  We present a novel parameter identification algorithm for the estimation of
parameters in models of cell motility using imaging data of migrating cells.
Two alternative formulations of the objective functional that measures the
difference between the computed and observed data are proposed and the
parameter identification problem is formulated as a minimisation problem of
nonlinear least squares type. A Levenberg-Marquardt based optimisation method
is applied to the solution of the minimisation problem and the details of the
implementation are discussed. A number of numerical experiments are presented
which illustrate the robustness of the algorithm to parameter identification in
the presence of large deformations and noisy data and parameter identification
in three dimensional models of cell motility. An application to experimental
data is also presented in which we seek to identify parameters in a model for
the monopolar growth of fission yeast cells using experimental imaging data.
