Tracking People on a Torus

    Abstract

    We model shape deformations corresponding to both view point and body configuration changes through the motion. Such observed shapes present a product space (different configurations x different views) and lie on a low dimensional manifold in the visual input space. The approach we introduce here is based on learning both the visual observation manifold and the kinematic manifold of the motion in a supervised manner. Instead of learning an embedding of the manifold, we learn the geometric deformation between an ideal manifold (conceptual equivalent topological structure) and a twisted version of the manifold (the data). We use a torus manifold to represent such data for both periodic and non-periodic motions. Experimental results show accurate estimation of 3D body pose and view from a single camera.

    Approach

  • Simultaneous inferring view and body pose using torus manifold
    • Represent spatio-temporal shape deformations according to view and body configuration change on a two dimensional torus manifold and nonlinear mapping from embedding manifold to visual input
    • Inferring view and body pose from a given image by estimating an embedding point from a given input since every view and body pose has a corresponding embedding point on the torus manifold.
  • View variant human motion tracking as tracking on a torus surface (spatio-temporal constraints)
    • 2 dimensional torus manifold: a state space for one dimensional body configuration and one dimensional view circle
    • Learning manifold deformation from ideal torus manifoldto the actual visual manifold and to the kinematic manifold through two nonlinear mapping functions