Abstract
We use a geometric approach to jointly characterize tumor shape and intensity along the tumor contour, as captured in magnetic resonance images, in the context of glioblastoma multiforme. Key properties of the proposed shape+intensity representation include invariance to translation, scale, rotation and reparameterization, which enable objective characterization and comparison of these crucial tumor features. The representation further allows the user to tune the emphasis of the shape and intensity components during registration, comparison and statistical summarization (averaging, computation of overall variance and exploration of variability via principal component analysis). In addition, we define a composite distance that is able to integrate shape and intensity information from two imaging modalities. The proposed framework can be integrated with distance-based clustering for the purpose of discovering groups of subjects with distinct survival prognosis. When applied to a cohort of subjects with glioblastoma multiforme, we discover groups with large median survival differences. We further tie the subjects' cluster memberships to tumor heterogeneity. Our results suggest that tumor shape variation plays an important role in disease prognosis.