Skip to main content
Log in

Mixed-State Auto-Models and Motion Texture Modeling

  • Published:
Journal of Mathematical Imaging and Vision Aims and scope Submit manuscript

Abstract

In image motion analysis as well as for several application fields like daily pluviometry data modeling, observations contain two components of different nature. A first part is made with discrete values accounting for some symbolic information and a second part records a continuous (real-valued) measurement. We call such type of observations “mixed-state observations”. In this work we introduce a generalization of Besag's auto-models to deal with mixed-state observations at each site of a lattice. A careful construction as well as important properties of the model will be given. A special class of positive Gaussian mixed-state auto-models is proposed for the analysis of motion textures from video sequences. This model is first explored via simulations. We then apply it to real images of dynamic natural scenes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D.J. Allcroft and C.A. Glasbey, “A latent gaussian markov random-field model for spatiotemporal rainfall disaggregation,” J. Roy. Statist. Soc. Ser. C, Vol. 52, No. 4, pp. 487–498, 2003.

    Article  MathSciNet  MATH  Google Scholar 

  2. M. Bartlett, “A further note on nearest neighbour models,” J. Roy. Statist. Soc., Vol. A, No. 131, pp. 579–580, 1968.

    Google Scholar 

  3. J. Besag, “Spatial interactions and the statistical analysis of lattice systems,” J. Roy. Statist. Soc., Vol. B, No. 148, pp. 1–36, 1974.

    Google Scholar 

  4. B. Chalmond, Modeling and Inverse Problems in Image Analysis, Vol. 155 of Applied Mathematical Sciences. Springer-Verlag: New York, 2003.

  5. G. Cross and A. Jain, “Markov random field texture models,” IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 5, No. 1, pp. 25–39, 1983.

    Article  Google Scholar 

  6. G. Doretto, A. Chiuso, Y. Wu, and S. Soatto, “Dynamic textures,” International Journal of Computer Vision, Vol. 51, No. 2, pp. 91–109, 2003.

    Article  MATH  Google Scholar 

  7. G. Doretto, E. Jones and S. Soatto, “Spatially homogeneous dynamic textures,” in Proc. 8th European Conf. on Computer Vision, LNCS 3022. Springer: Prague, 2004, pp. 591–602.

  8. R. Fablet and P. Bouthemy, “Motion recognition using non parametric image motion models estimated from temporal and multiscale cooccurrence statistics,” IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 25, No. 122, pp. 1619–1624, 2003.

    Article  Google Scholar 

  9. X. Guyon, Random Fields on a Network: Modeling, Statistics, and Applications. Springer-Verlag: New York, 1995.

    MATH  Google Scholar 

  10. C. Hardouin and J. Yao, “Multi parameter auto-models and application to mixed state data analysis,” Technical report, IRMAR/Université de Rennes 1, 2005.

  11. M. Irani, B. Rousso, and S. Peleg, “Detecting and tracking multiple moving objects using temporal integration,” in Proc of European Conf. on Computer Vision, ECCV’92. Springer-Verlag: Santa Margherita 1992, pp. 282–287.

  12. J. Odobez and P. Bouthemy, Separation of Moving Regions from Background in an Image Sequence Acquired with a Mobile Camera, Chapt. 8, pp. 283–311, Video Data Compression for Multimedia Computing, H.H. Li,S. Sun and H. Derin (Eds.). Kluwer Academic Publisher, 1997.

  13. J.-M. Odobez and P. Bouthemy, “Robust multiresolution estimation of parametric motion models,” J. of Visual Comm. and Image Repr., Vol. 6, No. 4, pp. 348–365, 1995.

    Article  Google Scholar 

  14. M. Szummer and R. Picard, “Temporal texture modeling,” in Proc. IEEE Int. Conf. on Image Processing, ICIP’96, Lausanne, 1996.

  15. P. Whittle, “Stochastic processes in several dimensions,” Bull. Inst. Statist. Inst., Vol. 40, pp. 974–994, 1963.

    Google Scholar 

  16. L. Yuan, F. Wen, C. Liu, and H.-Y. Shum, “Synthesizing dynamic texture with closed-loop linear dynamic system,” in Proc. 8th European Conf. on Computer Vision, LNCS 3022. Prague: Springer, 2004, pp. 603–616.

Download references

Author information

Authors and Affiliations

Authors

Additional information

Patrick Bouthemy graduated from ENST, Paris, in 1980, and received the Ph.D degree in Computer Science from the University of Rennes, France, in 1982. From December 1982 until February 1984, he was employed by INRS-Telecommunications, Montreal, in the Department of Visual Communications. Since April 1984 he has been with INRIA, at IRISA in Rennes. He is currently“Directeur de Recherche” Inria and head of Vista group. His main research interests are: statistical approaches for image sequence processing, motion analysis, learning, recognition and classification of dynamic contents in video. He has served as member of the program committees of the major conferences in image processing and computer vision. He was Associate Editor of the IEEE Transactions on Image Processing from 1999 to 2003.

Cécile Hardouin received the Ph.D degree in Applied Mathematics from University Paris 7, France, in 1992. Since July 1992 she is lecturer at University Paris 10, Nanterre. Since her Ph.D., she is member of the research center SAMOS - MATISSE, located in University Paris 1. After some works on long memory processes, her main research interests are now Spatial statistics: Markovian random fields, standards adoption dynamics, spatial coordination.

Gwenaëlle Piriou was born in 1976. She received the Ph.D. degree in signal processing and telecommunications from the university of Rennes, France, in 2005. She is currently an assistant professor with the computer science department of university of Rennes. Her main research interests are probabilistic motion modeling in image sequence, recognition and detection of dynamic content and temporal textures.

Jian-feng Yao recieved the Ph.D. degree in Applied Mathematics from Université Paris-Sud (Orsay), France, in 1990. From January 1990 to August 2000, he was a Maître de Conference in University of Paris I. Since September 2000, he is a full professor in Statistics in University of Rennes I. His current research interests are nonlinear time series analysis, spectral theory of large-dimensional random matrices and mathematical modeling for image understanding.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bouthemy, P., Hardouin, C., Piriou, G. et al. Mixed-State Auto-Models and Motion Texture Modeling. J Math Imaging Vis 25, 387–402 (2006). https://doi.org/10.1007/s10851-006-7251-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10851-006-7251-1

Keywords

Navigation