Natural metrics and least-committed priors for articulated tracking

In articulated tracking, one is concerned with estimating the pose of a person in every frame of a film. This pose is most often represented as a kinematic skeleton where the joint angles are the degrees of freedom. Least-committed predictive models are then phrased as a Brownian motion in joint angle space. However, the metric of the joint angle space is rather unintuitive as it ignores both bone lengths and how bones are connected. As Brownian motion is strongly linked with the underlying metric, this has severe impact on the predictive models. We introduce the spatial kinematic manifold of joint positions, which is embedded in a high dimensional Euclidean space. This Riemannian manifold inherits the metric from the embedding space, such that distances are measured as the combined physical length that joints travel during movements. We then develop a least-committed Brownian motion model on the manifold that respects the natural metric. This model is expressed in terms of a stochastic differential equation, which we solve using a novel numerical scheme. Empirically, we validate the new model in a particle filter based articulated tracking system. Here, we not only outperform the standard Brownian motion in joint angle space, we are also able to specialise the model in ways that otherwise are both difficult and expensive in joint angle space.