Accurate estimation of intracellular dynamics and underlying spatial structures using hierarchical trajectory smoothing

Biological imaging studies into the molecular mechanisms and underlying structures of intracellular dynamic processes require not only accurate particle tracking but also accurate analysis of the resulting trajectories. Although great efforts have been made to solve the particle tracking problem, there is a lack of methods for robust estimation of dynamic properties from extracted trajectories in the presence of measurement noise, or when particles exhibit jerky motion patterns. Here we propose a hierarchical energy-based trajectory smoothing approach for this purpose. It yields a parametric curve having second-order continuity that allows robust local estimation of dynamic properties requiring up to second-order derivatives at any point along the underlying trajectory. We present preliminary results of experiments on both synthetic and real data of microtubule dynamics demonstrating the advantage of our method over trajectory representations using piecewise-linear connection or Gaussian-process regression.