  Cell tracking algorithms which automate and systematise the analysis of time
lapse image data sets of cells are an indispensable tool in the modelling and
understanding of cellular phenomena. In this study we present a theoretical
framework and an algorithm for whole cell tracking. Within this work we
consider that "tracking" is equivalent to a dynamic reconstruction of the whole
cell data (morphologies) from static image datasets. The novelty of our work is
that the tracking algorithm is driven by a model for the motion of the cell.
This model may be regarded as a simplification of a recently developed
physically meaningful model for cell motility. The resulting problem is the
optimal control of a geometric evolution law and we discuss the formulation and
numerical approximation of the optimal control problem. The overall goal of
this work is to design a framework for cell tracking within which the recovered
data reflects the physics of the forward model. A number of numerical
simulations are presented that illustrate the applicability of our approach.
