In this work we consider the problem of detecting anomalous spatio-temporalbehavior in videos. Our approach is to learn the normative multiframe pixeljoint distribution and detect deviations from it using a likelihood basedapproach. Due to the extreme lack of available training samples relative to thedimension of the distribution, we use a mean and covariance approach andconsider methods of learning the spatio-temporal covariance in the low-sampleregime. Our approach is to estimate the covariance using parameter reductionand sparse models. The first method considered is the representation of thecovariance as a sum of Kronecker products as in (Greenewald et al 2013), whichis found to be an accurate approximation in this setting. We propose learningalgorithms relevant to our problem. We then consider the sparse multiresolutionmodel of (Choi et al 2010) and apply the Kronecker product methods to it forfurther parameter reduction, as well as introducing modifications for enhancedefficiency and greater applicability to spatio-temporal covariance matrices. Weapply our methods to the detection of crowd behavior anomalies in theUniversity of Minnesota crowd anomaly dataset, and achieve competitive results.
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