Abstract

Polygonal active contours (snakes) have been used with success for target segmentation and tracking. We propose to adapt a technique based on the minimum description length principle to estimate the complexity (proportional to the number of nodes) of the polygon used for the segmentation. We demonstrate that, provided that an up-and-down multiresolution strategy is implemented, it is possible to estimate efficiently this number of nodes without a priori knowledge and with a fast algorithm, leading to a segmentation criterion without free parameters. We also show that, for polygonal-shaped objects, this new technique leads to better results than using a simple regularization strategy based on the smoothness of the contour.

© 2001 Optical Society of America

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References

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  1. O. Germain and Ph. Réfrégier, “Optimal snake-based segmentation of a random luminance target on a spatially disjoint background,” Opt. Lett. 21, 1845–1847 (1996).
    [CrossRef] [PubMed]
  2. C. Chesnaud, V. Pagé, and Ph. Réfrégier, “Robustness improvement of the statistically independent region snake-based segmentation method,” Opt. Lett. 23, 488–490 (1998).
    [CrossRef]
  3. C. Chesnaud, Ph. Réfrégier, and V. Boulet, “Statistical region snake-based segmentation adapted to different physical noise models,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 1145–1157 (1999).
    [CrossRef]
  4. M. Kass, A. Witkin, and D. Terzopoulos, “Snakes: active contour models,” Int. J. Comput. Vision 1, 321–331 (1988).
    [CrossRef]
  5. R. Ronfard, “Region-based strategies for active contour models,” Int. J. Comput. Vision 2, 229–251 (1994).
    [CrossRef]
  6. S. C. Zhu and A. Yuille, “Region competition: Unifying snakes, region growing, and Bayes/MDL for multiband image segmentation,” IEEE Trans. Pattern Anal. Mach. Intell.874–900 (1996).
  7. M. A. T. Figueiredo, J. M. N. Leitão, and A. K. Jain, “Unsupervised contour representation and estimation using B-splines and a minimum description length criterion,” IEEE Trans. Image Process. 9, 1075–1087 (2000).
    [CrossRef]
  8. J. Rissanen, Stochastic Complexity in Statistical Inquiry (World Scientific, Singapore, 1989).
  9. C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J. 27, 379–423 (1948).
    [CrossRef]

2000 (1)

M. A. T. Figueiredo, J. M. N. Leitão, and A. K. Jain, “Unsupervised contour representation and estimation using B-splines and a minimum description length criterion,” IEEE Trans. Image Process. 9, 1075–1087 (2000).
[CrossRef]

1999 (1)

C. Chesnaud, Ph. Réfrégier, and V. Boulet, “Statistical region snake-based segmentation adapted to different physical noise models,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 1145–1157 (1999).
[CrossRef]

1998 (1)

1996 (2)

O. Germain and Ph. Réfrégier, “Optimal snake-based segmentation of a random luminance target on a spatially disjoint background,” Opt. Lett. 21, 1845–1847 (1996).
[CrossRef] [PubMed]

S. C. Zhu and A. Yuille, “Region competition: Unifying snakes, region growing, and Bayes/MDL for multiband image segmentation,” IEEE Trans. Pattern Anal. Mach. Intell.874–900 (1996).

1994 (1)

R. Ronfard, “Region-based strategies for active contour models,” Int. J. Comput. Vision 2, 229–251 (1994).
[CrossRef]

1988 (1)

M. Kass, A. Witkin, and D. Terzopoulos, “Snakes: active contour models,” Int. J. Comput. Vision 1, 321–331 (1988).
[CrossRef]

1948 (1)

C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J. 27, 379–423 (1948).
[CrossRef]

Boulet, V.

C. Chesnaud, Ph. Réfrégier, and V. Boulet, “Statistical region snake-based segmentation adapted to different physical noise models,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 1145–1157 (1999).
[CrossRef]

Chesnaud, C.

C. Chesnaud, Ph. Réfrégier, and V. Boulet, “Statistical region snake-based segmentation adapted to different physical noise models,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 1145–1157 (1999).
[CrossRef]

C. Chesnaud, V. Pagé, and Ph. Réfrégier, “Robustness improvement of the statistically independent region snake-based segmentation method,” Opt. Lett. 23, 488–490 (1998).
[CrossRef]

Figueiredo, M. A. T.

M. A. T. Figueiredo, J. M. N. Leitão, and A. K. Jain, “Unsupervised contour representation and estimation using B-splines and a minimum description length criterion,” IEEE Trans. Image Process. 9, 1075–1087 (2000).
[CrossRef]

Germain, O.

Jain, A. K.

M. A. T. Figueiredo, J. M. N. Leitão, and A. K. Jain, “Unsupervised contour representation and estimation using B-splines and a minimum description length criterion,” IEEE Trans. Image Process. 9, 1075–1087 (2000).
[CrossRef]

Kass, M.

M. Kass, A. Witkin, and D. Terzopoulos, “Snakes: active contour models,” Int. J. Comput. Vision 1, 321–331 (1988).
[CrossRef]

Leitão, J. M. N.

M. A. T. Figueiredo, J. M. N. Leitão, and A. K. Jain, “Unsupervised contour representation and estimation using B-splines and a minimum description length criterion,” IEEE Trans. Image Process. 9, 1075–1087 (2000).
[CrossRef]

Pagé, V.

Réfrégier, Ph.

Rissanen, J.

J. Rissanen, Stochastic Complexity in Statistical Inquiry (World Scientific, Singapore, 1989).

Ronfard, R.

R. Ronfard, “Region-based strategies for active contour models,” Int. J. Comput. Vision 2, 229–251 (1994).
[CrossRef]

Shannon, C. E.

C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J. 27, 379–423 (1948).
[CrossRef]

Terzopoulos, D.

M. Kass, A. Witkin, and D. Terzopoulos, “Snakes: active contour models,” Int. J. Comput. Vision 1, 321–331 (1988).
[CrossRef]

Witkin, A.

M. Kass, A. Witkin, and D. Terzopoulos, “Snakes: active contour models,” Int. J. Comput. Vision 1, 321–331 (1988).
[CrossRef]

Yuille, A.

S. C. Zhu and A. Yuille, “Region competition: Unifying snakes, region growing, and Bayes/MDL for multiband image segmentation,” IEEE Trans. Pattern Anal. Mach. Intell.874–900 (1996).

Zhu, S. C.

S. C. Zhu and A. Yuille, “Region competition: Unifying snakes, region growing, and Bayes/MDL for multiband image segmentation,” IEEE Trans. Pattern Anal. Mach. Intell.874–900 (1996).

Bell Syst. Tech. J. (1)

C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J. 27, 379–423 (1948).
[CrossRef]

IEEE Trans. Image Process. (1)

M. A. T. Figueiredo, J. M. N. Leitão, and A. K. Jain, “Unsupervised contour representation and estimation using B-splines and a minimum description length criterion,” IEEE Trans. Image Process. 9, 1075–1087 (2000).
[CrossRef]

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

S. C. Zhu and A. Yuille, “Region competition: Unifying snakes, region growing, and Bayes/MDL for multiband image segmentation,” IEEE Trans. Pattern Anal. Mach. Intell.874–900 (1996).

C. Chesnaud, Ph. Réfrégier, and V. Boulet, “Statistical region snake-based segmentation adapted to different physical noise models,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 1145–1157 (1999).
[CrossRef]

Int. J. Comput. Vision (2)

M. Kass, A. Witkin, and D. Terzopoulos, “Snakes: active contour models,” Int. J. Comput. Vision 1, 321–331 (1988).
[CrossRef]

R. Ronfard, “Region-based strategies for active contour models,” Int. J. Comput. Vision 2, 229–251 (1994).
[CrossRef]

Opt. Lett. (2)

Other (1)

J. Rissanen, Stochastic Complexity in Statistical Inquiry (World Scientific, Singapore, 1989).

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Figures (3)

Fig. 1
Fig. 1

Scene with speckle noise. (a) Boat whose shape is a polygon with 10 nodes in a 128 by 128 pixel image. (b) Speckled image of (a) with a contrast equal to 4 (initialization of the contour in white). (c) Final state of the snake after optimization of the log likelihood with the multiresolution strategy when the number of nodes on the contour is equal to the true one: k=10. (d) Final state of the snake after optimization of the MDL criterion with the up-and-down multiresolution strategy. (e) Final state of the snake after optimization of the log likelihood with a regularizing term and α=0.2 (a value that leads to the minimal number of misclassified pixels). (f) Final state of the snake after optimization of the log likelihood without a regularizing term.

Fig. 2
Fig. 2

Solid curve, values of the MDL criterion Δ obtained with a direct approach. Dashed curve, values of the MDL criterion Δ obtained with the up-and-down multiresolution strategy.

Fig. 3
Fig. 3

(a) Real image of a hand (240×320 pixel image) and initialization of the contour. (b) Result of the segmentation with the up-and-down multiresolution strategy.

Tables (1)

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Table 1 Expressions of the Pseudolikelihood l[sw,θ^a(s,w),θ^b[s,w)] for Different Gray-Level PDFsa

Equations (2)

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ΔNaSa+NbSb+klog2N.
Δ-le[s|w,θa,θb]+klnN,

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