Abstract

Knowledge of the position of the vanishing point is the key for geometrical modeling of an image containing a reflective surface or cast shadows. Such an image can be analyzed as two subimages that constitute a stereo pair. For this model-estimation task an automatic method is presented that utilizes motion statistics and the statistical properties of image points for the determination of point correspondence and the subsequent estimation of vanishing point position, optimized by use of a goodness-of-fit function. We show that this approach gives robust results in widely different real-world environments, even when the correspondence is corrupted with considerable amounts of noise.

© 2006 Optical Society of America

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References

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  1. H. Mitsumoto and S. Tamura, IEEE Trans. Pattern Anal. Mach. Intell. 941 (1992).
    [CrossRef]
  2. R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge U. Press, 2000).
  3. R. Penne, 'Mirror Symmetry in Perspective,' in Proceedings of Advanced Concepts for Intelligent Vision Systems, LNCS (Springer, 2005), p. 634.
    [CrossRef]
  4. R. J. Alexandre, G. G. Medioni, and R. Waupotitsch, 'Reconstructing mirror symmetric scenes from a single view using 2-view stereo geometry,' in Proceedings of International Conference on Pattern Recognition (2002), Vol. 4, p. 12.
  5. S. A. Shafer, Shadows and Silhouettes in Computer Vision (Kluwer Academic, 1985).
  6. Z. Szlávik, L. Havasi, and T. Szirányi, 'Estimation of common groundplane based on co-motion statistics,' in Proceedings of Image Analysis and Recognition, LNCS (Springer, 2004), p. 347.
    [CrossRef]
  7. Cs. Benedek, L. Havasi, T. Szirányi, and Z. Szlávik, in Proceedings of IEEE Conference on Advanced Video and Signal-Based Surveillance (Institute of Electrical and Electronics Engineers, 2005), p. 439.
    [CrossRef]
  8. R. A. Johnson and D. W. Wichern, Applied Multivariate Statistical Analysis (Prentice-Hall, 2002).

1992 (1)

H. Mitsumoto and S. Tamura, IEEE Trans. Pattern Anal. Mach. Intell. 941 (1992).
[CrossRef]

Alexandre, R. J.

R. J. Alexandre, G. G. Medioni, and R. Waupotitsch, 'Reconstructing mirror symmetric scenes from a single view using 2-view stereo geometry,' in Proceedings of International Conference on Pattern Recognition (2002), Vol. 4, p. 12.

Benedek, Cs.

Cs. Benedek, L. Havasi, T. Szirányi, and Z. Szlávik, in Proceedings of IEEE Conference on Advanced Video and Signal-Based Surveillance (Institute of Electrical and Electronics Engineers, 2005), p. 439.
[CrossRef]

Hartley, R.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge U. Press, 2000).

Havasi, L.

Z. Szlávik, L. Havasi, and T. Szirányi, 'Estimation of common groundplane based on co-motion statistics,' in Proceedings of Image Analysis and Recognition, LNCS (Springer, 2004), p. 347.
[CrossRef]

Cs. Benedek, L. Havasi, T. Szirányi, and Z. Szlávik, in Proceedings of IEEE Conference on Advanced Video and Signal-Based Surveillance (Institute of Electrical and Electronics Engineers, 2005), p. 439.
[CrossRef]

Johnson, R. A.

R. A. Johnson and D. W. Wichern, Applied Multivariate Statistical Analysis (Prentice-Hall, 2002).

Medioni, G. G.

R. J. Alexandre, G. G. Medioni, and R. Waupotitsch, 'Reconstructing mirror symmetric scenes from a single view using 2-view stereo geometry,' in Proceedings of International Conference on Pattern Recognition (2002), Vol. 4, p. 12.

Mitsumoto, H.

H. Mitsumoto and S. Tamura, IEEE Trans. Pattern Anal. Mach. Intell. 941 (1992).
[CrossRef]

Penne, R.

R. Penne, 'Mirror Symmetry in Perspective,' in Proceedings of Advanced Concepts for Intelligent Vision Systems, LNCS (Springer, 2005), p. 634.
[CrossRef]

Shafer, S. A.

S. A. Shafer, Shadows and Silhouettes in Computer Vision (Kluwer Academic, 1985).

Szirányi, T.

Cs. Benedek, L. Havasi, T. Szirányi, and Z. Szlávik, in Proceedings of IEEE Conference on Advanced Video and Signal-Based Surveillance (Institute of Electrical and Electronics Engineers, 2005), p. 439.
[CrossRef]

Z. Szlávik, L. Havasi, and T. Szirányi, 'Estimation of common groundplane based on co-motion statistics,' in Proceedings of Image Analysis and Recognition, LNCS (Springer, 2004), p. 347.
[CrossRef]

Szlávik, Z.

Z. Szlávik, L. Havasi, and T. Szirányi, 'Estimation of common groundplane based on co-motion statistics,' in Proceedings of Image Analysis and Recognition, LNCS (Springer, 2004), p. 347.
[CrossRef]

Cs. Benedek, L. Havasi, T. Szirányi, and Z. Szlávik, in Proceedings of IEEE Conference on Advanced Video and Signal-Based Surveillance (Institute of Electrical and Electronics Engineers, 2005), p. 439.
[CrossRef]

Tamura, S.

H. Mitsumoto and S. Tamura, IEEE Trans. Pattern Anal. Mach. Intell. 941 (1992).
[CrossRef]

Waupotitsch, R.

R. J. Alexandre, G. G. Medioni, and R. Waupotitsch, 'Reconstructing mirror symmetric scenes from a single view using 2-view stereo geometry,' in Proceedings of International Conference on Pattern Recognition (2002), Vol. 4, p. 12.

Wichern, D. W.

R. A. Johnson and D. W. Wichern, Applied Multivariate Statistical Analysis (Prentice-Hall, 2002).

Zisserman, A.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge U. Press, 2000).

IEEE Trans. Pattern Anal. Mach. Intell. (1)

H. Mitsumoto and S. Tamura, IEEE Trans. Pattern Anal. Mach. Intell. 941 (1992).
[CrossRef]

Other (7)

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge U. Press, 2000).

R. Penne, 'Mirror Symmetry in Perspective,' in Proceedings of Advanced Concepts for Intelligent Vision Systems, LNCS (Springer, 2005), p. 634.
[CrossRef]

R. J. Alexandre, G. G. Medioni, and R. Waupotitsch, 'Reconstructing mirror symmetric scenes from a single view using 2-view stereo geometry,' in Proceedings of International Conference on Pattern Recognition (2002), Vol. 4, p. 12.

S. A. Shafer, Shadows and Silhouettes in Computer Vision (Kluwer Academic, 1985).

Z. Szlávik, L. Havasi, and T. Szirányi, 'Estimation of common groundplane based on co-motion statistics,' in Proceedings of Image Analysis and Recognition, LNCS (Springer, 2004), p. 347.
[CrossRef]

Cs. Benedek, L. Havasi, T. Szirányi, and Z. Szlávik, in Proceedings of IEEE Conference on Advanced Video and Signal-Based Surveillance (Institute of Electrical and Electronics Engineers, 2005), p. 439.
[CrossRef]

R. A. Johnson and D. W. Wichern, Applied Multivariate Statistical Analysis (Prentice-Hall, 2002).

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Figures (5)

Fig. 1
Fig. 1

Odd sample from co-motion statistics for, left to right, Ants, Mice, and Shop sequences.

Fig. 2
Fig. 2

Sample correspondence of, left, Shadow and, right, Shop sequences corrupted with several outliers.

Fig. 3
Fig. 3

Goodness-of-fit function; the shaded area indicates better fit. The VP is marked by the black cross.

Fig. 4
Fig. 4

Computation steps: top, input image, co-motion statistics; bottom, foreground and shadow masks.

Fig. 5
Fig. 5

Collinearities of the three points: VP, the original point, and the reflected point.

Tables (1)

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Table 1 Experimental Results

Equations (4)

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f ( u , x ) = P co ( u x ) = t m ( t , x ) m ( t , u ) t m ( t , x ) .
V P = arg max u a A P g ( a ) P coll [ δ ( a , u ) a ] .
δ ( a , u ) = arg max v P coll ( v a ) , v a u ¯ .
f sh ( u , x ) = P co ( u x ) = t m ( t , x ) s ( t , u ) t [ m ( t , x ) + s ( t , u ) ] ,

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