Analysis and approximation of Hamilton-Jacobi equations
Development of semi-Lagrangian schemes for nonlinear PDEs, and related convergence analysis
Development of adaptive high-order numerical methods and related stability and convergence study for evolutionary problems, mostly in the area of fronts propagation with Level-Set approach and its variants.
Solving image processing problems, with a focus on astronomical and biomedical applications. Specifically:
- Shape-from-X problems (mainly Shape-from-Shading and Shape-from-Polarisation, using non-Lambertian reflectance models)
- Multi-View and Photometric Stereo Shape-from-X problems
- Image Segmentation
- Image Denoising
- Image Inpainting
Mathematical modelling for problems related to 3D printers of objects (infill, appearance, overhang, etc.)
Mathematical modelling for thermal insulation problems.
Numerical techniques for PDEs: Semi-Lagrangian schemes, Finite Difference schemes, Finite Element Method, acceleration techniques (like e.g. Fast Marching and Fast Sweeping), “Filtered” Schemes (a mixture of a High-order scheme and a monotone one)
