Herve Lombaert (ETS Montreal/Inria Sophia-Antipolis)

Title: Spectral Correspondence and Learning of Surface Data - Example on Brain Surfaces
Abstract:How to analyze complex shapes, such as of the highly folded surface of the brain? In this talk, I will show how spectral representations of shapes can benefit neuroimaging and, more generally, problems where data fundamentally lives on surfaces. Key operations, such as segmentation and registration, typically need a common mapping of surfaces, often obtained via slow and complex mesh deformations in a Euclidean space. Here, we exploit spectral coordinates derived from the Laplacian eigenfunctions of shapes and also address the inherent instability of spectral shape decompositions. Spectral coordinates have the advantage over Euclidean coordinates, to be geometry aware and to parameterize surfaces explicitly. This change of paradigm, from Euclidean to spectral representations, enables a classifier to be applied directly on surface data, via spectral coordinates. The talk will focus, first, on spectral representations of shapes, with an example on brain surface matching, and second, on the learning of surface data, with an example on automatic brain surface parcellation.