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A Hierarchical Parallel Semi-Markovian Framework
(HPaSMM) for Trajectory-Based Sport Video Understanding
To model activity phases observed in sports videos, we propose a hierarchical par-
allel semi-Markov model (HPaSMM). The proposed modeling is based upon a two-
level hierarchy. Upper level layer is modeled using a semi-Markovian model [6].
Each upper level state of the HPaSMM correspond to an activity phase. In the lower
layer, feature vectors are modeled using parallel hidden Markov models (PaHMMs,
see [25]). These PaHMMs are used to characterize the upper level states of the
HPaSMM.
Figure 1 contains an example of proposed framework which will be used in the
following of this section to describe HPaSMMs. Upper level states are here denoted
by S i .
Fig. 1 Example of a HPaSMM architecture composed of N = 4 upper level states S i . Each
state corresponds to a given phase of activity. A phase of activity is modeled by a n-layer
PaHMM (one layer for each feature vector, here n = 3) and by a GMM modeling state dura-
tions ( sd i is the state duration associated to state S i ). Upper level layer is surrounded by a red
square and lower level layer is surrounded by green squares.
 
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