Spectral Forests: Learning of Surface Data, Application to Cortical Parcellation

This paper presents a new method for classifying surface data via spectral representations of shapes. Our approach benefits classification problems that involve data living on surfaces, such as in cortical parcellation. For instance, current methods for labeling cortical points into surface parcels often involve a slow mesh deformation toward pre-labeled atlases, requiring as much as 4 hours with the established FreeSurfer. This may burden neuroscience studies involving region-specific measurements. Learning techniques offer an attractive computational advantage, however, their representation of spatial information, typically defined in a Euclidean domain, may be inadequate for cortical parcellation. Indeed, cortical data resides on surfaces that are highly variable in space and shape. Consequently, Euclidean representations of surface data may be inconsistent across individuals. We propose to fundamentally change the spatial representation of surface data, by exploiting spectral coordinates derived from the Laplacian eigenfunctions of shapes. They 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. In this paper, we decide to build upon the successful Random Decision Forests algorithm and improve its spatial representation with spectral features. Our method, Spectral Forests, is shown to significantly improve the accuracy of cortical parcellations over standard Random Decision Forests 74% versus 28% Dice overlaps, and produce accuracy equivalent to FreeSurfer in a fraction of its time 23 seconds versus 3 to 4 hours.