Using a Riemannian elastic metric for statistical analysis of tumor cell shape heterogeneity

We examine how a specific instance of the elastic metric, the Square Root Velocity (SRV) metric, can be used to study and compare cellular morphologies from the contours they form on planar surfaces. We process a dataset of images from osteocarcoma (bone cancer) cells that includes different treatments known to affect the cell morphology, and perform a comparative statistical analysis between the linear and SRV metrics. Our study indicates superior performance of the SRV at capturing the cell shape heterogeneity, with a better separation between different cell groups when comparing their distance to their mean shape, as well as a better low dimensional representation when comparing stress statistics. Therefore, our study suggests the use of a Riemannian metric, such as the SRV as a potential tool to enhance morphological discrimination for large datasets of cancer cell images.