The research in this project proceeded in three steps:
1. First, development of new state-of-the-art numerical methods for computational anatomy. A limiting factor in previous state-of-the-art algorithms is that they require large computational resources, i.e. the computational complexity is high. We have developed new algorithms with lower computational complexity, yet equal or better results in quality (especially for CT lung images). Implementations of these algorithms have been released as open-source software.
2. Second, mathematical analysis of robustness of the algorithm, so called “convergence analysis”. This is important to assert that the developed algorithms produce reliable results. Although work remains, we have so far established convergence analysis for one of the developed algorithms.
3. Third, as mathematicians, it is important to collaborate with medical experts, to assert that our results are disseminated and, ultimately, come to societal use. In this project we have worked together with experts on thoracic imaging (lung and heart region). We have demonstrated that our algorithm outperforms previous state-of-the-art in both computational complexity and quality. In the attached Figure 1 the Jacobian determinant, measuring compression and expansion, is illustrated for our new method (left) and previous state-of-the-art methods (middle and right). Notice that the left image gives a better results, since expansion (blue color) only occurs in regions of low density (essentially where there is no tissue).
