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Past approaches for statistical shape analysis of objects have focused mainly on objects within the same topological classes, e.g., scalar functions, Euclidean curves, or surfaces, etc. For objects that differ in more complex ways, the…
The surface morphology of the developing mammalian brain is crucial for understanding brain function and dysfunction. Computational modeling offers valuable insights into the underlying mechanisms for early brain folding. Recent findings…
Brain morphology is shaped by genetic and mechanical factors and is linked to biological development and diseases. Its fractal-like features, regional anisotropy, and complex curvature distributions hinder quantitative insights in medical…
Cross-subject electroencephalography (EEG) decoding remains a fundamental challenge in brain-computer interface (BCI) research due to substantial inter-subject variability and the scarcity of subject-invariant representations. This paper…
Statistical shape modeling (SSM) directly from 3D medical images is an underutilized tool for detecting pathology, diagnosing disease, and conducting population-level morphology analysis. Deep learning frameworks have increased the…
This paper provides theoretical and computational developments in statistical shape analysis of shape graphs, and demonstrates them using analysis of complex data from retinal blood-vessel (RBV) networks. The shape graphs are represented by…
How can one analyze detailed 3D biological objects, such as neurons and botanical trees, that exhibit complex geometrical and topological variation? In this paper, we develop a novel mathematical framework for representing, comparing, and…
We propose a novel machine learning strategy for studying neuroanatomical shape variation. Our model works with volumetric binary segmentation images, and requires no pre-processing such as the extraction of surface points or a mesh. The…
Structures of brain arterial networks (BANs) - that are complex arrangements of individual arteries, their branching patterns, and inter-connectivities - play an important role in characterizing and understanding brain physiology. One would…
Rotational head motions have been shown to play a key role in traumatic brain injury. There is great interest in developing methods to rapidly predict brain tissue strains and strain rates resulting from rotational head motions to estimate…
The brain is a highly complex system. Most of such complexity stems from the intermingled connections between its parts, which give rise to rich dynamics and to the emergence of high-level cognitive functions. Disentangling the underlying…
Identifying brain regions that exhibit altered functional connectivity across cognitive or emotional states is a key problem in neuroscience. Existing methods, such as edge-wise testing, seed-based psychophysiological interaction (PPI)…
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…
Quantification of anatomical shape changes currently relies on scalar global indexes which are largely insensitive to regional or asymmetric modifications. Accurate assessment of pathology-driven anatomical remodeling is a crucial step for…
Recent advances in deep learning have had a methodological and practical impact on brain-computer interface research. Among the various deep network architectures, convolutional neural networks have been well suited for…
Vascular networks play a crucial role in understanding brain functionalities. Brain integrity and function, neuronal activity and plasticity, which are crucial for learning, are actively modulated by their local environments, specifically…
Mental disorders present challenges in diagnosis and treatment due to their complex and heterogeneous nature. Electroencephalogram (EEG) has shown promise as a potential biomarker for these disorders. However, existing methods for analyzing…
Shape information is crucial for human perception and cognition, and should therefore also play a role in cognitive AI systems. We employ the interdisciplinary framework of conceptual spaces, which proposes a geometric representation of…
Quantification of brain morphology has become an important cornerstone in understanding brain structure. Measures of cortical morphology such as thickness and surface area are frequently used to compare groups of subjects or characterise…
Topological data analysis (TDA) has become a powerful approach over the last twenty years, mainly due to its ability to capture the shape and the geometry inherent in the data. Persistence homology, which is a particular tool in TDA, has…