Topographic regularity is an important biological principle in brain connections that has been observed in various anatomical studies. However, there has been limited research on mathematically characterizing this property and applying it in the analysis of in vivo connectome imaging data. In this work, we propose a general mathematical model of topographic regularity for white matter fiber bundles based on previous neuroanatomical understanding. Our model is based on a novel group spectral graph analysis (GSGA) framework motivated by spectral graph theory and tensor decomposition. The GSGA provides a common set of eigenvectors for the graphs formed by topographic proximity of nearby tracts, which gives rises to the group graph spectral distance, or G2SD, for measuring the topographic regularity of each fiber tract in a tractogram. Based on this novel model of topographic regularity in fiber tracts, we then develop a tract filtering algorithm that can generally be applied to remove outliers in tractograms generated by any tractography algorithm. In the experimental results, we show that our novel algorithm outperforms existing methods in both simulation data from ISMRM 2015 Tractography Challenge and real data from the Human Connectome Project (HCP). On a large-scale dataset from 215 HCP subjects, we quantitatively show our method can significantly improve the retinotopy in the reconstruction of the optic radiation bundle. The software for the tract filtering algorithm developed in this work has also been publicly released on NITRC (https://www.nitrc.org/projects/connectopytool).
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