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Machine Learning for Vision-Based Motion Analysis pp 77–115Cite as

Mixed-State Markov Models in Image Motion Analysis

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Part of the book series: Advances in Pattern Recognition ((ACVPR))

Abstract

When analyzing motion observations extracted from image sequences, one notes that the histogram of the velocity magnitude at each pixel shows a large probability mass at zero velocity, while the rest of the motion values may be appropriately modeled with a continuous distribution. This suggests the introduction of mixed-state random variables that have probability mass concentrated in discrete states, while they have a probability density over a continuous range of values. In the first part of the chapter, we give a comprehensive description of the theory behind mixed-state statistical models, in particular the development of mixed-state Markov models that permits to take into account spatial and temporal interaction. The presentation generalizes the case of simultaneous modeling of continuous values and any type of discrete symbolic states. For the second part, we present the application of mixed-state models to motion texture analysis. Motion textures correspond to the instantaneous apparent motion maps extracted from dynamic textures. They depict mixed-state motion values with a discrete state at zero and a Gaussian distribution for the rest. Mixed-state Markov random fields and mixed-state Markov chains are defined and applied to motion texture recognition and tracking.

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Notes

  1. 1.

    Copyright (c) 2003, UCLA Vision Lab. Thanks to Daniel Cremers and Stefano Soatto for providing this sequence.

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Author information

Authors and Affiliations

  1. University of Buenos Aires, Buenos Aires, Argentina

    Tomás Crivelli

  2. INRIA, Rennes, France

    Patrick Bouthemy

  3. CONICET, Buenos Aires, Argentina

    Bruno Cernuschi Frías

  4. Unviersity of Rennes 1, Rennes, France

    Jian-feng Yao

Authors
  1. Tomás Crivelli
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  2. Patrick Bouthemy
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  3. Bruno Cernuschi Frías
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  4. Jian-feng Yao
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Corresponding author

Correspondence to Tomás Crivelli .

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Bath, Bath, BA2 7AY, United Kingdom

    Liang Wang

  2. Dept. Electrical and Information Eng., University of Oulu, Oulu, 90014, Finland

    Guoying Zhao

  3. Bioinformatics Institute, A*STAR, 30 Biopolis Street, #07-01 Matrix, Singapore, 138671, Singapore

    Li Cheng

  4. Department of Electrical Engineering, Machine Vision & Media Processing Unit, University of Oulu, Oulu, Finland

    Matti Pietikäinen

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Crivelli, T., Bouthemy, P., Cernuschi Frías, B., Yao, Jf. (2011). Mixed-State Markov Models in Image Motion Analysis. In: Wang, L., Zhao, G., Cheng, L., Pietikäinen, M. (eds) Machine Learning for Vision-Based Motion Analysis. Advances in Pattern Recognition. Springer, London. https://doi.org/10.1007/978-0-85729-057-1_4

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  • DOI: https://doi.org/10.1007/978-0-85729-057-1_4

  • Publisher Name: Springer, London

  • Print ISBN: 978-0-85729-056-4

  • Online ISBN: 978-0-85729-057-1

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