Hyperbolic Wasserstein Distance for Shape Indexing

Statistical Learning Methods for Neuroimaging Data Analysis with Applications

The aim of this review is to provide a comprehensive survey of statistical challenges in neuroimaging data analysis, from neuroimaging techniques to large-scale neuroimaging studies and statistical learning methods. We briefly review eight popular neuroimaging techniques and their potential applications in neuroscience research and clinical translation. We delineate four themes of neuroimaging data and review major image processing analysis methods for processing neuroimaging data at the individual level. We briefly review four large-scale neuroimaging-related studies and a consortium on imaging genomics and discuss four themes of neuroimaging data analysis at the population level. We review nine major population-based statistical analysis methods and their associated statistical challenges and present recent progress in statistical methodology to address these challenges.

Cortical Surface Shape Analysis Based on Alexandrov Polyhedra

Shape analysis has been playing an important role in early diagnosis and prognosis of neurodegenerative diseases such as Alzheimer's diseases (AD). However, obtaining effective shape representations remains challenging. This paper proposes to use the Alexandrov polyhedra as surface-based shape signatures for cortical morphometry analysis. Given a closed genus-0 surface, its Alexandrov polyhedron is a convex representation that encodes its intrinsic geometry information. We propose to compute the polyhedra via a novel spherical optimal transport (OT) computation. In our experiments, we observe that the Alexandrov polyhedra of cortical surfaces between pathology-confirmed AD and cognitively unimpaired individuals are significantly different. Moreover, we propose a visualization method by comparing local geometry differences across cortical surfaces. We show that the proposed method is effective in pinpointing regional cortical structural changes impacted by AD.

Predicting future cognitive decline with hyperbolic stochastic coding

Hyperbolic geometry has been successfully applied in modeling brain cortical and subcortical surfaces with general topological structures. However, such approaches, similar to other surface-based brain morphology analysis methods, usually generate high dimensional features. It limits their statistical power in cognitive decline prediction research, especially in datasets with limited subject numbers. To address the above limitation, we propose a novel framework termed as hyperbolic stochastic coding (HSC). We first compute diffeomorphic maps between general topological surfaces by mapping them to a canonical hyperbolic parameter space with consistent boundary conditions and extracts critical shape features. Secondly, in the hyperbolic parameter space, we introduce a farthest point sampling with breadth-first search method to obtain ring-shaped patches. Thirdly, stochastic coordinate coding and max-pooling algorithms are adopted for feature dimension reduction. We further validate the proposed system by comparing its classification accuracy with some other methods on two brain imaging datasets for Alzheimer's disease (AD) progression studies. Our preliminary experimental results show that our algorithm achieves superior results on various classification tasks. Our work may enrich surface-based brain imaging research tools and potentially result in a diagnostic and prognostic indicator to be useful in individualized treatment strategies.