D. Geiger, B. Ladendorf, A. Yuille, “Occlusions and binocular stereo,” in Proceedings of the 2nd European Conference on Computer Vision (ECCV’92) (Springer, Berlin, 1992), pp. 423–433.
  4. S. S. Beauchemin, J. L. Barron, “The computation of optical flow,” ACM Comput. Surveys 27, 433–467 (1995).
    [CrossRef]
  5. S. M. Seitz, C. R. Dyer, “Photorealistic scene reconstruction by voxel colouring,” Int. J. Comput. Vision 35, 151–173 (1999).
    [CrossRef]
  6. Z. Hisayoshi, Y. Tosyoshi, “Reconstruction of outer surfaces by bi-directional rays,” in Proceedings of the 6th International Conference in Central Europe on Computer Graphics and Visualization, V. Skala, ed. (Eurographics, Plzen-Bory, Czech Republic, 1998), pp. 141–148.
  7. H. Saito, T. Kanade, “Shape reconstruction in projective grid space from large number of images,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE Computer Society, Los Alamitos, Calif.1999), Vol. 2, pp. 49–54, June 1999.
  8. P. Eisert, E. Steinbach, B. Girod, “Automatic reconstruction of stationary 3-D objects from multiple uncalibrated camera views,” IEEE Trans. Circuits Syst. Video Technol. 10, 261–277 (2000).
    [CrossRef]
  9. Q. Chen, G. Medioni, “A volumetric stereo matching method: application to image-based modeling,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE Computer Society, Los Alamitos, Calif.1999), Vol. 1, pp. 29–34.
  10. D. T. Gering, W. W. Wells, “Object modeling using tomography and photography,” in Proceedings of the IEEE Workshop on Multi-View Modeling and Analysis of Visual Sciences (IEEE Computer Society, Los Alamitos, Calif., 1999), pp. 11–18.
  11. R. Szeliski, P. Golland, “Stereo matching with transparency and matting,” in Proceedings of the 6th International Conference on Computer Vision (Narosa, London, 1998), pp. 517–524.
  12. J. S. De Bonet, P. Viola, “Roxels: responsibility weighted 3D volume reconstruction,” in Proceedings of the 7th International Conference on Computer Vision (IEEE Computer Society, Los Alamitos, Calif., 1999), pp. 418–425.
  13. J. T. Preddey, R. G. Lane, “A tomographic technique for depth estimation from moving camera image sequences,” in Joint Australian and New Zealand Conference on Digital Image Computing, Techniques and Applications: DICTA’97/IVCNZ’97 (Massey University, Auckland, New Zealand, 1998), pp. 23–28.
  14. C. M. Harding, A. Bainbridge-Smith, R. G. Lane, “Limits of tomographic depth estimation,” in High-Speed Imaging and Sequence Analysis II, A. M. Frank, J. S. Walton, eds., Proc. SPIE3968, 81–92 (2000).
    [CrossRef]
  15. C. M. Harding, “How far away is it? Depth estimation by a robot with a camera,” Ph.D. thesis (University of Canterbury, Christchurch, New Zealand, 2001).
  16. A. S. L. Bainbridge-Smith, R. G. Lane, “Measuring image flow from colour imagery,” in Proceedings of the Electronic Colour Imaging and Applications Workshop, DICTA-94 (Australian Pattern Recognition Society, Canberra, Australia, 1994), pp. 9–14.
  17. M. G. Nagle, M. V. Srinivasan, D. L. Wilson, “Image interpolation technique for measurement of egomotion in 6 degrees of freedom,” J. Opt. Soc. Am. A 14, 3233–3241 (1997).
    [CrossRef]
  18. E. E. Hemayed, M. G. Mostafa, A. A. Farag, “3D object reconstruction from a sequence of images using voxel coloring,” in Three Dimensional Image Capture and Applications III, B. D. Corner, J. H. Nurre, eds., Proc. SPIE3958, 207–214 (2000).
    [CrossRef]
  19. C. Braccini, A. Grattarola, S. Zappatore, “3D volumetric and pictorial reconstruction from correspondences in 2D sequences,” in Proceedings of the 3rd International Workshop on Time-Varying Image Processing and Moving Object Recognition (Elsevier, Amsterdam, 1989), Vol. 2, pp. 207–214.
  20. E. Boyer, “Object models from contour sequences,” in Proceedings of the 4th European Conference on Computer Vision (Springer, Berlin, 1996), Vol. 2, pp. 109–118.
  21. R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, Reading, Mass., 1992).
  22. P. Moulin, R. Krishnamurthy, J. W. Woods, “Multiscale modelling and estimation of motion fields for video coding,” IEEE Trans. Image Process. 12, 1606–1620 (1997).
    [CrossRef]
  23. S. Haykin, Neural Networks (Macmillan College, New York, 1994).
  24. A. S. L. Bainbridge-Smith, R. G. Lane, “Determining optical flow using a differential method,” Image Vision Comput. 15, 11–22 (1997).
    [CrossRef]
  25. M. Campani, A. Verri, “Motion analysis from first-order properties of optical flow,” CVGIP Image Understand. 56, 90–107 (1992).
    [CrossRef]

2000 (1)

P. Eisert, E. Steinbach, B. Girod, “Automatic reconstruction of stationary 3-D objects from multiple uncalibrated camera views,” IEEE Trans. Circuits Syst. Video Technol. 10, 261–277 (2000).
[CrossRef]

1999 (1)

S. M. Seitz, C. R. Dyer, “Photorealistic scene reconstruction by voxel colouring,” Int. J. Comput. Vision 35, 151–173 (1999).
[CrossRef]

1997 (3)

M. G. Nagle, M. V. Srinivasan, D. L. Wilson, “Image interpolation technique for measurement of egomotion in 6 degrees of freedom,” J. Opt. Soc. Am. A 14, 3233–3241 (1997).
[CrossRef]

P. Moulin, R. Krishnamurthy, J. W. Woods, “Multiscale modelling and estimation of motion fields for video coding,” IEEE Trans. Image Process. 12, 1606–1620 (1997).
[CrossRef]

A. S. L. Bainbridge-Smith, R. G. Lane, “Determining optical flow using a differential method,” Image Vision Comput. 15, 11–22 (1997).
[CrossRef]

1995 (1)

S. S. Beauchemin, J. L. Barron, “The computation of optical flow,” ACM Comput. Surveys 27, 433–467 (1995).
[CrossRef]

1992 (1)

M. Campani, A. Verri, “Motion analysis from first-order properties of optical flow,” CVGIP Image Understand. 56, 90–107 (1992).
[CrossRef]

1981 (1)

B. K. P. Horn, B. G. Schunck, “Determining optical flow,” Artif. Intel. 17, 185–203 (1981).
[CrossRef]

Bainbridge-Smith, A.

C. M. Harding, A. Bainbridge-Smith, R. G. Lane, “Limits of tomographic depth estimation,” in High-Speed Imaging and Sequence Analysis II, A. M. Frank, J. S. Walton, eds., Proc. SPIE3968, 81–92 (2000).
[CrossRef]

Bainbridge-Smith, A. S. L.

A. S. L. Bainbridge-Smith, R. G. Lane, “Determining optical flow using a differential method,” Image Vision Comput. 15, 11–22 (1997).
[CrossRef]

A. S. L. Bainbridge-Smith, R. G. Lane, “Measuring image flow from colour imagery,” in Proceedings of the Electronic Colour Imaging and Applications Workshop, DICTA-94 (Australian Pattern Recognition Society, Canberra, Australia, 1994), pp. 9–14.

Barron, J. L.

S. S. Beauchemin, J. L. Barron, “The computation of optical flow,” ACM Comput. Surveys 27, 433–467 (1995).
[CrossRef]

Beauchemin, S. S.

S. S. Beauchemin, J. L. Barron, “The computation of optical flow,” ACM Comput. Surveys 27, 433–467 (1995).
[CrossRef]

Boyer, E.

E. Boyer, “Object models from contour sequences,” in Proceedings of the 4th European Conference on Computer Vision (Springer, Berlin, 1996), Vol. 2, pp. 109–118.

Braccini, C.

C. Braccini, A. Grattarola, S. Zappatore, “3D volumetric and pictorial reconstruction from correspondences in 2D sequences,” in Proceedings of the 3rd International Workshop on Time-Varying Image Processing and Moving Object Recognition (Elsevier, Amsterdam, 1989), Vol. 2, pp. 207–214.

Campani, M.

M. Campani, A. Verri, “Motion analysis from first-order properties of optical flow,” CVGIP Image Understand. 56, 90–107 (1992).
[CrossRef]

Chen, Q.

Q. Chen, G. Medioni, “A volumetric stereo matching method: application to image-based modeling,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE Computer Society, Los Alamitos, Calif.1999), Vol. 1, pp. 29–34.

De Bonet, J. S.

J. S. De Bonet, P. Viola, “Roxels: responsibility weighted 3D volume reconstruction,” in Proceedings of the 7th International Conference on Computer Vision (IEEE Computer Society, Los Alamitos, Calif., 1999), pp. 418–425.

Dyer, C. R.

S. M. Seitz, C. R. Dyer, “Photorealistic scene reconstruction by voxel colouring,” Int. J. Comput. Vision 35, 151–173 (1999).
[CrossRef]

Eisert, P.

P. Eisert, E. Steinbach, B. Girod, “Automatic reconstruction of stationary 3-D objects from multiple uncalibrated camera views,” IEEE Trans. Circuits Syst. Video Technol. 10, 261–277 (2000).
[CrossRef]

Farag, A. A.

E. E. Hemayed, M. G. Mostafa, A. A. Farag, “3D object reconstruction from a sequence of images using voxel coloring,” in Three Dimensional Image Capture and Applications III, B. D. Corner, J. H. Nurre, eds., Proc. SPIE3958, 207–214 (2000).
[CrossRef]

Geiger, D.

D. Geiger, B. Ladendorf, A. Yuille, “Occlusions and binocular stereo,” in Proceedings of the 2nd European Conference on Computer Vision (ECCV’92) (Springer, Berlin, 1992), pp. 423–433.

Gering, D. T.

D. T. Gering, W. W. Wells, “Object modeling using tomography and photography,” in Proceedings of the IEEE Workshop on Multi-View Modeling and Analysis of Visual Sciences (IEEE Computer Society, Los Alamitos, Calif., 1999), pp. 11–18.

Girod, B.

P. Eisert, E. Steinbach, B. Girod, “Automatic reconstruction of stationary 3-D objects from multiple uncalibrated camera views,” IEEE Trans. Circuits Syst. Video Technol. 10, 261–277 (2000).
[CrossRef]

Golland, P.

R. Szeliski, P. Golland, “Stereo matching with transparency and matting,” in Proceedings of the 6th International Conference on Computer Vision (Narosa, London, 1998), pp. 517–524.

Gonzalez, R. C.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, Reading, Mass., 1992).

Grattarola, A.

C. Braccini, A. Grattarola, S. Zappatore, “3D volumetric and pictorial reconstruction from correspondences in 2D sequences,” in Proceedings of the 3rd International Workshop on Time-Varying Image Processing and Moving Object Recognition (Elsevier, Amsterdam, 1989), Vol. 2, pp. 207–214.

Haralick, R. M.

R. M. Haralick, L. G. Shapiro, Computer and Robot Vision (Addison-Wesley, Reading, Mass., 1993), Vol. 2.

Harding, C. M.

C. M. Harding, “How far away is it? Depth estimation by a robot with a camera,” Ph.D. thesis (University of Canterbury, Christchurch, New Zealand, 2001).

C. M. Harding, A. Bainbridge-Smith, R. G. Lane, “Limits of tomographic depth estimation,” in High-Speed Imaging and Sequence Analysis II, A. M. Frank, J. S. Walton, eds., Proc. SPIE3968, 81–92 (2000).
[CrossRef]

Haykin, S.

S. Haykin, Neural Networks (Macmillan College, New York, 1994).

Hemayed, E. E.

E. E. Hemayed, M. G. Mostafa, A. A. Farag, “3D object reconstruction from a sequence of images using voxel coloring,” in Three Dimensional Image Capture and Applications III, B. D. Corner, J. H. Nurre, eds., Proc. SPIE3958, 207–214 (2000).
[CrossRef]

Hisayoshi, Z.

Z. Hisayoshi, Y. Tosyoshi, “Reconstruction of outer surfaces by bi-directional rays,” in Proceedings of the 6th International Conference in Central Europe on Computer Graphics and Visualization, V. Skala, ed. (Eurographics, Plzen-Bory, Czech Republic, 1998), pp. 141–148.

Horn, B. K. P.

B. K. P. Horn, B. G. Schunck, “Determining optical flow,” Artif. Intel. 17, 185–203 (1981).
[CrossRef]

Kanade, T.

H. Saito, T. Kanade, “Shape reconstruction in projective grid space from large number of images,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE Computer Society, Los Alamitos, Calif.1999), Vol. 2, pp. 49–54, June 1999.

Krishnamurthy, R.

P. Moulin, R. Krishnamurthy, J. W. Woods, “Multiscale modelling and estimation of motion fields for video coding,” IEEE Trans. Image Process. 12, 1606–1620 (1997).
[CrossRef]

Ladendorf, B.

D. Geiger, B. Ladendorf, A. Yuille, “Occlusions and binocular stereo,” in Proceedings of the 2nd European Conference on Computer Vision (ECCV’92) (Springer, Berlin, 1992), pp. 423–433.

Lane, R. G.

A. S. L. Bainbridge-Smith, R. G. Lane, “Determining optical flow using a differential method,” Image Vision Comput. 15, 11–22 (1997).
[CrossRef]

A. S. L. Bainbridge-Smith, R. G. Lane, “Measuring image flow from colour imagery,” in Proceedings of the Electronic Colour Imaging and Applications Workshop, DICTA-94 (Australian Pattern Recognition Society, Canberra, Australia, 1994), pp. 9–14.

C. M. Harding, A. Bainbridge-Smith, R. G. Lane, “Limits of tomographic depth estimation,” in High-Speed Imaging and Sequence Analysis II, A. M. Frank, J. S. Walton, eds., Proc. SPIE3968, 81–92 (2000).
[CrossRef]

J. T. Preddey, R. G. Lane, “A tomographic technique for depth estimation from moving camera image sequences,” in Joint Australian and New Zealand Conference on Digital Image Computing, Techniques and Applications: DICTA’97/IVCNZ’97 (Massey University, Auckland, New Zealand, 1998), pp. 23–28.

Medioni, G.

Q. Chen, G. Medioni, “A volumetric stereo matching method: application to image-based modeling,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE Computer Society, Los Alamitos, Calif.1999), Vol. 1, pp. 29–34.

Mostafa, M. G.

E. E. Hemayed, M. G. Mostafa, A. A. Farag, “3D object reconstruction from a sequence of images using voxel coloring,” in Three Dimensional Image Capture and Applications III, B. D. Corner, J. H. Nurre, eds., Proc. SPIE3958, 207–214 (2000).
[CrossRef]

Moulin, P.

P. Moulin, R. Krishnamurthy, J. W. Woods, “Multiscale modelling and estimation of motion fields for video coding,” IEEE Trans. Image Process. 12, 1606–1620 (1997).
[CrossRef]

Nagle, M. G.

Preddey, J. T.

J. T. Preddey, R. G. Lane, “A tomographic technique for depth estimation from moving camera image sequences,” in Joint Australian and New Zealand Conference on Digital Image Computing, Techniques and Applications: DICTA’97/IVCNZ’97 (Massey University, Auckland, New Zealand, 1998), pp. 23–28.

Saito, H.

H. Saito, T. Kanade, “Shape reconstruction in projective grid space from large number of images,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE Computer Society, Los Alamitos, Calif.1999), Vol. 2, pp. 49–54, June 1999.

Schunck, B. G.

B. K. P. Horn, B. G. Schunck, “Determining optical flow,” Artif. Intel. 17, 185–203 (1981).
[CrossRef]

Seitz, S. M.

S. M. Seitz, C. R. Dyer, “Photorealistic scene reconstruction by voxel colouring,” Int. J. Comput. Vision 35, 151–173 (1999).
[CrossRef]

Shapiro, L. G.

R. M. Haralick, L. G. Shapiro, Computer and Robot Vision (Addison-Wesley, Reading, Mass., 1993), Vol. 2.

Srinivasan, M. V.

Steinbach, E.

P. Eisert, E. Steinbach, B. Girod, “Automatic reconstruction of stationary 3-D objects from multiple uncalibrated camera views,” IEEE Trans. Circuits Syst. Video Technol. 10, 261–277 (2000).
[CrossRef]

Szeliski, R.

R. Szeliski, P. Golland, “Stereo matching with transparency and matting,” in Proceedings of the 6th International Conference on Computer Vision (Narosa, London, 1998), pp. 517–524.

Tosyoshi, Y.

Z. Hisayoshi, Y. Tosyoshi, “Reconstruction of outer surfaces by bi-directional rays,” in Proceedings of the 6th International Conference in Central Europe on Computer Graphics and Visualization, V. Skala, ed. (Eurographics, Plzen-Bory, Czech Republic, 1998), pp. 141–148.

Verri, A.

M. Campani, A. Verri, “Motion analysis from first-order properties of optical flow,” CVGIP Image Understand. 56, 90–107 (1992).
[CrossRef]

Viola, P.

J. S. De Bonet, P. Viola, “Roxels: responsibility weighted 3D volume reconstruction,” in Proceedings of the 7th International Conference on Computer Vision (IEEE Computer Society, Los Alamitos, Calif., 1999), pp. 418–425.

Wells, W. W.

D. T. Gering, W. W. Wells, “Object modeling using tomography and photography,” in Proceedings of the IEEE Workshop on Multi-View Modeling and Analysis of Visual Sciences (IEEE Computer Society, Los Alamitos, Calif., 1999), pp. 11–18.

Wilson, D. L.

Woods, J. W.

P. Moulin, R. Krishnamurthy, J. W. Woods, “Multiscale modelling and estimation of motion fields for video coding,” IEEE Trans. Image Process. 12, 1606–1620 (1997).
[CrossRef]

Woods, R. E.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, Reading, Mass., 1992).

Yuille, A.

D. Geiger, B. Ladendorf, A. Yuille, “Occlusions and binocular stereo,” in Proceedings of the 2nd European Conference on Computer Vision (ECCV’92) (Springer, Berlin, 1992), pp. 423–433.

Zappatore, S.

C. Braccini, A. Grattarola, S. Zappatore, “3D volumetric and pictorial reconstruction from correspondences in 2D sequences,” in Proceedings of the 3rd International Workshop on Time-Varying Image Processing and Moving Object Recognition (Elsevier, Amsterdam, 1989), Vol. 2, pp. 207–214.

ACM Comput. Surveys (1)

S. S. Beauchemin, J. L. Barron, “The computation of optical flow,” ACM Comput. Surveys 27, 433–467 (1995).
[CrossRef]

Artif. Intel. (1)

B. K. P. Horn, B. G. Schunck, “Determining optical flow,” Artif. Intel. 17, 185–203 (1981).
[CrossRef]

CVGIP Image Understand. (1)

M. Campani, A. Verri, “Motion analysis from first-order properties of optical flow,” CVGIP Image Understand. 56, 90–107 (1992).
[CrossRef]

IEEE Trans. Circuits Syst. Video Technol. (1)

P. Eisert, E. Steinbach, B. Girod, “Automatic reconstruction of stationary 3-D objects from multiple uncalibrated camera views,” IEEE Trans. Circuits Syst. Video Technol. 10, 261–277 (2000).
[CrossRef]

IEEE Trans. Image Process. (1)

P. Moulin, R. Krishnamurthy, J. W. Woods, “Multiscale modelling and estimation of motion fields for video coding,” IEEE Trans. Image Process. 12, 1606–1620 (1997).
[CrossRef]

Image Vision Comput. (1)

A. S. L. Bainbridge-Smith, R. G. Lane, “Determining optical flow using a differential method,” Image Vision Comput. 15, 11–22 (1997).
[CrossRef]

Int. J. Comput. Vision (1)

S. M. Seitz, C. R. Dyer, “Photorealistic scene reconstruction by voxel colouring,” Int. J. Comput. Vision 35, 151–173 (1999).
[CrossRef]

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

Other (17)

R. M. Haralick, L. G. Shapiro, Computer and Robot Vision (Addison-Wesley, Reading, Mass., 1993), Vol. 2.

Z. Hisayoshi, Y. Tosyoshi, “Reconstruction of outer surfaces by bi-directional rays,” in Proceedings of the 6th International Conference in Central Europe on Computer Graphics and Visualization, V. Skala, ed. (Eurographics, Plzen-Bory, Czech Republic, 1998), pp. 141–148.

H. Saito, T. Kanade, “Shape reconstruction in projective grid space from large number of images,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE Computer Society, Los Alamitos, Calif.1999), Vol. 2, pp. 49–54, June 1999.

S. Haykin, Neural Networks (Macmillan College, New York, 1994).

D. Geiger, B. Ladendorf, A. Yuille, “Occlusions and binocular stereo,” in Proceedings of the 2nd European Conference on Computer Vision (ECCV’92) (Springer, Berlin, 1992), pp. 423–433.

Q. Chen, G. Medioni, “A volumetric stereo matching method: application to image-based modeling,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE Computer Society, Los Alamitos, Calif.1999), Vol. 1, pp. 29–34.

D. T. Gering, W. W. Wells, “Object modeling using tomography and photography,” in Proceedings of the IEEE Workshop on Multi-View Modeling and Analysis of Visual Sciences (IEEE Computer Society, Los Alamitos, Calif., 1999), pp. 11–18.

R. Szeliski, P. Golland, “Stereo matching with transparency and matting,” in Proceedings of the 6th International Conference on Computer Vision (Narosa, London, 1998), pp. 517–524.

J. S. De Bonet, P. Viola, “Roxels: responsibility weighted 3D volume reconstruction,” in Proceedings of the 7th International Conference on Computer Vision (IEEE Computer Society, Los Alamitos, Calif., 1999), pp. 418–425.

J. T. Preddey, R. G. Lane, “A tomographic technique for depth estimation from moving camera image sequences,” in Joint Australian and New Zealand Conference on Digital Image Computing, Techniques and Applications: DICTA’97/IVCNZ’97 (Massey University, Auckland, New Zealand, 1998), pp. 23–28.

C. M. Harding, A. Bainbridge-Smith, R. G. Lane, “Limits of tomographic depth estimation,” in High-Speed Imaging and Sequence Analysis II, A. M. Frank, J. S. Walton, eds., Proc. SPIE3968, 81–92 (2000).
[CrossRef]

C. M. Harding, “How far away is it? Depth estimation by a robot with a camera,” Ph.D. thesis (University of Canterbury, Christchurch, New Zealand, 2001).

A. S. L. Bainbridge-Smith, R. G. Lane, “Measuring image flow from colour imagery,” in Proceedings of the Electronic Colour Imaging and Applications Workshop, DICTA-94 (Australian Pattern Recognition Society, Canberra, Australia, 1994), pp. 9–14.

E. E. Hemayed, M. G. Mostafa, A. A. Farag, “3D object reconstruction from a sequence of images using voxel coloring,” in Three Dimensional Image Capture and Applications III, B. D. Corner, J. H. Nurre, eds., Proc. SPIE3958, 207–214 (2000).
[CrossRef]

C. Braccini, A. Grattarola, S. Zappatore, “3D volumetric and pictorial reconstruction from correspondences in 2D sequences,” in Proceedings of the 3rd International Workshop on Time-Varying Image Processing and Moving Object Recognition (Elsevier, Amsterdam, 1989), Vol. 2, pp. 207–214.

E. Boyer, “Object models from contour sequences,” in Proceedings of the 4th European Conference on Computer Vision (Springer, Berlin, 1996), Vol. 2, pp. 109–118.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, Reading, Mass., 1992).

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Figures (15)

Fig. 1
Fig. 1

Two-dimensional techniques such as optical flow and stereo matching try to match pixels at the image plane. Three-dimensional direct depth techniques, however, compare pixels over a volume of space by backprojecting image intensities.

Fig. 2
Fig. 2

(a) If the surface S is at the true object depth, then the camera images backprojected onto it give consistent intensity values at each point and a low variance. (b) If, however, the surface is at the wrong depth, the backprojected intensities do not agree at each point in the image.

Fig. 3
Fig. 3

Notation and coordinate axes. The jth camera is displaced from the world coordinates by (Xj, Yj, Zj) and rotated by αj,βj,θj. For an array of cameras with regular spacing of (ΔX, ΔY, ΔZ) the jth camera will be at position j(ΔX, ΔY, ΔZ).    

Fig. 4
Fig. 4

Scanning the volume. The most intuitive approach is (a) to backproject to each depth, one after another. For our application, however, it is more useful (b) to reconstruct along a row or column at a time. This also allows the algorithm to be used in a manner better suited to navigation and makes parallel implementation very straightforward.

Fig. 5
Fig. 5

Fifth and twenty-seventh frames from the sideways goblin sequence showing a goblin figurine with the bookcase backdrop behind it. Camera motion is in X, parallel to the scene.

Fig. 6
Fig. 6

First and thirty-first frames from the forward goblin sequence showing a goblin figurine with the bookcase backdrop behind it. Camera motion is in Z, toward the scene.

Fig. 7
Fig. 7

Depth map obtained for the uncalibrated sideways goblin sequence.

Fig. 8
Fig. 8

Residual variance versus θ for low-resolution 970-point reconstructions and for higher-resolution 830,000 point reconstructions. Both show a minimum at approximately θ=-1.6 deg.

Fig. 9
Fig. 9

Depth maps for the goblin sequence with θ=-1.6 deg. (a) Original depth map results. (b) Applying a 5×5 median filter to the depth map reduces noise while preserving edges.

Fig. 10
Fig. 10

Three-dimensional plot of the goblin and background for the sideways goblin sequence.

Fig. 11
Fig. 11

Raw depth map obtained for the forward goblin sequence median filtered with a 5×5 filter to reduce noise. Extreme values in the center of the depth map correspond to the sequence’s focus of expansion.

Fig. 12
Fig. 12

Residual variance versus the X coordinate of the sixth camera image for low-resolution 1090-point reconstructions and for high-resolution 920,000-point reconstructions. Both show a minimum at 1.35 mm.

Fig. 13
Fig. 13

Comparison with optical flow. (a) A synthetic sequence showing spheres against a planar background. Motion is in Z, toward the scene; pixel motion ranges from 0 pixel/frame to 1.6 pixels/frame. (b) The filtered depth map obtained by the volumetric algorithm. (c) The depths obtained by a standard optical flow algorithm with use of a window size of 41×41 pixels. 25 The depth maps in (b) and (c) are displayed on the same gray scale.

Fig. 14
Fig. 14

Forward goblin sequence: the effect of reducing the accuracy of the camera positions on the obtained depth map. (a), (c) Noise with variance of 5 and 10 steps, has been added to the Z positions of the camera, moving the camera backward and forward relative to its expected position. (b), (d) Noise with variance of 5 and 10 steps has been added to the X positions, moving the camera sideways relative to its expected position.

Fig. 15
Fig. 15

Forward goblin sequence. Reducing the number of frames has little effect on the accuracy of reconstruction until fewer than approximately five frames are used. This number of frames has been validated on other real sequences. (a) six frames, (b) four frames, (c) two frames.

Equations (10)

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

Var(X, Y, Z)
=iCi(X, Y, Z)2-iCi(X, Y, Z)2n-1,
EV=EM+EN,
ri(xj, yj)=-f (X-Xj)cθjcβj+(Y-Yj)cβjsθj-(Z-Zj)sβj(X-Xj)(sαjsθj+cαjsβjcθj)+(Y-Yj)(cαjsβjsθj-sαjcθj)+(Z-Zj)cαjcβj,
-f (X-Xj)(sαjsβjcθj-cαjsθj)+(Y-Yj)(sαjsβjsθj+cαjcθj)+(Z-Zj)sαjcβj(X-Xj)(sαjsθj+cθj sβjcθj)-(Y-Yj)(sαjcθj-cαjsβjsθj)+(Z-Zj)cαjcβj,
Error[R(i)]=E[R(i)]=j{I[ri(xj, yj)]}2-jI[xj, yj]2(n-1),
θj=k1,j,
βj=k2,j,
αj=k3,j.
(Xj, Yj, Zj)=j(ΔX, ΔY, ΔZ).

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