  This paper develops a generative statistical model for representing,
modeling, and comparing the morphological evolution of biological cells
undergoing motility. It uses the elastic shape analysis to separate cell
kinematics (overall location, rotation, speed, etc.) from its morphology and
represents morphological changes using transported square-root vector fields
(TSRVFs). This TSRVF representation, followed by a PCA-based dimension
reduction, provides a convenient mathematical representation of a shape
sequence in the form of a Euclidean time series. Fitting a vector
auto-regressive (VAR) model to this TSRVF-PCA time series leads to statistical
modeling of the overall shape dynamics. We use the parameters of the fitted VAR
model to characterize morphological evolution. We validate VAR models through
model comparisons, synthesis, and sequence classifications. For classification,
we use the VAR parameters in conjunction with different classifiers: SVM,
Random Forest, and CNN, and obtain high classification rates. Extensive
experiments presented here demonstrate the success of the proposed pipeline.
These results are the first of the kind in classifying cell migration videos
using shape dynamics.
