Computational anatomy (CA) is a state-of-the-art mathematical framework for deformation based registration of medical images and other shapes, for example of human organs acquired by magnetic resonance imaging (MRI). Registration consists in warping a template image into a target image, thereby obtaining a mapping between anatomical correspondences for meaningful voxel-by-voxel comparisons.
CA is rigorously founded in geometric PDE analysis and infinite-dimensional Riemannian geometry, allowing analysis of robustness and accuracy by well-developed tools. Consequently, CA produces better registration results than heuristically engineered algorithms, especially for heavily non-linear warps.
In this project we combine geometric numerical integration (GNI) with CA to address 3 numerical challenges. (1) Convergence analysis of spectral methods for CA, where powerful results in geometric analysis are used for the first time in a numerical context. (2) New CA algorithms based on finite elements, including adaptivity, in combination with geometric integrators. (3) A new approach to tomographic shape reconstruction, where CA techniques are used for regularization of the inverse problem. The developed algorithms are implemented in a high-quality, open-source software library.
In addition to CA and its accompanying mathematical fields, the project will have a significant impact on the availability of efficient and stable registration algorithms for medical and other applications.
Docent vid Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
Funding Chalmers participation during 2018–2021 with 3,400,000.00 SEK