All students must validate 30 ECTS per semester.We offer two speciality tracks:

Track 1: Vision and Applications
The first track focuses on various applications of computer vision: biomedical applications, people detection, object tracking, computational photography.

Track 2: Vision and devices
The second track focuses on devices to capture images (intelligent sensors, medical imaging systems) and to visualise and interact with them (augmented reality)




Course name: Variational Methods and PDEs and optimisation for Image Processing Credits: 6

  • Class type: lecture/practical
  • Hours per week: 4 hours
  • Type of the exam: practical works + final exam



A first objective of this class is to present variational approaches and partial differential equations in image processing. Students will learn to model mathematically image processing problems. The students are given the basis in order to be able to adapt classical variational models and PDEs to situations they might encounter in their future professional life. 

A second objective of this class is to introduce some basics of optimization. Thanks to the first part of the course, the students can propose mathematically sounded criterion to minimize. They then need to be able to efficiently tackle them, which is the second objective of this course.

Pratical labs will illustrate the theoretical principles developed in the course.

Plan of the course:
1) PDEs in image processing (convolution, heat equation, nonlinear PDEs).
2) Variational methods in image processing (Tychnonov regularization, nonlinear regularization, functions with bounded variations, the direct method of the calculus of variations)
3) Optimization (convex functions, Euler equation, smooth optimization, nonsmooth optimization)
  • Lecturer (name, position, degree): Pr. Jean-Fran├žois Aujol

The European Credit Transfer and Accumulation System (ECTS) is a student-centred system based on the student workload required to achieve the objectives of a programme of study. Its aim is to facilitate the recognition of study periods undertaken abroad by mobile students through the transfer credits. The ECTS is based on the principle that 60 credits are equivalent to the workload of full-time student during one academic year.