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K
k = 1 P ( S k | S k 1 )
P
(
y
,
S
| θ )=
K
k = 1 P ( y k | φ ; S k 1 ) .
×
Fig. 3 Example of a HPaHMM 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).
3
HPaSMM Squash Activity Recognition
To show the efficiency of the HPaSMM framework for sports video understanding
issues, an application of HPaSMM to squash video is here presented. It corresponds
to a quite simple use of the HPaSMM model, with only two moving players. In
Section 4, a more complex application of the novel model to handball video under-
standing is also proposed.
3.1
Squash Invariant Feature Representation
The proposed modeling must be able to process squash video shootings from a vari-
ety of point of view. Hence, low level activity representation should be invariant to
irrelevant transformations of the trajectory data. In the video context, invariance to
2D translation, 2D rotation and scale has to be considered. In the following, we de-
scribed the invariant feature values used to characterize players movements as well
as their interactions.
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