Abstract
Interpretation of human activity and the detection of associated events are eased if appropriate models of context are available. A method is presented for automatically learning a context-specific spatial model in terms of semantic regions, specifically inactivity zones and entry zones. Maximium a posteriori estimation of Gaussian mixtures is used in conjunction with minumum description length for selection of the number of mixture components. Learning is performed using expectation-maximisation algorithms to maximise penalised likelihood functions that incorporate prior knowledge of the size and shape of the semantic regions. This encourages a one-to-one correspondence between the Gaussian mixture components and the regions. The resulting contextual model enables human-readable summaries of activity to be produced and unusual inactivity to be detected. Results are presented using overhead camera sequences tracked using a particle filter. The method is developed and described within the context of supportive home environments which have as their aim the extension of independent, quality living for older people.
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Notes
1 bit ≡ ln 2 nats
The Wishart distribution has the form:
$$p\left( {{\mathbf{\Sigma }}^{ - 1} |\alpha ,\beta } \right) = c|{\mathbf{\Sigma }}^{ - 1} |^{\left( {\alpha - d - 1} \right)/2} \exp \left[ { - \frac{1} {2}tr\left( {\mbox{\boldmath$\beta$}{\mathbf{ \Sigma }}^{ - 1} } \right)} \right]$$where c is a normalisation factor and α is the degrees of freedom.
Analysis is simplified if the prior is chosen such that the posterior has the same functional form as the prior. The prior and posterior are then said to be conjugate.
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Acknowledgments
Dr. Nait Charif was supported by UK EPSRC EQUAL grant GR/R27419/01. The authors are grateful to the reviewers for helpful comments on an earlier version of this paper.
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McKenna, S.J., Charif, H.N. Summarising contextual activity and detecting unusual inactivity in a supportive home environment. Pattern Anal Applic 7, 386–401 (2004). https://doi.org/10.1007/s10044-004-0233-2
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DOI: https://doi.org/10.1007/s10044-004-0233-2