  Statistical analysis on object data presents many challenges. Basic summaries
such as means and variances are difficult to compute. We apply ideas from
topology to study object data. We present a framework for using persistence
landscapes to vectorize object data and perform statistical analysis. We apply
to this pipeline to some biological images that were previously shown to be
challenging to study using shape theory. Surprisingly, the most persistent
features are shown to be "topological noise" and the statistical analysis
depends on the less persistent features which we refer to as the "geometric
signal". We also describe the first steps to a new approach to using topology
for object data analysis, which applies topology to distributions on object
spaces.
