Summary of contributions

Though similar approaches have been used to model human motion [34], as far as we are aware, this is the first time the approach has been applied to facial behaviour.

As well as this, the contributions include :

1)

A heuristic for breaking a trajectory into pathlets. An efficient heuristic has been developed to break a trajectory into pathlets. By observing that similar pathlets should have similar beginning and similar ends, points of high density in the parameter space are used to split the trajectory.

2)

A compact pathlet model. By modelling the pathlet groups using a multivariate Gaussian, it has been shown how timing information can be included in the model, thus allowing modelling groups of pathlets of different speeds.

3)

An effective pathlet grouping algorithm. Two pathlet grouping algorithms have been presented. The most effective one is based on a greedy merging strategy. At each step, the variance of the pathlet groups are kept as low as possible, leading to compact models.

4)

Improvements to the performance of the VLMM. We have shown how different ways of estimating the probabilities of samples can affect the performance of the VLMM. Improvement in performance has been achieved by replacing the Kullback-Leibler measure by the Bhattacharyya measure for comparing the probability distributions.

5)

A quantitative similarity measure for the behaviour model. A quantitative similarity measure has been developed to assess the quality of different models of behaviour. Although the measure is crude, it has been shown that it gives similar results than the intuitive comparisons done by people.

6)

A demonstration of improved performance. A psychophysical experiment has been set up to assess the performance of our model. It shows an improvement of the performance for structured behaviours compared to an alternative technique, while performance for unstructured behaviours remains similar.