Brain Shape Correspondence Analysis Using Functional Maps

Abstract

Modeling neurodevelopment in brain asphyxia is a crucial task in pediatric medical imaging. One of the significant challenges is that brain structures that are affected by encephalopathy lose their mass due to the injury. Thus, quantifying neurodevelopmental changes is often performed using 2D approaches where the neuroradiologist performs fiducial landmarks to monitor clinical outcomes. We showed how non-rigid correspondence analysis allows relevant quantification of shape relations on brain structures. We use functional maps to automatically compute shape correspondences based on partially observed 3D shapes (i.e., affected brain areas). We perform the brain structure representation as partial functional correspondences between the affected brain area at a post-injury time and model shapes related to the first brain representation (i.e., the first month after birth). Hence, eigenfunctions with the Laplace-Beltrami operator are computed from the training shapes. Then, we apply an optimization process where fine-tuning the functional maps results in meaningful matches between brain structures. The experimental results show that our approach computes reliability correspondences, and establishes candidate matches for robust neurodevelopmental quantification.