Variational problems on flows of diffeomorphisms for image matching
Quarterly of Applied Mathematics
Computational anatomy: an emerging discipline
Quarterly of Applied Mathematics - Special issue on current and future challenges in the applications of mathematics
Variational Methods for Multimodal Image Matching
International Journal of Computer Vision
Geodesic image interpolation: parameterizing and interpolating spatiotemporal images
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
| Hi-index | 0.00 |
Medical image analysis based on diffeomorphisms (differentiable one to one and onto maps with differentiable inverse) has placed computational analysis of anatomy and physiology on firm theoretical ground. We detail our approach to diffeomorphic computational anatomy while highlighting both theoretical and practical benefits. We first introduce the metric used to locate geodesics in the diffeomorphic space. Second, we give a variational energy that parameterizes the image normalization problem in terms of a geodesic diffeomorphism, enabling a fundamentally symmetric solution. This approach to normalization is extended for optimal template population studies using general imaging data. Finally, we show how the temporal parameterization and large deformation capabilities of diffeomorphisms make them appropriate for longitudinal analysis, particularly of neurodegenerative data.