Understanding Sports Video Using Players Trajectories - Intelligent Video Event Analysis and Understanding - page 135

Fig. 4 A frame of a squash video. Red and blue squares correspond to players positions, d is
the spatial distance between the two players.

invariant feature vector D that characterizes interaction between the two players P 1
and P 2 during activity S i is the vector containing the successive values of d j :

d 1 d 2 d n i − 1 d n i ] ,

D S i

=[ , , ..., ,

S i

k and D S i
feature vectors characterizes invariantly (to translation, rotation and scale transfor-
mations in the image plane) both the single players motions and their interaction.

where n i is the size of the processed trajectories in activity S i . Hence, ˙ γ

3.2 Squash Activity Modeling Using HPaSMM

This section describes the HPaSMM used to process squash videos. As illustrated
by Figure 5, it relies on two upper level states S 1 and S 2 , and on the three feature
values defined in the Section 3.1.
Upper layer: Activity modeling by semi-Markov chains

Upper level states S 1 and S 2 of the squash HPaSMM define “rally” and “passive”
activity phases. In the illustration in Figure 5, the upper level layer is surrounded in
red and is composed of two upper level states S 1 and S 2 .
A is the HPaSMM state transition probability matrix at

the time index of the
end-point of the i th segment (see Section 2.4). In the proposed modeling with only
two upper level states, a 21 =

{ q i }

1. Indeed, when a segment of activity ends, the
system necessarily passes from one upper level state to the other one ( i.e. , from S 1
to S 2 or from S 2 to S 1 ).

a 12 =