Experimental results

Figure 3: Figure 3(a) represents the extraction of nodes from the training video sequence. The plan of the graph represents the two first components of the seven components of the appearance parameter space. The points representing the sequence are linked by lines if they follow each other. The extracted nodes are represented by black circles. Figure 3(b) represents the points of a new sequence generated using the model.

[Extraction of nodes] [Generated new sequence]

Figure 4: The six groups obtained after the grouping of sub-trajectories. Groups 1 and 2 look similar because one group models trajectories that go from left to right while the other one models trajectories that go from right to left. The same applies for groups 3 and 4. The group 5 corresponds to several really small trajectories.

We have applied the algorithm to a sequence of a person repeatedly shaking their head. Frames extracted from the training sequence can be seen on figure 5(a). Those frames are the synthesis of the appearance parameters sequence after tracking. The whole sequence has 317 frames. Each face is encoded using seven parameters including the scale, pose and position. The sequence of the two first components is represented on figure 3(a) along with the nodes extracted from the sequence. The nodes are extracted using $n=10$ and $k=20$.

Figure 5: Figure 5(a) represents some frames extracted from the video sequence used to train the model, while figure 5(b) represents some frames extracted from the sequence generated by the model.

[Training sequence of a face gesturing "no"] [Generated sequence]

Figure 4 shows the result of the grouping algorithm if we ask for 6 clusters. Figure 3(b) shows an example of trajectory that can be generated using those 6 clusters and a variable length Markov model that has been trained with a threshold of $0.001$ for both the probabilities stored and the statistical difference. The synthesis of a generated sequence can be found on figure 5(b).