Multiresolution elastic matching
Computer Vision, Graphics, and Image Processing
A New Algorithm For Computing Liquid Crystal Stable Configurations: The Harmonic Mapping Case
SIAM Journal on Numerical Analysis
A Digital Brain Atlas for Surgical Planning, Model-Driven Segmentation, and Teaching
IEEE Transactions on Visualization and Computer Graphics
Cortical Constraints for Non-Linear Cortical Registration
VBC '96 Proceedings of the 4th International Conference on Visualization in Biomedical Computing
Automatic Quantification of Multiple Sclerosis Lesion Volume Using Stereotaxic Space
VBC '96 Proceedings of the 4th International Conference on Visualization in Biomedical Computing
A method for identifying geometrically simple surfaces from three-dimensional images
A method for identifying geometrically simple surfaces from three-dimensional images
Deformable templates using large deformation kinematics
IEEE Transactions on Image Processing
IPMI'05 Proceedings of the 19th international conference on Information Processing in Medical Imaging
Brain image analysis using spherical splines
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
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The rapid creation of comprehensive brain image databases mandates the development of mathematical algorithms to uncover disease-specific patterns of brain structure and function in human populations. We describe our construction of probabilistic atlases that store detailed information on how the brain varies across age and gender, across time, in health and disease, and in large human populations. Specifically, we introduce a mathematical framework based on covariant partial differential equations (PDEs), pull-backs of mappings under harmonic flows, and high-dimensional random tensor fields to encode variations in cortical patterning, asymmetry and tissue distribution in a population-based brain image database (N=94 scans). We use this information to detect disease-specific abnormalities in Alzheimer's disease and schizophrenia, including dynamic changes over time. Illustrative examples are chosen to show how group patterns of cortical organization, asymmetry, and disease-specific trends can be resolved that are not apparent in individual brain images. Finally, we create four-dimensional (4D) maps that store probabilistic information on the dynamics of brain change in development and disease. Digital atlases that generate these maps show considerable promise in identifying general patterns of structural and functional variation in diseased populations, and revealing how these features depend on demographic, genetic, clinical and therapeutic parameters.