A fast and gridless ORKA algorithm for tracking moving and deforming
  objects
Florian Bossmann Jianwei Ma Wenze wu
Identifying objects in given data is a task frequently encountered in many
applications. Finding vehicles or persons in video data, tracking seismic waves
in geophysical exploration data, or predicting a storm front movement from
meteorological measurements are only some of the possible applications. In many
cases, the object of interest changes its form or position from one measurement
to another. For example, vehicles in a video may change its position or angle
to the camera in each frame. Seismic waves can change its arrival time,
frequency, or intensity depending on the sensor position. Storm fronts can
change its form and position over time. This complicates the identification and
tracking as the algorithm needs to deal with the changing object over the given
measurements. In a previous work, the authors presented a new algorithm to
solve this problem - Object reconstruction using K-approximation (ORKA). The
algorithm can solve the problem at hand but suffers from two disadvantages. On
the one hand, the reconstructed object movement is bound to a grid that depends
on the data resolution. On the other hand, the complexity of the algorithm
increases exponentially with the resolution. We overcome both disadvantages by
introducing an iterative strategy that uses a resampling method to create
multiple resolutions of the data. In each iteration the resolution is increased
to reconstruct more details of the object of interest. This way, we can even go
beyond the original resolution by artificially upsampling the data. We give
error bounds and a complexity analysis of the new method. Furthermore, we
analyze its performance in several numerical experiments as well as on real
data. We also give a brief introduction on the original ORKA algorithm.
Knowledge of the previous work is thus not required.