  Tracking by Deblatting stands for solving an inverse problem of deblurring
and image matting for tracking motion-blurred objects. We propose non-causal
Tracking by Deblatting which estimates continuous, complete and accurate object
trajectories. Energy minimization by dynamic programming is used to detect
abrupt changes of motion, called bounces. High-order polynomials are fitted to
segments, which are parts of the trajectory separated by bounces. The output is
a continuous trajectory function which assigns location for every real-valued
time stamp from zero to the number of frames. Additionally, we show that from
the trajectory function precise physical calculations are possible, such as
radius, gravity or sub-frame object velocity. Velocity estimation is compared
to the high-speed camera measurements and radars. Results show high performance
of the proposed method in terms of Trajectory-IoU, recall and velocity
estimation.
