Unveiling cellular morphology: statistical analysis using a Riemannian elastic metric in cancer cell image datasets

Elastic metrics can provide a powerful tool to study the heterogeneity arising from cellular morphology. To assess their potential application (e.g. classifying cancer treated cells), we consider a specific instance of the elastic metric, the Square Root Velocity (SRV) metric and evaluate its performance against the linear metric for two datasets of osteosarcoma (bone cancer) cells including pharmacological treatments, and normal and cancerous breast cells. Our comparative statistical analysis shows superior performance of the SRV at capturing cell shape heterogeneity when comparing distance to the mean shapes, with better separation and interpretation between different cell groups. Secondly, when using multidimensional scaling (MDS) to find a low-dimensional embedding for unrescaled contours, we observe that while the linear metric better preserves original pairwise distances, the SRV yields better classification.