Geodesic Image Normalization and Temporal Parameterization in the Space of Diffeomorphisms
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.
KeywordsImage Registration Frontotemporal Dementia Image Match Medical Image Analysis Topology Preserve
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