Cell motility is an integral part of a diverse set of biological processes. The quest for
mathematical models of cell motility has prompted the development of automated approaches
for gathering quantitative data on cell morphology, and the distribution of molecular
players involved in cell motility. Here we review recent approaches for quantifying cell
motility, including automated cell segmentation and tracking. Secondly, we present our own
novel method for tracking cell boundaries of moving cells, the Electrostatic Contour
Migration Method (ECMM), as an alternative to the generally accepted level set method
(LSM). ECMM smoothly tracks regions of the cell boundary over time to compute local
membrane displacements using the simple underlying concept of electrostatics. It offers
substantial speed increases and reduced computational overheads in comparison to the LSM.
We conclude with general considerations regarding boundary tracking in the context of
mathematical modelling.