synthetic field
noisy image
reconstructed image
Tracking neuronal fibers inside the brain
Several methods in image processing are based on PDEs, that need to be solved numerically. We are interested in PDE-based methods for multidimensional images. The scope is to use the geometric properties of the data as a base for the construction of the numerical integrator. An important application is biomedical imaging (diffusion tensor imaging, image registration).
In diffusion tensor imaging, each voxel corresponds to a 3x3 symmetric matrix that can be represented by an ellipsoid. Below, an example of a synthetic field, to which we impose noise and then denoise, by a method that preserves eigenvalues (images by master student Sjur Kvammen). Diffusion tensor imaging is used, among other things to track neuronal fibers within the brain (image from the web).
For further informations, see also the activities of the BBG group in image processing at MI.
Geometric methods in...