analysis of the total variation based denoising problem: total variation
The role of total variation in developing image models and algorithms
has been increasing since its introduction by Rudin-Osher-Fatemi in
1992. To understand its qualitative properties, we propose to compute
explicit solutions of the total variation denoising problem. We propose
also to study the regularity properties of its solutions of and of
solutions of the minimizing total variation flow. We will study
primal-dual algorithms and work on the development of fast algorithms to
solve these problems. Finally, we will consider its application to image
segmentation and disparity computation in stereo.
formulation of the image inpainting problem and High Angular Resolution
Diffusion Imaging: a multi-scale geometrical point of view.
The unification of geometric
and texture-based methods is a very interesting research trend that can
lead to the development of robust and performant inpainting methods.
Resonance Imaging is a biomedical acquisition protocol that produces in
vivo images of fibrous tissue, such as brain white matter and muscle.
Popular approaches utilise Diffusion Tensor Imaging (DTI) or, more
generally, High Angular Resolution Diffusion Imaging (HARDI), to obtain
information on local water diffusivity profiles, which are believed to
be indicative of underlying fibrous structures. Tractography and
connectivity analysis can be employed to extract candidate fibres in the
form of geodesic curves, or congruences of such curves emanating from a
fiducial origin or region of interest in a Hamilton-Jacobi framework.
Adaptive and directional local processing in Image processing
We propose to go
beyond of this idea (proposed by Bruckstein et al in 1994) in several
different directions. In particular connecting this idea with a
different approach to image processing and analysis, closely related to
and influenced by a multi-scale view that comes from diffusion-based
“scale-space” ideas: an approach based on a new way of doing harmonic
analysis by wavelet bases.
Variational methods in Image Processing: application to
An application of
variational methods is related to optical flow based upon mean curvature
will be developed with special application to models which initially are
ill-posed (as it is the case of the Perona-Malik equation)
but for which it
is possible to get a coherent theory on their solutions, at least for
suitable initial data.