Abstract
We define a new birth and death dynamics dealing with configurations of disks in the plane. We prove the convergence of the continuous process and propose a discrete scheme converging to the continuous case. This framework is developed to address image processing problems consisting in detecting a configuration of objects from a digital image. The derived algorithm is applied for tree crown extraction and bird detection from aerial images. The performance of this approach is shown on real data.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Bertini, L., Cancrini, N., Cesi, F.: The spectral gap for a Glauber-type dynamics in a continuous gas. Ann. Inst. Henri Poincare B Probab. Stat. 38, 91–108 (2002)
Kondratiev, Y.G., Minlos, R.A., Zhizhina, E.A.: One particle subspace of the Glauber dynamics generator for continuous particle systems. Rev. Math. Phys. 16(9), 1073–1114 (2004)
Stoica, R., Descombes, X., Zerubia, J.: A Gibbs point process for road extraction in remotely sensed images. Int. J. Comput. Vis. 57(2), 121–136 (2004)
Lacoste, C., Descombes, X., Zerubia, J.: Point processes for unsupervised line network extraction in remote sensing. IEEE Trans. Pattern Anal. Mach. Intell. 27(10), 1568–1579 (2005)
Ortner, M., Descombes, X., Zerubia, J.: Building outline extraction from digital elevation models using marked point processes. Int. J. Comput. Vis. 72(2), 107–132 (2007)
Perrin, G., Descombes, X., Zerubia, J.: 2D and 3D vegetation resource parameters assessment using marked point processes. In: Proc. International Conference on Pattern Recognition (ICPR), Hong-Kong, August 2006
Green, P.J.: Reversible jump Markov chain Monte-Carlo computation and Bayesian model determination. Biometrika 57, 97–109 (1995)
Fedoriuk, M.V.: The Laplace method for multiple integrals. In: Saddle Point Method. Nauka, Moscow (1977) (in Russian). Chap. II.4
Erdelyi, A.: Asymptotic Expansions. Dover, New York (1956)
Ripley, B.D.: Modeling spatial patterns. J. R. Stat. Soc. B 39, 172–212 (1977)
Liggett, T.M.: Interacting Particle Systems. Springer, New York (1985)
Reed, M., Simon, B.: Methods of Modern Mathematical Physics, vol. 4. Academic Press, San Diego (1978)
Preston, C.: Spatial birth-and-death processes. Bull. Int. Stat. Inst. 46, 377–391 (1977)
Pollock, R.: The automatic recognition of individual trees in aerial images of forests based on a synthetic tree crown image model. Ph.D. thesis, University of British Colombia, Vancouver, Canada (1996)
Gougeon, F.: A crown-following approach to the automatic delineation of individual tree crowns in high spatial resolution aerial images. Can. J. Remote Sens. 21(3), 274–284 (1995)
Eriksson, M., Perrin, G., Descombes, X., Zerubia, J.: A comparative study of three methods for identifying individual tree crowns in aerial images covering different types of forests. In: Proc. International Society for Photogrammetry and Remote Sensing (ISPRS, commission I symposium), Marne La Vallee, France, July 2006
Ethier, S.N., Kurtz, T.G.: Markov Processes: Characterization and Convergence. Wiley, New York (1986)
Descamps, S., Descombes, X., Béchet, A., Zerubia, J.: Détection de flamants roses par processus ponctuels marqués pour l’estimation de la taille des populations. INRIA Research Report, No. 6328, Oct. 2007 (in French)
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was partially supported by EGIDE within the ECO-NET project 18902PK, by INRIA COLORS “Flamants” and by the INRIA Associated team “ODESSA”. We would like to thank the French National Forest Inventory (IFN) and Arnaud Béchet from “La Station Biologique Tour du Valat” for kindly providing the data. R. Minlos and E. Zhizhina are partially supported by RFFI grant 08-01-00105a.
Rights and permissions
About this article
Cite this article
Descombes, X., Minlos, R. & Zhizhina, E. Object Extraction Using a Stochastic Birth-and-Death Dynamics in Continuum. J Math Imaging Vis 33, 347–359 (2009). https://doi.org/10.1007/s10851-008-0117-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10851-008-0117-y