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Multi-resolutional Shape Features via Non-Euclidean Wavelets: Applications to Statistical Analysis of Cortical Thickness

Kim WH, Singh V, Chung MK, Hinrichs C, Pachauri D, Okonkwo OC, Johnson SC; Alzheimer's Disease Neuroimaging Initiative.

Neuroimage. 2014 Jun;93 Pt 1:107-23. Epub 2014 Mar 12.


Statistical analysis on arbitrary surface meshes such as the cortical surface is an important approach to understanding brain diseases such as Alzheimer's disease (AD). Surface analysis may be able to identify specifi c cortical patterns that relate to certain disease characteristics or exhibit di fferences between groups. Our goal in this paper is to make group analysis of signals on surfaces more sensitive. To do this, we derive multi-scale shape descriptors that characterize the signal around each mesh vertex, i.e., its local context, at varying levels of resolution. In order to define such a shape descriptor, we make use of recent results from harmonic analysis that extend traditional continuous wavelet theory from the Euclidean to a non-Euclidean setting (i.e., a graph, mesh or network). Using this descriptor, we conduct experiments on two diff erent datasets, the Alzheimer's Disease NeuroImaging Initiative (ADNI) data and images acquired at the Wisconsin Alzheimer's Disease Research Center (W-ADRC), focusing on individuals labeled as having Alzheimer's Disease (AD), Mild Cognitive Impairment (MCI) and healthy controls. In particular, we contrast traditional univariate methods with our multi-resolution approach which show increased sensitivity and improved statistical power to detect a group-level eff ects. We also provide an open source implementation.


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