Geometric Observers for Dynamically Evolving Curves

Abstract-- This paper proposes a deterministic observer design for visual tracking based on non-parametric implicit (level-set) curve descriptions. The observer is continuous-discrete, with continuous-time system dynamics and discrete-time measurements. Its state-space consists of an estimated curve position augmented by additional states (e.g., velocities) associated with every point on the estimated curve. Multiple simulation models are proposed for state prediction. Measurements are performed through standard static segmentation algorithms and optical-flow computations. Special emphasis is given to the geometric formulation of the overall dynamical system. The discretetime measurements lead to the problem of geometric curve interpolation and the discrete-time filtering of quantities propagated along with the estimated curve. Interpolation and filtering are intimately linked to the correspondence problem between curves. Correspondences are established by a Laplace-equation approach. ...

• Type: Journal
• Year: 2008
• Where: PAMI
• Authors: Marc Niethammer, Patricio A. Vela, Allen Tannenbaum
• Keywords: Curve, Deterministic Observer Design, Geometric Curve Interpolation, PAMI 2006, PAMI 2008