  We introduce a new Lagrangian particle tracking algorithm that tracks
particles in three dimensions to separations between trajectories approaching
contact. The algorithm also detects low Weber number binary collisions that
result in coalescence as well as droplet break-up. Particles are identified in
two-dimensional high-resolution digital images by finding sets of circles to
describe the edge of each body. This allows identification of particles that
overlap in projection by over 80% even for noisy images and without invoking
additional temporal data. The algorithm builds trajectories from
three-dimensional particle coordinates by minimizing a penalty function that is
a weighted sum of deviations from the expected particle coordinates using
information from four moments in time. This new hybrid algorithm is validated
against synthetic data and found to perfectly reproduce more trajectories than
other commonly used methods. Collisions are detected with 95% accuracy for
particles that move on average less than one tenth the distance to their
nearest neighbor.
