Modeling the product manifold of posture and motion

Long-term human motion is composed of an ensemble of different activities with varying complexity. This makes it challenging to develop models to accurately estimate human motion. In this paper, we exploit the dependencies that exist between posture and motion for long-term human motion estimation. We propose to model the nonlinear motion manifold as a collection of local linear models, noting that given a particular posture, the variation in motion for that posture can be well-approximated by a linear model. A collection of local linear models is easy to fit and also has the expressiveness to encode several activities in any arbitrary order. Furthermore, to account for the varying complexity of different activities, each local linear model can have a different dimensionality. A collection of local linear models, thus, avoids the limitation of global models that require a uniform dimensionality for the latent motion manifold. This model allows us to linearly regularize motion estimation algorithms over the nonlinear human motion manifold. Our results demonstrate that a collection of local linear models provides an effective representation for the motion manifold when compared to other global models such as the bilinear model and the Principal Component Analysis.