  Ridge detection is a classical tool to extract curvilinear features in image
processing. As such, it has great promise in applications to material science
problems; specifically, for trend filtering relatively stable atom-shaped
objects in image sequences, such as Transmission Electron Microscopy (TEM)
videos. Standard analysis of TEM videos is limited to frame-by-frame object
recognition. We instead harness temporal correlation across frames through
simultaneous analysis of long image sequences, specified as a spatio-temporal
image tensor. We define new ridge detection algorithms to non-parametrically
estimate explicit trajectories of atomic-level object locations as a continuous
function of time. Our approach is specially tailored to handle temporal
analysis of objects that seemingly stochastically disappear and subsequently
reappear throughout a sequence. We demonstrate that the proposed method is
highly effective and efficient in simulation scenarios, and delivers notable
performance improvements in TEM experiments compared to other material science
benchmarks.
