# Statistical estimation of the dynamics of watershed dams

International Journal of Applied Mathematics and Computer Science (2009)

- Volume: 19, Issue: 2, page 349-360
- ISSN: 1641-876X

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topZbisław Tabor. "Statistical estimation of the dynamics of watershed dams." International Journal of Applied Mathematics and Computer Science 19.2 (2009): 349-360. <http://eudml.org/doc/207941>.

@article{ZbisławTabor2009,

abstract = {In the present study the notion of watershed contour dynamics, defined within the framework of mathematical morphology, is examined. It is shown that the dynamics are a direct measure of the “sharpness” of transition between neighboring watershed basins. The expressions for the expected value and the statistical error of the estimation of contour dynamics are derived in the presence of noise, based on extreme value theory. The sensitivity of contour dynamics to noise is studied. A statistical approach to the notion of contour dynamics is developed and a definition of statistical dynamics is proposed.},

author = {Zbisław Tabor},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {hierarchical segmentation; contour dynamics; mathematical morphology; statistical analysis},

language = {eng},

number = {2},

pages = {349-360},

title = {Statistical estimation of the dynamics of watershed dams},

url = {http://eudml.org/doc/207941},

volume = {19},

year = {2009},

}

TY - JOUR

AU - Zbisław Tabor

TI - Statistical estimation of the dynamics of watershed dams

JO - International Journal of Applied Mathematics and Computer Science

PY - 2009

VL - 19

IS - 2

SP - 349

EP - 360

AB - In the present study the notion of watershed contour dynamics, defined within the framework of mathematical morphology, is examined. It is shown that the dynamics are a direct measure of the “sharpness” of transition between neighboring watershed basins. The expressions for the expected value and the statistical error of the estimation of contour dynamics are derived in the presence of noise, based on extreme value theory. The sensitivity of contour dynamics to noise is studied. A statistical approach to the notion of contour dynamics is developed and a definition of statistical dynamics is proposed.

LA - eng

KW - hierarchical segmentation; contour dynamics; mathematical morphology; statistical analysis

UR - http://eudml.org/doc/207941

ER -

## References

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- Beucher, S. (1994). Watershed, hierarchical segmentation and waterfall algorithm, in J. Serra and P. Soille (Eds.), Mathematical Morphology and Its Application to Image Processing, Kluwer Academic Publishers, Dordrecht, pp.69-76.
- Burry, K. V. (1975). Statistical Methods in Applied Science, John Wiley & Sons, New York, NY.
- Haris, K., Efstratiadis, S. N., Maglaveras, N. and Katsaggelos, A.K. (1998). Hybrid image segmentation using watersheds and fast region merging, IEEE Transactions on Image Processing 7(12): 1684-1699.
- Haris, K., Efstratiadis, S. N. and Maglaveras, N. (2001). Hierarchical image segmentation based on contour dynamics, Proceedings of the International Conference on Image Processing, Thessaloniki, Greece, Vol. 1, pp. 54-57.
- Grimaud, M. (1992). A new measure of contrast: Dynamics, Proceedings of the SPIE Conference on Image Algebra and Morphological Processing III, San Diego, CA, USA, Vol. 1769, pp.292-305.
- Najman, L. and Schmitt, M. (1996). Geodesic saliency of watershed contours and hierarchical segmentation, IEEE Transactions on Pattern Analysis and Machine Intelligence 18(12): 1163-1173.
- Vincent, L. and Soille, P. (1991). Watersheds in digital spaces: An efficient algorithm based on immersion simulations, IEEE Transactions on Pattern Analysis and Machine Intelligence 13(6): 583-598.

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