Statistics on Shape Data: Correcting an Asymptotic Bias in Template Shape Estimation

Seminar | February 20 | 4-5 p.m. | 1011 Evans Hall

 Nina Miolane, Stanford University

 Department of Statistics

Computational Anatomy aims to model and analyze healthy and pathological distributions of organ shapes. We are interested in the computational representation of the brain anatomy using brain MRIs (Magnetic Resonance Imaging). How can we define the notion of brain shapes and how can we learn their distribution in the population? Landmarks’ shapes, curve shapes or surface shapes can be seen as the remainder after we have filtered out the object position and orientation. As such, shape data belong to quotient spaces. We present “Geometric Statistics”, a framework for data belonging to non-Euclidean spaces like quotient spaces of Riemannian manifolds. We use tools of Geometric Statistics and Riemannian geometry to prove that the “template shape estimation” algorithm, used for more than 15 years in medical imaging (and signal processing), has an asymptotic bias. The geometric intuition provided by the study leads us to design new bias correction methods. We present experimental results on simulated and real data, including a first bias quantification of the brain template computed from MRIs.