A natural approach to modeling the evolution of an object (e.g., the growth of a leaf) is to estimate a plausible deformation path between two observations. However, interpolation can produce misleading results if the set of considered deformations does not accurately reflect the properties of the observed data. The implicit deformation module framework enables the generation of advanced structured deformations in a user-friendly and efficient manner.
First, we introduce the concept of deformation modules, which incorporate structural properties inspired by the object's elasticity. We then establish the well-posedness of the deformations generated by these modules and demonstrate the existence of solutions to the resulting registration problem. Finally, we present the IMODAL library, which enables registration through structured deformations and integrates key computational optimizations to ensure scalability to high-dimensional data.
This work has been done with B. Gris (LJLL, CNRS) and A. Trouvé (Centre Borelli, ENS Paris-Saclay)
