Characterizing Cell Populations Using Statistical Shape Modes

We consider the problem of characterizing shape populations using highly frequent representative shapes. Framing such shapes as statistical modes -- shapes that correspond to (significant) local maxima of the underlying pdfs -- we develop a nonparametric approach for estimating sample modes. Using an elastic shape metric, we define epsilon-neighborhoods in the shape space and shortlist shapes that are central and have the most neighbors. A critical issue -- How to automatically select the threshold epsilon? -- is resolved using a combination of ANOVA and empirical mode distribution. The resulting modal set, in turn, helps characterize the shape population and performs better than the traditional cluster means. We demonstrate this framework using amoeba shapes from brightfield microscopy images and highlight its advantages over existing ideas.