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ABSTRACT Mediation analysis is widely utilized in neuroscience to investigate the role of brain image phenotypes in the neurological pathways from genetic exposures to clinical outcomes. However, it is still difficult to conduct mediation analyses with whole genome‐wide exposures and brain subcortical shape mediators due to several challenges including (i) large‐scale genetic exposures, that is, millions of single‐nucleotide polymorphisms (SNPs); (ii) nonlinear Hilbert space for shape mediators; and (iii) statistical inference on the direct and indirect effects. To tackle these challenges, this paper proposes a genome‐wide mediation analysis framework with brain subcortical shape mediators. First, to address the issue caused by the high dimensionality in genetic exposures, a fast genome‐wide association analysis is conducted to discover potential genetic variants with significant genetic effects on the clinical outcome. Second, the square‐root velocity function representations are extracted from the brain subcortical shapes, which fall in an unconstrained linear Hilbert subspace. Third, to identify the underlying causal pathways from the detected SNPs to the clinical outcome implicitly through the shape mediators, we utilize a shape mediation analysis framework consisting of a shape‐on‐scalar model and a scalar‐on‐shape model. Furthermore, the bootstrap resampling approach is adopted to investigate both global and spatial significant mediation effects. Finally, our framework is applied to the corpus callosum shape data from the Alzheimer's Disease Neuroimaging Initiative. 

This paper presents a generative statistical model for analyzing time series of planar shapes. Using elastic shape analysis, we separate object kinematics (rigid motions and speed variability) from morphological evolution, representing the latter through transported velocity fields (TVFs). A principal component analysis (PCA) based dimensionality reduction of the TVF representation provides a finite-dimensional Euclidean framework, enabling traditional time-series analysis. We then fit a vector auto-regressive (VAR) model to the TVF-PCA time series, capturing the statistical dynamics of shape evolution. To characterize morphological changes,we use VAR model parameters for model comparison, synthesis, and sequence classification. Leveraging these parameters, along with machine learning classifiers, we achieve high classification accuracy. Extensive experiments on cell motility data validate our approach, demonstrating its effectiveness in modeling and classifying migrating cells based on morphological evolution—marking a novel contribution to the field. 

We propose a novel framework for the statistical analysis of genus-zero 4D surfaces, i.e., 3D surfaces that deform and evolve over time. This problem is particularly challenging due to the arbitrary parameterizations of these surfaces and their varying deformation speeds, necessitating effective spatiotemporal registration. Traditionally, 4D surfaces are discretized, in space and time, before computing their spatiotemporal registrations, geodesics, and statistics. However, this approach may result in suboptimal solutions and, as we demonstrate in this paper, is not necessary. In contrast, we treat 4D surfaces as continuous functions in both space and time. We introduce Dynamic Spherical Neural Surfaces (D-SNS), an efficient smooth and continuous spatiotemporal representation for genus-0 4D surfaces. We then demonstrate how to perform core 4D shape analysis tasks such as spatiotemporal registration, geodesics computation, and mean 4D shape estimation, directly on these continuous representations without upfront discretization and meshing. By integrating neural representations with classical Riemannian geometry and statistical shape analysis techniques, we provide the building blocks for enabling full functional shape analysis. We demonstrate the efficiency of the framework on 4D human and face datasets. The source code and additional results are available at https://4d-dsns.github.io/DSNS/.