teacher: Silvia Tozza
affiliation: Dipartimento di Matematica, Università di Bologna
date: July 18-22^th, 2022
venue: Genoa (Italy), Polo Valletta Puggia – Università di Genova: DIBRIS-DIMA

Some nonlinear PDEs and their applications in image processing

brief description: The course will focus on nonlinear partial differential equations of Hamilton-Jacobi type and their approximation. We introduce this kind of equations and the notion of viscosity solutions with their major properties. Then we present some stationary and evolutive problems in image processing which can be modeled by first order Hamilton-Jacobi equations. For the stationary case, we deal with the orthographic Shape-from-Shading problem, a classical ill-posed problem in Computer Vision, and how it is possible to derive a well-posed problem using more than one input image. For the evolutive case, we present a numerical method for the image segmentation problem based on the level-set approach, a very popular method that is able to track interfaces and follow topological changes.
The course also includes a small laboratory activity, with examples of construction of algorithms in MATLAB and numerical simulations.

The course will take place on the following days / times:

• Monday 18 July
  2.30 pm - 4.30 pm
• Tuesday 19 July
  11.00 am - 01.00 pm and 2:30 pm - 4:30 pm (laboratory)
• Wednesday 20 July
  2.30 pm - 4.30 pm
• Thursday 21 July
  2.30 pm - 4.30 pm
• Friday 22 July 11.00 am - 01.00 pm (laboratory)
  
  Lectures will take place in room 704.
  Laboratory in PC1.